A Working Memory Account of the Interaction between Numbers and Spatial Attention

Modal and amodal cognition: an overarching principle in various domains of psychology

Accounting for how the human mind represents the internal and external world is a crucial feature of many theories of human cognition. Central to this question is the distinction between modal as opposed to amodal representational formats. It has often been assumed that one but not both of these two types of representations underlie processing in specific domains of cognition (e.g., perception, mental imagery, and language). However, in this paper, we suggest that both formats play a major role in most cognitive domains. We believe that a comprehensive theory of cognition requires a solid understanding of these representational formats and their functional roles within and across different domains of cognition, the developmental trajectory of these representational formats, and their role in dysfunctional behavior. Here we sketch such an overarching perspective that brings together research from diverse subdisciplines of psychology on modal and amodal representational formats so as to unravel their functional principles and their interactions.

No conclusive evidence for number-induced attentional shifts in a temporal order judgement task

The Spatial Numerical Association of Response Codes (SNARC) effect refers to the observation that relatively small (e.g., 1) and large numbers (e.g., 9) elicit faster left- and right-sided manual responses, respectively. In a variation known as the attentional SNARC effect, merely looking at numbers caused a left- or right-ward shift in covert spatial attention, depending on the number's magnitude. In our study, we probed the notion that numbers induce shifts of spatial attention in accordance with their position on a mental number line (MNL). Critically, we removed any putative spatial response code that may contaminate the responses. We used a square and a tilted square as targets, thereby situating the decisive response dimension in the ventral, non-spatial processing stream. In two experiments where numbers were used as non-informative cues preceding a temporal order judgement (TOJ) task, we did not observe a deflection of the locus of spatial attention as a function of the numerical magnitude of the cue. In a third experiment, finding a significant modulation of TOJ performance as a function of the pointing direction of arrow cues allowed us to rule out the possibility that the absence of any significant modulation in Experiments 1 and 2 was due to a lack of sensitivity of our task set-up. We conclude from the current findings that the spatial codes that the perception and naming of numbers potentially elicit are not in and by themselves sufficient to elicit deflections of spatial attention.

How time gets spatial: factors determining the stability and instability of the mental time line

Left-to-right readers classify faster past events with motor responses on the left side of space and future events with responses on the right side. This suggests a left-to-right spatial organization in the mental representation of time. Here, we show that the significance and reliability of this representation are linked to the joint use of temporal and spatial codes in the task at hand. In a first unimanual Go/No-Go Implicit Association Test (IAT), attending selectively to "past" or to "future" words did not activate corresponding "left" or "right" spatial concepts and vice versa. In a second IAT, attending to both temporal (i.e., "past" and "future") words and spatial targets (i.e., "left" and "right") pointing arrows produced faster responses for congruent rather than incongruent combinations of temporal and spatial concepts in task instructions (e.g., congruent = "Go with past words and left-pointing arrows"; incongruent = "Go with past words and right-pointing arrows"). This effect increased markedly in a STEARC task where spatial codes defined the selection between "left-side" and "right-side" button presses that were associated with "past" and "future" words. Two control experiments showed only partial or unreliable space-time congruency effects when (a) participants attended to superordinate semantic codes that included both spatial "left"/"right" or temporal "past/future" subordinate codes; (b) a primary speeded response was assigned to one dimension (e.g., "past vs. future") and a nonspeeded one to the other dimension (e.g., "left" vs. "right"). These results help to define the conditions that trigger a stable and reliable spatial representation of time-related concepts.

Optimized experimental designs to best detect spatial positional association of response codes in working memory

The SPoARC (Spatial Positional Association of Response Codes) effect refers to spatialization of information in working memory. Among the potential factors that could influence how order is mapped onto a mental space during the recognition process, we selected the following two factors: i) the type of stimuli, in particular their verbal vs. visual aspects and ii) the number of probes. In this study, 137 participants memorized sequences of either words or pictures and subsequently performed a recognition test for which they responded using lateralized keys. For half of the participants, only one probe was presented after each sequence, whereas the other half was administered several probes. A significantly greater number of participants presented a SPoARC using a single probe. We discuss that spatialization is best detected when the sequence is scanned only once. Results also showed no difference between the two types of stimuli (i.e., verbal vs. visual). This finding raises the question of the respective roles of verbalization and visualization in the SPoARC.

