One, two, three, many - subitizing in active touch

Humans can sense large numbers of objects in a box by touch alone

Everyday experiences suggest that a container, such as a box of cereal, can convey pertinent information about the nature and quantity of its content. This study investigated how well people can judge large quantities of objects in a container through haptic perception. Stimuli consisted of plastic drinking straws cut to "small" (1.5 cm) or "big" (4.5 cm) pieces contained in plastic food containers. Participants performed both a magnitude estimation of the number of objects and a direct estimation of the proportion of the container perceived to be filled with objects. Overall, participants demonstrated considerable accuracy for both tasks and irrespective of the size of the content. Post-experiment interviews revealed three potential strategies. Participants either focused on the container's contents, the excess space in the container, or the perceived weight of the container (content).

Humans can sense small numbers of objects in a box by touch alone

Everyday experiences suggest that a container, such as a box of chocolate sprinkles, can convey pertinent information about the nature of its content. Despite the familiarity of the experience, we do not know whether people can perceive the number of objects in the container from touch alone and how accurately they can do so. In three experiments, participants handled containers holding between one and five objects and verbally estimated their number. Containers were small cardboard jewelry boxes, and objects were round beads of varying diameter and weight. Any useful visual and auditory cues were precluded. Experiment 1 demonstrated very accurate performance, provided the objects were of sufficient weight. Experiment 2 demonstrated that withholding information about the possible number of objects inside the container does not affect accuracy at a group level but does produce occasional overestimations at an individual level. Experiment 3 demonstrated that removing the weight cue leads to systematic underestimations but does not eliminate people's ability to distinguish between different numbers of objects in the container. This study contributes to a growing picture that container haptics is surprisingly capable.

Keeping quantifier meaning in mind: Connecting semantics, cognition, and pragmatics

A complete theory of the meaning of linguistic expressions needs to explain their semantic properties, their links to non-linguistic cognition, and their use in communication. Even though in principle interconnected, these areas are generally not pursued in tandem. We present a novel take on the semantics-cognition-pragmatics interface. We propose that formal semantic differences in expressions' meanings lead those meanings to activate distinct cognitive systems, which in turn have downstream effects on when speakers prefer to use those expressions. As a case study, we focus on the quantifiers "each" and "every", which can be used to talk about the same state of the world, but have been argued to differ in meaning. In particular, we adopt a mentalistic proposal about these quantifiers on which "each" has a purely individualistic meaning that interfaces with the psychological system for representing object-files, whereas "every" has a meaning that implicates a group and interfaces with the psychological system for representing ensembles. In seven experiments, we demonstrate that this account correctly predicts both known and newly-observed constraints on how "each" and "every" are pragmatically used. More generally, this integrated approach to semantics, cognition, and pragmatics suggests that canonical patterns of language use can be affected in predictable ways by fine-grained differences in semantic meanings and the cognitive systems to which those meanings connect.

Manipulation of Attention Affects Subitizing Performance: A Systematic Review and Meta-analysis

Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p <.010; p <.001; p <.001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Groupitizing Improves Estimation of Numerosity of Auditory Sequences

Groupitizing is a recently described phenomenon of numerosity perception where clustering items of a set into smaller "subitizable" groups improves discrimination. Groupitizing is thought to be rooted on the subitizing system, with which it shares several properties: both phenomena accelerate counting and decrease estimation thresholds irrespective of stimulus format (for both simultaneous and sequential numerosity perception) and both rely on attention. As previous research on groupitizing has been almost completely limited to vision, the current study investigates whether it generalizes to other sensory modalities. Participants estimated the numerosity of a series of tones clustered either by proximity in time or by similarity in frequency. We found that compared with unstructured tone sequences, grouping lowered auditory estimation thresholds by up to 20%. The groupitizing advantage was similar across different grouping conditions, temporal proximity and tone frequency similarity. These results mirror the groupitizing effect for visual stimuli, suggesting that, like subitizing, groupitizing is an a-modal phenomenon.

Tuned neural responses to haptic numerosity in the putamen

The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.

