The Spatial Representation of Numerical and Non-Numerical Ordered Sequences: Insights from a Random Generation Task

Keeping track of time: Horizontal spatial biases for hours, days, and months

In many Western cultures, the processing of temporal words related to the past and to the future is associated with left and right space, respectively - a phenomenon known as the horizontal Mental Time Line (MTL). While this mapping is apparently quite ubiquitous, its regularity and consistency across different types of temporal concepts remain to be determined. Moreover, it is unclear whether such spatial mappings are an essential and early constituent of concept activation. In the present study, we used words denoting time units at different scales (hours of the day, days of the week, months of the year) associated with either left space (e.g., 9 a.m., Monday, February) or right space (e.g., 8 p.m., Saturday, November) as cues in a line bisection task. Fifty-seven healthy adults listened to temporal words and then moved a mouse cursor to the perceived midpoint of a horizontally presented line. We measured movement trajectories, initial line intersection coordinates, and final bisection response coordinates. We found movement trajectory displacements for left- vs. right-biasing hour and day cues. Initial line intersections were biased specifically by month cues, while final bisection responses were biased specifically by hour cues. Our findings offer general support to the notion of horizontal space-time associations and suggest further investigation of the exact chronometry and strength of this association across individual time units.

How to not induce SNAs: The insufficiency of directional force

People respond faster to smaller numbers in their left space and to larger numbers in their right space. Here we argue that movements in space contribute to the formation of spatial-numerical associations (SNAs). We studied the impact of continuous isometric forces along the horizontal or vertical cardinal axes on SNAs while participants performed random number production and arithmetic verification tasks. Our results suggest that such isometric directional force do not suffice to induce SNAs.

Counting on random number generation: Uncovering mild executive dysfunction in congenital heart disease

Congenital heart disease (CHD) is associated with various neurocognitive deficits, particularly targeting executive functions (EFs), of which random number generation (RNG) is one indicator. RNG has, however, never been investigated in CHD. We administered the Mental Dice Task (MDT) to 67 young adults with CHD and 55 healthy controls. This 1-minute-task requires the generation of numbers 1 to 6 in a random sequence. RNG performance was correlated with a global EF score. Participants underwent MRI to examine structural-volumetric correlates of RNG. Compared to controls, CHD patients showed increased backward counting, reflecting deficient inhibition of automatized behavior. They also lacked a small-number bias (higher frequency of small relative to large numbers). RNG performance was associated with global EF scores in both groups. In CHD patients, MRI revealed an inverse association of counting bias with most of the volumetric measurements and the amount of small numbers was positively associated with corpus callosum volume, suggesting callosal involvement in the "pseudoneglect in number space". In conclusion, we found an impaired RNG performance in CHD patients, which is associated with brain volumetric measures. RNG, reportedly resistant to learning effects, may be an ideal task for the longitudinal assessment of EFs in patients with CHD.

Spatial-numerical associations from a novel paradigm support the mental number line account

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants' responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Random word generation reveals spatial encoding of syllabic word length

Existing random number generation studies demonstrate the presence of an embodied attentional bias in spontaneous number production corresponding to the horizontal Mental Number Line: Larger numbers are produced on right-hand turns and smaller numbers on left-hand turns (Loetscher et al.,2008, Curr. Biol., 18, R60). Furthermore, other concepts were also shown to rely on horizontal attentional displacement (Di Bono and Zorzi, 2013, Quart. J. Exp. Psychol., 66, 2348). In two experiments, we used a novel random word generation paradigm combined with two different ways to orient attention in horizontal space: Participants randomly generated words on left and right head turns (Experiment 1) or following left and right key presses (Experiment 2). In both studies, syllabically longer words were generated on right-hand head turns and following right key strokes. Importantly, variables related to semantic magnitude or cardinality (whether the generated words were plural-marked, referred to uncountable concepts, or were associated with largeness) were not affected by lateral manipulations. We discuss our data in terms of the ATOM (Walsh, 2015, The Oxford handbook of numerical cognition, 552) which suggests a general magnitude mechanism shared by different conceptual domains.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity

Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

Acute peripheral vestibular deficit increases redundancy in random number generation