Stronger spatial bias induced more by numbers in mind than numbers in eye: Evidence from event-related potentials

The relationship between number and space is an important issue in numerical cognition. The spatial-numerical association of response codes (SNARC) effect is a classic example of the association between numbers and spaces. It refers to the phenomenon whereby left-handed responses occur faster to small number and right-handed responses occur faster to large number. The current study explored the shared and distinct neural correlates of the SNARC effect considering numbers in eye and numbers in mind, by using event-related potentials (ERPs) technology. In each trial of the task, participants were asked to press freely one of two keys as a response to a number presented visually (numbers in eye) or via imagination (numbers in mind). The behavioral results indicated that the free-choice key presses were affected by the magnitudes of the numbers either in eye or in mind. Electrophysiological results observed that the SNARC effect appeared only in the 110 - 140 ms time window for numbers in eye. In contrast, for numbers in mind, the SNARC effect appeared during a longer time window (110 - 330 ms). These results suggest that both, numbers in eye and numbers in mind, can induce spatial bias at the early stimulus-representation stage, but the time duration of the spatial bias is longer for numbers in mind than numbers in eye. This may reflect a closer connection between numbers in mind and mental number line.

The role of cognitive control in the SNARC effect: A review

The spatial-numerical association of response codes (SNARC) effect, in which people respond to small numbers faster with the left hand and to large numbers faster with the right hand, is a popular topic in cognitive psychology. Some well-known theoretical accounts explaining this effect include the mental number line model, polarity correspondence principle, dual-route model, and working memory account. However, these fail to explain the finding that the size of the SNARC effect is modulated by cognitive control. Here, we propose a new account-a cognitive control-based view of the SNARC effect. This view argues that the SNARC effect is fundamentally determined by cognitive control in resolving conflicts during stimulus-response mapping. Several subcomponents of cognitive control, such as working memory, mental or task set shifting, inhibition control, and conflict adaptation, can easily modulate the SNARC effect. The cognitive control-based view can account for the flexible SNARC effect observed in diverse task situations while providing new insight into its mechanism.

Redundancy and Reducibility in the Formats of Spatial Representations

Mental representations are the essence of cognition. Yet to understand how the mind works, one must understand not just the content of mental representations (i.e., what information is stored) but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a "case study" of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly "redundant" formats may support the flexible spatial behavior observed in humans and that researchers should approach the study of all mental representations with this possibility in mind.

A SPoARC of Music: Musicians Spatialize Melodies but not All-Comers

Recent studies on the spatial positional associated response codes (SPoARC) effect have shown that when Western adults are asked to keep in mind sequences of verbal items, they mentally spatialize them along the horizontal axis, with the initial items being associated with the left and the last items being associated with the right. The origin of this mental line is still debated, but it has been theorized that it necessitates specific spatial cognitive structures to emerge, which are built through expertise. This hypothesis is examined by testing for the first time whether Western individuals spatialize melodies from left to right and whether expertise in the musical domain is necessary for this effect to emerge. Two groups (musicians and non-musicians) of participants were asked to memorize sequences of four musical notes and to indicate if a subsequent probe was part of the sequence by pressing a "yes" key or a "no" key with the left or right index finger. Left/right-hand key assignment was reversed at mid-experiment. The results showed a SPoARC effect only for the group of musicians. Moreover, no association between pitch and hand responses was observed in either of the two groups. These findings suggest a crucial role of expertise in the SPoARC effect.

Neural Patterns in Parietal Cortex and Hippocampus Distinguish Retrieval of Start versus End Positions in Working Memory

Coding serial order of information is a fundamental ability of our cognitive system, and still, little is known about its neural substrate. This study examined the neural substrates involved in the retrieval of information that is serially stored in verbal working memory task using a sensitive multivariate analysis approach. We compared neural activity for memorized items stemming from the beginning versus the end of a memory list assessing the degree of neural pattern discordance between order positions (beginning vs. end). The present results confirmed and refined the role of the intraparietal sulcus in the processing of serial order information in working memory. An important finding is that the hippocampus showed sensitivity to serial order information. Our results indicate that the representation of serial order information relies on a broader set of neural areas and highlight the role of the intraparietal sulcus and the hippocampus, in addition to the supramarginal gyrus and the SMA. The contribution of different neural regions might reflect the involvement of distinct levels of serial order coding (i.e., spatial, attentional, temporal) that support the representation of serial order information.

Pupil size variations reveal covert shifts of attention induced by numbers

The pupil light response is more than a pure reflexive mechanism that reacts to the amount of light entering the eye. The pupil size may also react to the luminance of objects lying in the visual periphery, revealing the locus of covert attention. In the present study, we took advantage of this response to study the spatial coding of abstract concepts with no physical counterpart: numbers. The participants' gaze was maintained fixed in the middle of a screen whose left and right parts were dark or bright, and variations in pupil size were recorded during an auditory number comparison task. The results showed that small numbers accentuated pupil dilation when the darker part of the screen was on the left, while large numbers accentuated pupil dilation when the darker part of the screen was on the right. This finding provides direct evidence for covert attention shifts on a left-to-right oriented mental spatial representation of numbers. From a more general perspective, it shows that the pupillary response to light is subject to modulation from spatial attention mechanisms operating on mental contents.