Topographic maps representing haptic numerosity reveals distinct sensory representations in supramodal networks

Dedicated maps for cognitive quantities such as timing, size and numerosity support the view that topography is a general principle of brain organization. To date, however, all of these maps were driven by the visual system. Here, we ask whether there are supramodal topographic maps representing cognitive dimensions irrespective of the stimulated sensory modality. We measured haptically and visually driven numerosity-selective neural responses using model-based analyses and ultra-high field (7T) fMRI. We found topographically organized neural populations tuned to haptic numerosity. The responses to visual or haptic numerosity shared a similar cortical network. However, the maps of the two modalities only partially overlap. Thus, although both visual and haptic numerosities are processed in a similar supramodal functional network, the underlying neural populations may be related, but distinct. Therefore, we hypothesize that overlap between modality-specific maps facilitates cross-modal interactions and supramodal representation of cognitive quantities.

Topographically organized tuned responses to haptic numerosity were found in the human brain. The responses to visual or haptic numerosity shared a similar large-scale cortical network, yet the maps of the two modalities only partially overlapped, suggesting distinct underlying neural populations.

Raised Dot Enumeration Via Haptic Exploration

In two experiments we investigated blindfolded, sighted participants' capacity to extract the number of raised dots from arrays of braille cells that they scanned once via active touch. The arrays could contain between one and 12 raised dots and estimates were based on scanning with one or more fingers on one or both hands (Experiment 1), or when the dots were as maximally or minimally spaced as the braille code permits (Experiment 2). We sought evidence of discontinuities in performance that reflect more than one mode of enumeration. We found that participants' estimates of numerosity increased in a linear fashion with actual numerosity, but were increasingly underestimated beyond numerosity of six, and confidence in the judgment declined linearly with increasing numerosity. Finger combinations made no difference to accuracy, errors, or confidence. Increasing dot density had the effect of diminishing perceptual accuracy, exaggerating underestimation and reducing confidence. While perceptual accuracy was generally high up to six raised dots, patterns of confusions and scaling analyses suggest that numerosities of four or less are perceptually unique. In this article, we discuss these data in terms of enumeration in touch and other modalities, and consider whether this discontinuity in enumeration signifies a subitize-to-count or a count-to-estimate transition.

The Magnitude Effect on Tactile Spatial Representation: The Spatial-Tactile Association for Response Code (STARC) Effect

The human brain uses perceptual information to create a correct representation of the external world. Converging data indicate that the perceptual processing of, space, and quantities frequently is based on a shared mental magnitude system, where low and high quantities are represented in the left and right space, respectively. The present study explores how the magnitude affects spatial representation in the tactile modality. We investigated these processes using stimulus-response (S-R) compatibility tasks (i.e., sensorimotor tasks that present an association/dissociation between the perception of a stimulus and the required action, generally increasing/decreasing accuracy and decreasing/increasing reaction times of the subject). In our study, the participant performed a discrimination task between high- and low-frequency vibrotactile stimuli, regardless of the stimulation’s spatial position. When the response code was incompatible with the mental magnitude line (i.e., left button for high-frequency and right button for low-frequency responses), we found that the participants bypassed the spatial congruence, showing a magnitude S-R compatibility effect. We called this phenomenon the Spatial–Tactile Association of Response Codes (STARC) effect. Moreover, we observed that the internal frame of reference embodies the STARC effect. Indeed, the participants’ performance reversed between uncrossed- and crossed-hands posture, suggesting that spatial reference frames play a role in the process of expressing mental magnitude, at least in terms of the tactile modality.

Representing Numerosity Through Vibration Patterns

It can be useful to display information about numerosity haptically. For instance, to display the time of day or distances when visual or auditory feedback is not possible or desirable. Here, we investigated the possibility of displaying numerosity information by means of a sequence of vibration pulses. From previous studies on numerosity perception in vision, haptics and audition it is known that numerosity judgment can be facilitated by grouping. Therefore, we investigated whether perception of the number of vibration pulses in a sequence can be facilitated by temporally grouping the pulses. We found that indeed temporal grouping can lead to considerably smaller errors and lower error rates indicating that this facilitated the task, but only when participants knew in advance whether the pulses would be temporally grouped. When grouped and ungrouped series of pulses were presented randomly interleaved, there was no difference in performance. This means that temporally grouping vibration sequences can allow the sequence to be displayed at a faster rate while it remains possible to perceive the number of vibration pulses accurately if the users is aware of the temporal grouping.