Unilateral peripheral vestibular deficit leads to broad cognitive difficulties and biases in spatial orientation. More specifically, vestibular patients typically show a spatial bias toward their affected ear in the subjective visual vertical, head and trunk orientation, fall tendency, and walking trajectory. By means of a random number generation task, we set out to investigate how an acute peripheral vestibular deficit affects the mental representation of numbers in space. Furthermore, the random number generation task allowed us to test if patients with peripheral vestibular deficit show evidence of impaired executive functions while keeping the head straight and while performing active head turns. Previous research using galvanic vestibular stimulation in healthy people has shown no effects on number space, but revealed increased redundancy of the generated numbers. Other studies reported a spatial bias in number representation during active and passive head turns. In this experiment, we tested 43 patients with acute vestibular neuritis (18 patients with left-sided and 25 with right-sided vestibular deficit) and 28 age-matched healthy controls. We found no bias in number space in patients with peripheral vestibular deficit but showed increased redundancy in patients during active head turns. Patients showed worse performance in generating sequences of random numbers, which indicates a deficit in the updating component of executive functions. We argue that RNG is a promising candidate for a time- and cost-effective assessment of executive functions in patients suffering from a peripheral vestibular deficit.

Culturally inconsistent spatial structure reduces learning

Human adults tend to use a spatial continuum to organize any information they consider to be well-ordered, with a sense of initial and final position. The directionality of this spatial mapping is mediated by the culture of the subject, largely as a function of the prevailing reading and writing habits (for example, from left-to-right for English speakers or right-to-left for Hebrew speakers). In the current study, we tasked American and Israeli subjects with encoding and recalling a set of arbitrary pairings, consisting of frequently ordered stimuli (letters with shapes: Experiment 1) or infrequently ordered stimuli (color terms with shapes: Experiment 2), that were serially presented in a left-to-right, right-to-left, or central-only manner. The subjects were better at recalling information that contained ordinal stimuli if the spatial flow of presentation during encoding matched the dominant directionality of the subjects' culture, compared to information encoded in the non-dominant direction. This phenomenon did not extend to infrequently ordered stimuli (e.g., color terms). These findings suggest that adults implicitly harness spatial organization to support memory, and this harnessing process is culturally mediated in tandem with our spatial biases.

The oculomotor resonance effect in spatial-numerical mapping

We investigated automatic Spatial-Numerical Association of Response Codes (SNARC) effect in auditory number processing. Two experiments continually measured spatial characteristics of ocular drift at central fixation during and after auditory number presentation. Consistent with the notion of a spatially oriented mental number line, we found spontaneous magnitude-dependent gaze adjustments, both with and without a concurrent saccadic task. This fixation adjustment (1) had a small-number/left-lateralized bias and (2) it was biphasic as it emerged for a short time around the point of lexical access and it received later robust representation around following number onset. This pattern suggests a two-step mechanism of sensorimotor mapping between numbers and space - a first-pass bottom-up activation followed by a top-down and more robust horizontal SNARC. Our results inform theories of number processing as well as simulation-based approaches to cognition by identifying the characteristics of an oculomotor resonance phenomenon.

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

Rather than reflecting the long-term memory construct of a mental number line, it has been proposed that the relation between numbers and space is of a more temporary nature and constructed in working memory during task execution. In three experiments we further explored the viability of this working memory account. Participants performed a speeded dot detection task with dots appearing left or right, while maintaining digits or letters in working memory. Just before presentation of the dot, these digits or letters were used as central cues. These experiments show that the “attentional SNARC-effect” (where SNARC is the spatial–numerical association of response codes) is not observed when only the lastly perceived number cue—and no serially ordered sequence of cues—is maintained in working memory (Experiment 1). It is only when multiple items (numbers in Experiment 2; letters in Experiment 3) are stored in working memory in a serially organized way that the attentional cueing effect is observed as a function of serial working memory position. These observations suggest that the “attentional SNARC-effect” is strongly working memory based. Implications for theories on the mental representation of numbers are discussed.