The Effect of Verbal Task Instruction on Spatial-Numerical Associations of Response Codes Effect Coding of Spatial-Numerical Associations: Evidence From Event-Related Potential

The spatial-numerical associations of response codes (SNARC) effect reveals that individuals can represent numbers spatially. In this study, event-related potential (ERP) technology was used to probe the effect of verbal-spatial task instructions on spatial-numerical association coding by using digit parity and magnitude judgment tasks, with the numbers 1–9 (except 5) and Chinese word labels (“left” and “right”) as experimental materials. The behavioral results of Experiment 1 showed that the SNARC effect was mainly based on verbal-spatial coding and appeared when the stimulus onset asynchrony (SOA) between the presentation of the verbal labels and the target digit was 0 ms. ERP results did not reveal any significant SNARC-related effects in either the N1 or P3 components. The behavioral results of Experiment 2 again showed that the SNARC effect was dominated by verbal-spatial coding. ERP results showed that significant effects related to verbal-spatial coding were found in both the early positive deflection of the stimulus-locked lateralized readiness potential (S-LRP) and the latency of the response-locked LRP (R-LRP). Hence, in this study, the nature of the spatial coding of the digit magnitudes was influenced by the processing of the word labels and affected both the response selection and response preparation stages.

Eye-movements reveal the serial position of the attended item in verbal working memory

The problem of how the mind can retain sequentially organized information has a long research tradition that remains unresolved. While various computational models propose a mechanism of binding serial order information to position markers, the representational nature and processes that operate on these position markers are not clear. Recent behavioral work suggests that space is used to mark positions in serial order and that this process is governed by spatial attention. Based on the assumption that brain areas controlling spatial attention are also involved in saccadic planning, we continuously tracked the eye-movements as a direct measure of the spatial attention during retrieval from a verbal WM sequence. Participants memorized a sequence of auditory numbers. During retention, they heard a number-cue that did or did not belong to the memorized set. After this number-cue, a target-beep could be presented to which they had to respond if the number-cue belonged to the memorized sequence. In Experiment 1, the target-beep was either presented to the left or right ear, and in Experiment 2 bilaterally (removing any spatial aspect). We tested the hypothesis that systematic eye-movements are made when people retrieve items of sequences of auditory words and found that the retrieval of begin items resulted in leftward eye-movements and the retrieval of end items in rightward eye-movements. These observations indicate that the oculomotor system is also involved in the serial order processes in verbal WM thereby providing a promising novel approach to get insight into abstract cognitive processes.

Early is left and up: Saccadic responses reveal horizontal and vertical spatial associations of serial order in working memory

Maintaining serial order in working memory is crucial for cognition. Recent theories propose that serial information is achieved by positional coding of items on a spatial frame of reference. In line with this, an early-left and late-right spatial-positional association of response code (SPoARC) effect has been established. Various theoretical accounts have been put forward to explain the SPoARC effect (the mental whiteboard hypothesis, conceptual metaphor theory, polarity correspondence, or the indirect spatial-numerical association effect). Crucially, while all these accounts predict a left-to-right orientation of the SPoARC effect, they make different predictions regarding the direction of a possible vertical SPoARC effect. In this study, we therefore investigated SPoARC effects along the horizontal and vertical spatial dimension by means of saccadic responses. We replicated the left-to-right horizontal SPoARC effect and established for the first time an up-to-down vertical SPoARC effect. The direction of the vertical SPoARC effect was in contrast to that predicted by metaphor theory, polarity correspondence, or by the indirect spatial-numerical association effect. Rather, our results support the mental whiteboard-hypothesis, according to which positions can be flexibly coded on an internal space depending on the task demands. We also found that the strengths of the horizontal and vertical SPoARC effects were correlated, showing that some people are more prone than others to use spatial references for position coding. Our results therefore suggest that context templates used for position marking are not necessarily spatial in nature but depend on individual strategy preferences.

Is the attentional SNARC effect truly attentional? Using temporal order judgements to differentiate attention from response

The spatial–numerical association of response codes (SNARC) effect reflects the phenomenon that low digits are responded to faster with the left hand and high digits with the right. Recently, a particular variant of the SNARC effect known as the attentional SNARC (which reflects that attention can be shifted in a similar manner) has had notable replicability issues. However, a potentially useful method for measuring it was revealed by Casarotti et al. using a temporal order judgement (TOJ) task. Accordingly, the present study evaluated whether Casarotti et al.’s results were reproducible by presenting a low (1) or high (9) digit prior to a TOJ task where participants had to indicate which of two peripherally presented targets appeared first (Experiment 1) or second (Experiment 2). In Experiment 1, it was revealed that the findings of Casarotti et al.’s were indeed observable upon replication. In Experiment 2, when attention and response dimensions were put in opposition, the SNARC effect corresponded to the side of response rather than attention. Taken together, the present study confirms the robustness of the attentional SNARC in TOJ tasks, but that it is not likely due to shifts in attention.

Perceiving numerosity does not cause automatic shifts of spatial attention

It is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space.