"Groupitizing": a strategy for numerosity estimation

Previous work has shown that when arrays of objects are grouped within clusters, participants can enumerate their numerosity more rapidly than when objects are randomly scattered, a phenomenon termed "groupitizing". Importantly, the magnitude of the grouping advantage correlates with math abilities in children. Here we show that sensory precision of numerosity estimation is also improved when grouping cues are available, by up to 20%. The grouping can be induced by color and/or spatial proximity, and occurs in temporal sequences as well as spatial arrays. The improvement is strongest for participants with the highest thresholds in the random, ungrouped conditions. Taken together with previous research, our data suggest that measurements correlations between numerosity estimation and formal math skills may be driven by grouping strategies, which require a minimal level of basic arithmetic.

Parametric Representation of Tactile Numerosity in Working Memory

Estimated numerosity perception is processed in an approximate number system (ANS) that resembles the perception of a continuous magnitude. The ANS consists of a right lateralized frontoparietal network comprising the lateral prefrontal cortex (LPFC) and the intraparietal sulcus. Although the ANS has been extensively investigated, only a few studies have focused on the mental representation of retained numerosity estimates. Specifically, the underlying mechanisms of estimated numerosity working memory (WM) is unclear. Besides numerosities, as another form of abstract quantity, vibrotactile WM studies provide initial evidence that the right LPFC takes a central role in maintaining magnitudes. In the present fMRI multivariate pattern analysis study, we designed a delayed match-to-numerosity paradigm to test what brain regions retain approximate numerosity memoranda. In line with parametric WM results, our study found numerosity-specific WM representations in the right LPFC as well as in the supplementary motor area and the left premotor cortex extending into the superior frontal gyrus, thus bridging the gap in abstract quantity WM literature.

If it looks, sounds, or feels like subitizing, is it subitizing? A modulated definition of subitizing

Research in cognitive psychology has focused mainly on the visual modality as the input interface for mental processes. We suggest that integrating studies from different modalities can aid in resolving theoretical controversies. We demonstrate this in the case of subitizing. Subitizing, the quick and accurate enumeration of small quantities, has been studied since the 19th century. Nevertheless, to date, the underlying mechanism is still debated. Two mechanisms have been suggested: a domain-general mechanism-attention, and a domain-specific mechanism-pattern recognition. Here, we review pivotal studies in the visual, tactile, and auditory modalities. The accumulative findings shed light on the theoretical debate. Accordingly, we suggest that subitizing is a subprocess of counting that occurs in the presence of facilitating factors, such as attentional resources and familiar patterns.

Why the whole is more than the sum of its parts: Salience-driven overestimation in aggregated tactile sensations

Experimental psychology often studies perception analytically, reducing its focus to minimal sensory units, such as thresholds or just noticeable differences in a single stimulus. Here, in contrast, we examine a synthetic aspect: how multiple inputs to a sensory system are aggregated into an overall percept. Participants in three experiments judged the total stimulus intensity for simultaneous electrical shocks to two digits. We tested whether the integration of component somatosensory stimuli into a total percept occurs automatically, or rather depends on the ability to consciously perceive discrepancy among components (Experiment 1), whether the discrepancy among these components influences sensitivity or/and perceptual bias in judging totals (Experiment 2), and whether the salience of each individual component stimulus affects perception of total intensity (Experiment 3). Perceptual aggregation of two simultaneous component events occurred both when participants could perceptually discriminate the two intensities, and also when they could not. Further, the actual discrepancy between the stimuli modulated both participants' sensitivity and perceptual bias: increasing discrepancies produced a systematic and progressive overestimation of total intensity. The degree of this bias depended primarily on the salience of the stronger stimulus in the pair. Overall, our results suggest that important nonlinear mechanisms contribute to sensory aggregation. The mind aggregates component inputs into a coherent and synthetic perceptual experience in a salience-weighted fashion that is not based on simple summation of inputs.

The role of connectedness in haptic object perception

We can efficiently detect whether there is a rough object among a set of smooth objects using our sense of touch. We can also quickly determine the number of rough objects in our hand. In this study, we investigated whether the perceptual processing of rough and smooth objects is influenced if these objects are connected. In Experiment 1, participants were asked to identify whether there were exactly two rough target spheres among smooth distractor spheres, while we recorded their response times. The spheres were connected to form pairs: rough spheres were paired together and smooth spheres were paired together ('within pairs arrangement'), or a rough and a smooth sphere were connected ('between pairs arrangement'). Participants responded faster when the spheres in a pair were identical. In Experiment 2, we found that the advantage for within pairs arrangements was not driven by feature saliency. Overall our results show that haptic information is processed faster when targets were connected together compared to when targets were connected to distractors.