No horizontal numerical mapping in a culture with mixed-reading habits

Reading habits are thought to play an important role in the emergence of cultural differences in visuo-spatial and numerical tasks. Left-to-right readers show a slight visuo-spatial bias to the left side of space, and automatically associate small numbers to the left and larger numbers to the right side of space, respectively. A paradigm that demonstrated an automatic spatial-numerical association involved the generation of random numbers while participants performed lateral head turns. That is, Westerners have been shown to produce more small numbers when the head was turned to the left compared to the right side. We here employed the head turning/random number generation (RNG) paradigm and a line bisection (LB) task with a group of 34 Iranians in their home country. In the participants’ native language (Farsi) text is read from right-to-left, but numbers are read from left-to-right. If the reading direction for text determines the layout of spatial-numerical mappings we expected to find more small numbers after right than left head turns. Yet, the generation of small or large numbers was not modulated by lateral head turns and the Iranians showed therefore no association of numbers with space. There was, however, a significant rightward shift in the LB task. Thus, while the current results are congruent with the idea that text reading habits play an important role in the cultural differences observed in visuo-spatial tasks, our data also imply that these habits on their own are not strong enough to induce significant horizontal spatial-numerical associations. In agreement with previous suggestions, we assume that for the emergence of horizontal numerical mappings a congruency between reading habits for words and numbers is required.

Dissociable effects of auditory attention switching and stimulus-response compatibility

Using a task-switching variant of dichotic listening, we examined the ability to intentionally switch auditory attention between two speakers. We specifically focused on possible interactions with stimulus-response compatibility. In each trial, two words, one spoken by a male and another by a female, were presented dichotically via headphones. In one experimental group, two animal names were presented, and the relevant animal had to be judged as smaller or larger than a sheep by pressing a left or right response key. In another group, two number words were presented and had to be judged as smaller or larger than 5. In each trial, a visual cue indicated the gender of the relevant speaker. Performance was worse when the gender of the relevant speaker switched from trial to trial. These switch costs were larger for animal names than for number words, suggesting stronger interference with slower access to semantic categories. Responses were slower if the side of the target stimulus (as defined by the relevant gender) was spatially incompatible with the required response (as defined by the size judgment). This stimulus-response compatibility effect did not differ across stimulus material and did not interact with attentional switch costs. These results indicate that auditory switch costs and stimulus-response compatibility effects are dissociable, referring to target selection and response selection, respectively.

Not all numbers are equal: preferences and biases among children and adults when generating random sequences

We investigate the number preferences of children and adults when generating random digit sequences. Previous research has shown convincingly that adults prefer smaller numbers when randomly choosing between responses 1–6. We analyze randomization choices made by both children and adults, considering a range of experimental studies and task configurations. Children – most of whom are between 8 and 11~years – show a preference for relatively large numbers when choosing numbers 1–10. Adults show a preference for small numbers with the same response set. We report a modest association between children’s age and numerical bias. However, children also exhibit a small number bias with a smaller response set available, and they show a preference specifically for the numbers 1–3 across many datasets. We argue that number space demonstrates both continuities (numbers 1–3 have a distinct status) and change (a developmentally emerging bias toward the left side of representational space or lower numbers).

Gaining the upper hand: comparison of alphabetic and keyboard positions as spatial features of letters producing distinct S-R compatibility effects

The present study explored which stimulus feature, alphabetic or keyboard position, primarily influences letter processing in different task settings. In Experiment 1 (alphabetic position judgment) a response side effect (faster responses when the location of letters within the alphabet or on the keyboard maps onto the response hand) could be observed for alphabetic position as task-relevant stimulus feature. In Experiments 2 and 3 participants responded to a non-spatial stimulus feature (uppercase-lowercase classification) so that both attributes can be characterized as task-irrelevant. The pattern indicated that a keyboard position-hand correspondence effect emerged independent of the time window (after stimulus onset) in which the response was given. However, an alphabetic position-hand correspondence effect only emerged when participants were forced to delay their responses by 450ms. The overall pattern indicated that although both features were processed and translated into a spatial code reflecting their position within the alphabet vs. on the keyboard, the relevance of these features to the task as well as the time that elapsed since stimulus onset determined which attribute of the letters was effective in yielding a stimulus-response compatibility effect.