Using space to remember: Short-term spatial structure spontaneously improves working memory

Spatial information plays an important role in how we remember. In general, there are two (non mutually exclusive) views regarding the role that space plays in memory. One view is that objects overlapping in space interfere with each other in memory. For example, objects presented in the same location (at different points in time) are more frequently confused with one another than objects that are not. Another view is that spatial information can 'bootstrap' other kinds of information. For example, remembering a phone number is easier one can see the arrangement of a keypad. Here, building on both perspectives, we test the hypothesis that task-irrelevant spatial structure (i.e., objects appearing in stable locations over repeated iterations) improves working memory. Across 7 experiments, we demonstrate that (1) irrelevant spatial structure improves memory for sequences of objects; (2) this effect does not depend on long-term spatial associations; (3) this effect is unique to space (as opposed to features like color); and (4) spatial structure can be teased apart from spatial interference, and the former drives memory improvement. We discuss how these findings relate to and challenge 'spatial interference' accounts as well as 'visuospatial bootstrapping'.

Electrophysiological Evidence of Space-Number Associations in 9-Month-Old Infants

Infant research is providing accumulating evidence that number-space mappings appear early in development. Here, a Posner cueing paradigm was used to investigate the neural mechanisms underpinning the attentional bias induced by nonsymbolic numerical cues in 9-month-old infants (N = 32). Event-related potentials and saccadic reaction time were measured to the onset of a peripheral target flashing right after the offset of a centered small or large numerical cue, with the location of the target being either congruent or incongruent with the number's relative position on a left-to-right oriented representational continuum. Results indicated that the cueing effect induced by numbers on infants' orienting of eye gaze brings about sensory facilitation in processing visual information at the cued location.

Number space is made by response space: Evidence from left spatial neglect

Whether the semantic representation of numbers is endowed with an intrinsic spatial component, so that smaller numbers are inherently represented to the left of larger ones on a Mental Number Line (MNL), is a central matter of debate in numerical cognition. To gain an insight into this issue, we investigated the performance of right brain damaged patients with left spatial neglect (N+) in a bimanual Magnitude Comparison SNARC task and in a uni-manual Magnitude Comparison Go/No-Go task (i.e. "is the number smaller or larger than 5?"). While the first task requires the use of contrasting left/right spatial codes for response selection, the second task does not require the use of these codes. In line with previous evidence, in the SNARC task N+ patients displayed a significant asymmetry in Reaction Times (RTs), with slower RTs to number "4", that was immediately precedent to the numerical reference "5", with respect to the number "6", that immediately followed the same reference. This RTs asymmetry was correlated with lesion of white matter tracts, i.e. Fronto-Occipital-Fasciculus, that allows prefrontal Ba 8 and 46 to regulate the distribution of attention on sensory and memory traces in posterior occipital, temporal and parietal areas. In contrast, no similar RTs asymmetry was found in the Go/No-Go task. These findings suggest that while in the SNARC task numbers get mentally organised from left-to-right as a function of their increasing magnitude, so that N+ patients display a delay in the processing of number-magnitudes that are immediately smaller than a given numerical reference, in the Go/No-Go task no left-to-right organization is activated. These results support the idea that it is the use of contrasting left/right spatial codes, whether motor or conceptual, that triggers the generation of a spatially left-to-right organised MNL and that the representation of number magnitude is not endowed with an inherent spatial component.

Measuring spontaneous and automatic processing of magnitude and parity information of Arabic digits by frequency-tagging EEG

Arabic digits (1–9) are everywhere in our daily lives. These symbols convey various semantic information, and numerate adults can easily extract from them several numerical features such as magnitude and parity. Nonetheless, since most studies used active processing tasks to assess these properties, it remains unclear whether and to what degree the access to magnitude and especially to parity is automatic. Here we investigated with EEG whether spontaneous processing of magnitude or parity can be recorded in a frequency-tagging approach, in which participants are passively stimulated by fast visual sequences of Arabic digits. We assessed automatic magnitude processing by presenting a stream of frequent small digit numbers mixed with deviant large digits (and the reverse) with a sinusoidal contrast modulation at the frequency of 10 Hz. We used the same paradigm to investigate numerical parity processing, contrasting odd digits to even digits. We found significant brain responses at the frequency of the fluctuating change and its harmonics, recorded on electrodes encompassing right occipitoparietal regions, in both conditions. Our findings indicate that both magnitude and parity are spontaneously and unintentionally extracted from Arabic digits, which supports that they are salient semantic features deeply associated to digit symbols in long-term memory.

Spatial Attention in Serial Order Working Memory: An EEG Study

Theoretical models explaining serial order processing link order information to specified position markers. However, the precise characteristics of position marking have remained largely elusive. Recent studies have shown that space is involved in marking serial position of items in verbal working memory (WM). Furthermore, it has been suggested, but not proven, that accessing these items involves horizontal shifts of spatial attention. We used continuous electroencephalography recordings to show that memory search in serial order verbal WM involves spatial attention processes that share the same electrophysiological signatures as those operating on the visuospatial WM and external space. Accessing an item from a sequence in verbal WM induced posterior “early directing attention negativity” and “anterior directing attention negativity” contralateral to the position of the item in mental space (i.e., begin items on the left; end items on the right). In the frequency domain, we observed posterior alpha suppression contralateral to the position of the item. Our results provide clear evidence for the involvement of spatial attention in retrieving serial information from verbal WM. Implications for WM models are discussed.

How to trigger and keep stable directional Space-Number Associations (SNAs)

Humans are prone to mentally organise the ascending series of integers according to reading habits so that in western cultures small numbers are positioned to the left of larger ones on a mental number line. Despite 140 years since seminal observations by Sir Francis Galton (Galton, 1880a, b), the functional mechanisms that give rise to directional Space-Number Associations (SNAs) remain elusive. Here, we contrasted three different experimental conditions, each including a different version of a Go/No-Go task with intermixed numerical and arrow-targets (Shaki and Fischer, 2018; Pinto et al., 2019a). We show that directional SNAs are not "all or none" phenomena. We demonstrate that SNAs get progressively less noisy and more stable the more contrasting small/large magnitude-codes and contrasting left/right spatial-codes are explicitly and fully combined in the task set. The analyses of the time-course of space-number congruency effects showed that both the absence and presence of the SNA were independent of the speed of reaction times. In agreement with our original proposal (Aiello et al., 2012), these findings show that conceptualising the ascending series of integers in spatial terms depends on the use of spatial codes in the numerical task at hand rather than on the presence of an inherent spatial dimension in the semantic representation of numbers. This evidence suggests that directional SNAs, like the SNARC effect, are secondary to the primary transfer of spatial response codes to number stimuli, rather than deriving from a primary congruency or incongruence between independent spatial-response and spatial-number codes.

SNARC effect modulated by central executive control: revealed in a cue-based trisection task

People respond to small numbers faster with the left hand and respond to large numbers faster with the right hand, a phenomenon known as the Spatial-Numerical Association of Response Codes (SNARC) effect. Whether the SNARC effect originates from culturally determined long-term experience or the task-set-influenced temporary associations among spaces, locations, and numerical magnitudes in working memory (WM) is still controversial. In the present study, we used a trisection paradigm in which numbers were divided into three categories (small: 1, 2; middle: 4, 5, 6; and large: 8, 9) to explore whether the central executive control can modulate the SNARC effect. Participants were serially presented with a cue and a target number. The cue denoted a task rule, which informed participants to compare the target number with either 3 or 7. The cue was either switched or repeated across trials. We found that the SNARC effects were observed in the cue-switching condition. In the cue-repeat condition, the SNARC effect disappeared. These findings suggest that the SNARC effect is modulated by set-shifting-related central executive control in WM, supporting the view that the SNARC effect is WM-dependent.

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space.

Does Number Perception Cause Automatic Shifts of Spatial Attention? A Study of the Att-SNARC Effect in Numbers and Chinese Months

The Attentional Spatial Numerical Association of Response Codes (Att-SNARC) effect has shown that number perception induces shifts in spatial attention (Fischer et al., 2003; Dodd et al., 2008). However, many replications were attempted and they often failed. In the present study, we investigated whether the Att-SNARC effect can be found for numbers in different notations: months in Arabic form, Simplified Chinese form, Traditional Chinese form (includes numerical ordinal information) and in Chinese non-numerical form (an ordinal sequence). By varying the cognitive task, we also examined whether the effect is a consequence of automatic perceptual processing. In Experiment 1, an Att-SNARC effect was observed for numbers regardless of notation. In Experiment 2 (order-irrelevant task) and Experiment 3 (order-relevant task), the effect was also found consistently for months in Arabic form, Simplified Chinese form, and Traditional Chinese form. This effect was not observed for months in Chinese non-numerical form in Experiment 3. These results show that number and numerical sequence perception automatically causes a spatial shift of attention. Our study provides positive evidence for the Att-SNARC effect and indicates that the effect can generalize to other numerical ordinal sequences that contain numeric information.

Can Implicit or Explicit Time Processing Impact Numerical Representation? Evidence From a Dual Task Paradigm

Whether the human brain processes various types of magnitude, such as numbers and time, through a shared representation or whether there are different representations for each type of magnitude is still debated. Here, we investigated two aspects of number-time interaction: the effects of implicit and explicit processing of time on numbers and the bi-directional interaction between time and number processing. Thirty-two participants were randomly assigned into two experimental groups that performed, respectively, a Single task (number comparison, with implicit time processing) and a Dual task (number comparison as a primary task, with explicit time processing as a secondary task). Results showed that participants, only in the Dual task, were faster and more accurate when processing large numbers paired with long rather than short durations, whereas the opposite pattern was not evident for small numbers. Moreover, participants were more accurate when judging long durations after having processed large rather than small numbers, whereas the opposite pattern emerged for short durations. We propose that number processing influences time processing more than vice versa, suggesting that numbers and time might be at least partially independently represented. This finding can pave the way for investigating the hierarchical representation of space, numbers, and time.

Low numbers from a low head? Effects of observed head orientation on numerical cognition

The present research shows effects of observed vertical head orientation of another person on numerical cognition in the observer. Participants saw portrait-like photographs of persons from a frontal view with gaze being directed at the camera and the head being tilted up or down (vs. not tilted). The photograph appeared immediately before each trial in different numerical cognition tasks. In Experiment 1, participants produced smaller numbers in a random number generation task after having viewed persons with a down-tilted head orientation relative to up-tilted and non-tilted head orientations. In Experiment 2, numerical estimates in an anchoring-like trivia question task were smaller following presentations of persons with a down-tilted head orientation relative to a non-tilted head orientation. In Experiment 3, a response key that was associated with larger numbers in a numerical magnitude task was pressed less frequently in a randomly intermixed free choice task when the photograph showed a person with a down-tilted relative to an up-tilted head orientation. These findings consistently show that social displays can influence numerical cognition across a variety of task settings.

Contrasting left/right codes for response selection must not be necessarily associated with contrasting numerical features to get the SNARC

The SNARC effect consists of faster reaction times to small numerical magnitudes when manual responses are delivered in the left-side of space and to large magnitudes when responses are delivered in the right-side. This spatial compatibility effect points at the interaction between the representations of space and that of numbers. Several studies have highlighted that an important determinant for the production of the SNARC is the use of contrasting left/right spatial codes in the selection of motor responses. In these studies, one spatial code for response selection, e.g. "left", is usually associated with one number feature, e.g. "lower than 5", while the contrasting spatial code, e.g. "right", is associated with the contrasting number feature, e.g. "higher than 5". Using a task with intermixed number and letter targets, here we show that significant and reliable SNARC effects are also produced when: a) one spatial response is associated with the intra-categorical discrimination of a number feature (i.e. magnitude or parity) and the contrasting response with the simple detection of letter targets; b) or when one spatial response is associated with the intra-categorical discrimination of the position of a letter in the alphabet (i.e. before or after "m") and the contrasting spatial response with the simple detection of numerical targets (Experiments 1 and 2). In contrast, no reliable SNARC is found when no intra-categorical number or letter discrimination is required and contrasting left/right spatial response codes are simply associated with the discrimination between numbers and letters, e.g. "push left if the target is a number/push right if it is a letter" (Experiment 3). In a final control test (Experiment 4), we found no SNARC when the magnitude or parity classification of Arabic digits presented at central fixation was made unimanually with a left side or a right side-key and no left/right contrast was present in response selection. These results show that the use of contrasting left/right spatial response codes elicits reliable SNARC effects independently of their assignment to contrasting number features and confirm the important role played by the use of spatial codes in the genesis of the number-space interaction.

The influence of semantic processing and response latency on the SNARC effect

The Spatial-Numerical Association of Response Code (SNARC) effect refers to the finding that small or large numbers elicit faster leftward or rightward responses, respectively. Traditionally, this effect has been thought to reflect the intrinsic spatial orientation of the mental number line (MNL account) and thus to be modulated by the amount of semantic processing required by the task. This study aimed to test this hypothesis. Participants performed two tasks requiring semantic processing (magnitude classification and parity judgement) and two tasks requiring the processing of non-semantic features of the number (phoneme detection and color judgement). Contrary to the MNL account, the SNARC effect in the four tasks was not modulated by the amount of semantic processing, but rather by response latency. These results provide evidence against the MNL account and in favor of alternative accounts (dual-route model, working memory account).

Spatial-numerical associations: Shared symbolic and non-symbolic numerical representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial-numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

Spatial-Numerical Associations Enhance the Short-Term Memorization of Digit Locations

Little is known about how spatial-numerical associations (SNAs) affect the way individuals process their environment, especially in terms of learning and memory. In this study, we investigated the potential effects of SNAs in a digit memory task in order to determine whether spatially organized mental representations of numbers can influence the short-term encoding of digits positioned on an external display. To this aim, we designed a memory game in which participants had to match pairs of identical digits in a 9 × 2 matrix of cards. The nine cards of the first row had to be turned face up and then face down, one by one, to reveal a digit from 1 to 9. When a card was turned face up in the second row, the position of the matching digit in the first row had to be recalled. Our results showed that performance was better when small numbers were placed on the left side of the row and large numbers on the right side (i.e., congruent) as compared to the inverse (i.e., incongruent) or a random configuration. Our findings suggests that SNAs can enhance the memorization of digit positions and therefore that spatial mental representations of numbers can play an important role on the way humans process and encode the information around them. To our knowledge, this study is the first that reaches this conclusion in a context where digits did not have to be processed as numerical values.

Systematic spatial patterns of the sense of familiarity: Hierarchical modelling based on eye-tracking experiments

Using different types of stimuli, such as pictures, horizontally written Japanese words, and vertically written Japanese words, this study investigated the spatial patterns of the sense of familiarity within the visual field. The perceptual asymmetry theory predicted that stimuli in the lower visual field would be processed more fluently and would therefore be perceived as more familiar. The working memory theory, originally proposed in space-number research, envisaged type-specific spatial patterns for different stimuli. Participants made old/new recognition memory judgements for stimuli, presented at random positions, while their eye movements were recorded. The observed spatial patterns changed according to the stimulus type (e.g., "more left = older" for horizontally written words and "upper = older" for vertically written words), and this flexibility is encapsulated by the working memory theory as follows: (a) stimulus-type-specific spatial configurations are encoded in long-term memory on the basis of one's experience (e.g., vertically written words are empirically associated with the "upper = older" spatial configuration), (b) the presentation of a stimulus automatically cues the temporal activation of the associated spatial configuration in working memory, and (c) the referential process between the stimulus and configuration unconsciously affects the viewer's sense of familiarity.

Time dependency of the SNARC effect for different number formats: evidence from saccadic responses

In line with the suggestion that the strength of the spatial numerical association of response codes (SNARC) effect was time dependent, the aim of the present study was to assess whether the association strength depends on the processing time of numerical quantity and/or of the time to initiate responses. More specifically, we examined whether and how the SNARC effect could be modulated by number format and effector type. Experiment 1 compared the effect induced by Arabic numbers and number words on the basis of saccadic responses in a parity judgment task. Indeed, previous studies have shown that Arabic numbers lead to faster processing than number words. The results replicated the SNARC effect with Arabic numbers, but not with number words. Experiment 2 was similar to Experiment 1, but this time manual responses (i.e., responses far slower than saccadic ones) were recorded. A strong SNARC effect was observed for both number formats. Further analyses revealed a correlation between mean individual response times and the strength of the SNARC effect. We proposed that the initiation times for saccadic responses may be too short for the SNARC effect to appear, in particular with the written number format for which activation of magnitude takes time. We conclude in terms of time variations resulting from processing specificities related with number format, effector type and also individual reaction and processing speed.

Developmental Changes in the Effect of Active Left and Right Head Rotation on Random Number Generation

Numbers are thought to be spatially organized along a left-to-right horizontal axis with small/large numbers on its left/right respectively. Behavioral evidence for this mental number line (MNL) comes from studies showing that the reallocation of spatial attention by active left/right head rotation facilitated the generation of small/large numbers respectively. While spatial biases in random number generation (RNG) during active movement are well established in adults, comparable evidence in children is lacking and it remains unclear whether and how children’s access to the MNL is affected by active head rotation. To get a better understanding of the development of embodied number processing, we investigated the effect of active head rotation on the mean of generated numbers as well as the mean difference between each number and its immediately preceding response (the first order difference; FOD) not only in adults (n = 24), but also in 7- to 11-year-old elementary school children (n = 70). Since the sign and absolute value of FODs carry distinct information regarding spatial attention shifts along the MNL, namely their direction (left/right) and size (narrow/wide) respectively, we additionally assessed the influence of rotation on the total of negative and positive FODs regardless of their numerical values as well as on their absolute values. In line with previous studies, adults produced on average smaller numbers and generated smaller mean FODs during left than right rotation. More concretely, they produced more negative/positive FODs during left/right rotation respectively and the size of negative FODs was larger (in terms of absolute value) during left than right rotation. Importantly, as opposed to adults, no significant differences in RNG between left and right head rotations were observed in children. Potential explanations for such age-related changes in the effect of active head rotation on RNG are discussed. Altogether, the present study confirms that numerical processing is spatially grounded in adults and suggests that its embodied aspect undergoes significant developmental changes.

Hemispatial neglect and serial order in verbal working memory

Working memory refers to our ability to actively maintain and process a limited amount of information during a brief period of time. Often, not only the information itself but also its serial order is crucial for good task performance. It was recently proposed that serial order is grounded in spatial cognition. Here, we compared performance of a group of right hemisphere-damaged patients with hemispatial neglect to healthy controls in verbal working memory tasks. Participants memorized sequences of consonants at span level and had to judge whether a target consonant belonged to the memorized sequence (item task) or whether a pair of consonants were presented in the same order as in the memorized sequence (order task). In line with this idea that serial order is grounded in spatial cognition, we found that neglect patients made significantly more errors in the order task than in the item task compared to healthy controls. Furthermore, this deficit seemed functionally related to neglect severity and was more frequently observed following right posterior brain damage. Interestingly, this specific impairment for serial order in verbal working memory was not lateralized. We advance the hypotheses of a potential contribution to the deficit of serial order in neglect patients of either or both (1) reduced spatial working memory capacity that enables to keep track of the spatial codes that provide memorized items with a positional context, (2) a spatial compression of these codes in the intact representational space.

Grounding Verbal Working Memory: The Case of Serial Order

The maintenance of serial order in verbal working memory (WM) is a major unsolved puzzle in cognitive science. Here we review a series of studies showing that serial order in verbal WM closely interacts with spatial processing. Accordingly, we outline the “mental whiteboard hypothesis,” which postulates that serial order in verbal WM is grounded in the spatial attention system. Specifically, serial context in verbal WM is provided by binding the memoranda to coordinates within an internal, spatially defined system within which (internal) spatial attention is at play to the purpose of searching for and retrieving information. Challenges and opportunities to be considered in future studies are discussed.

Order Information in Verbal Working Memory Shifts the Subjective Midpoint in Both the Line Bisection and the Landmark Tasks

A largely substantiated view in the domain of working memory is that the maintenance of serial order is achieved by generating associations of each item with an independent representation of its position, so-called position markers. Recent studies reported that the ordinal position of an item in verbal working memory interacts with spatial processing. This suggests that position markers might be spatial in nature. However, these interactions were so far observed in tasks implying a clear binary categorization of space (i.e., with left and right responses or targets). Such binary categorizations leave room for alternative interpretations, such as congruency between non-spatial categorical codes for ordinal position (e.g., begin and end) and spatial categorical codes for response (e.g., left and right). Here we discard this interpretation by providing evidence that this interaction can also be observed in a task that draws upon a continuous processing of space, the line bisection task. Specifically, bisections are modulated by ordinal position in verbal working memory, with lines bisected more towards the right after retrieving items from the end compared to the beginning of the memorized sequence. This supports the idea that position markers are intrinsically spatial in nature.

Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection

Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants' verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

Counteracting Implicit Conflicts by Electrical Inhibition of the Prefrontal Cortex

Cognitive conflicts and distractions by task-irrelevant information often counteract effective and goal-directed behaviors. In some cases, conflicting information can even emerge implicitly, without an overt distractor, by the automatic activation of mental representations. For instance, during number processing, magnitude information automatically elicits spatial associations resembling a mental number line. This spatial–numerical association of response codes (SNARC) effect can modulate cognitive-behavioral performance but is also highly flexible and context-dependent, which points toward a critical involvement of working memory functions. Transcranial direct current stimulation to the PFC, in turn, has been effective in modulating working memory-related cognitive performance. In a series of experiments, we here demonstrate that decreasing activity of the left PFC by cathodal transcranial direct current stimulation consistently and specifically eliminates implicit cognitive conflicts based on the SNARC effect, but explicit conflicts based on visuospatial distraction remain unaffected. This dissociation is polarity-specific and appears unrelated to functional magnitude processing as classified by regular numerical distance effects. These data demonstrate a causal involvement of the left PFC in implicit cognitive conflicts based on the automatic activation of spatial–numerical processing. Corroborating the critical interaction of brain stimulation and neurocognitive functions, our findings suggest that distraction from goal-directed behavior by automatic activation of implicit, task-irrelevant information can be blocked by the inhibition of prefrontal activity.

The associations between space and order in numerical and non-numerical sequences

Spatial-numerical associations have been found across different studies, yet the basis for these associations remains debated. The current study employed an order judgment task to adjudicate between two competing accounts of such associations, namely the Mental Number Line (MNL) and Working Memory (WM) models. On this task, participants judged whether number pairs were in ascending or descending order. Whereas the MNL model predicts that ascending and descending orders should map onto opposite sides of space, the WM model predicts no such mapping. Moreover, we compared the spatial-order mapping for numerical and non-numerical sequences because the WM model predicts no difference in mapping. Across two experiments, we found consistent spatial mappings for numerical order along both horizontal and vertical axes, consistent with a MNL model. In contrast, we found no consistent mappings for letter sequences. These findings are discussed in the context of conflicting extant data related to these two models.

How Does Working Memory Enable Number-Induced Spatial Biases?

Number-space associations are a robust observation, but their underlying mechanisms remain debated. Two major accounts have been identified. First, spatial codes may constitute an intrinsic part of number representations stored in the brain – a perspective most commonly referred to as the Mental Number Line account. Second, spatial codes may be generated at the level of working memory when number (or other) representations are coordinated in function of a specific task. The aim of the current paper is twofold. First, whereas a pure Mental Number Line account cannot capture the complexity of observations reported in the literature, we here explore if and how a pure working memory account can suffice. Second, we make explicit (more than in our earlier work) the potential building blocks of such a working memory account, thereby providing clear and concrete foci for empirical efforts to test the feasibility of the account.