The effects of training on tactile enumeration

Subitizing is a fast and accurate process of enumerating small quantities. Whether subitizing carried out in the tactile modality is under debate. We previously found a moderately increasing RT slope from one to four stimuli and a large decrease in RT for five stimuli when using one hand. Yet, a high error rate was observed, making it difficult to determine if the RT pattern found was indeed subitizing. To increase accuracy, we carried out training of the tactile enumeration task using one hand for 6 days. We compared performance in the trained and additional non-trained tasks between two groups-the 6-day training group (6DT) and the non-trained controls (C)-after three periods (1 week, 1 and 6 months after the training of the 6DT group ended). Results showed an increase in accuracy rates for both groups but a decrease in RT for the 6DT group only for the trained task. This RT improvement was present even after 6 months. Importantly, the RT slope of one-hand enumeration did not change after training, showing a moderately increased slope up to four stimuli and a decrease for five stimuli. Our study shows the training long-term effect on tactile enumeration and emphasizes the embodiment of finger counting on enumeration. Two possible enumeration processes are discussed-accelerated counting and subitizing-both based on spatial cues and pattern recognition of familiarized finger-counting patterns.

Comparison of Tactile Temporal Numerosity Judgments Between Unimanual and Bimanual Presentations

In recent years a growing interest has emerged in numerosity perception in touch. Most of the studies on tactile numerosity perception have investigated its spatial aspect by testing the ability to count the number of items presented simultaneously. On the other hand, only a small number of studies have examined its temporal aspect, and the underlying mechanisms of tactile temporal numerosity judgments (TTNJs) remain elusive. In this study, we presented a rapid sequence of vibrations, each of which was presented to one of two bodily locations, and then compared the performance of the TTNJ between two stimulus-location conditions. In one condition, each of the vibration trains was presented to one of two fingers of the left hand (unimanual condition). In the other condition, each of the vibration trains was presented to the index finger of either the right or left hand (bimanual condition). With these conditions, we aimed to examine how the differences in stimulus locations and in types of tasks affect TTNJ performance. Our results showed that when the participants were asked to count the total number of vibrations presented at two locations, the performance (proportion of correct answers) was not so much different between the two conditions. In contrast, when the participants had to report the two numbers of vibrations presented at each location or to focus on the number of vibrations at a single location, the TTNJ performance in the bimanual condition was drastically better than in the unimanual condition. These results suggest that the underlying mechanism for tactile temporal numerosity perception can segregate the interhemispheric information (bimanual condition) more precisely than the within-hemispheric information (unimanual condition), when spatiotemporal tasks are performed.

Children’s Approximate Number System in Haptic Modality

The approximate number system (ANS) is a primitive system used to estimate quantities. It can process quantities in visual and auditory modalities. The aim of the present study was to examine whether ANS can process quantities presented haptically. Moreover, to assess age-related changes, two groups of children (5- and 7-year-olds) were compared. In a newly designed haptic task, children compared two arrays of dots by touching them simultaneously using both hands, without seeing them, and for limited duration to prevent counting. Using Panamath, a frequently used visual ANS task, we verified that our population exhibited the typical pattern of approximation with visual arrays: Older children outperformed younger children, and an increased ratio between the two quantities to be compared led to more accurate responses. Performance in the haptic task revealed that children, in both age-groups, were able to haptically compare two quantities above chance level, with improved performance in older compared with younger children. Moreover, our results revealed a ratio effect, a well-known signature of the ANS. These findings suggest that haptic numerical discrimination in children is dictated by the ANS, and that ANS acuity measured with a haptic task improves with age, as commonly observed with the visual task.

Effects of Numerosity Range on Tactile and Visual Enumeration

Our study explores tactile enumeration using both hands and investigates the effects of numerosity range's (NR) on general enumeration. In Experiment 1, using custom-made vibro-tactile apparatus, we replicated results of Cohen, Naparstek, and Henik (2014, Acta Psychologica, 150C, 26-34) and again found a moderate increase in RT up to four stimuli and then a decrease for five stimuli. In Experiment 2, we used a within participants design and compared NR 1 to 5 and 1 to 10 in tactile and visual enumeration. The results showed that enumeration for NR 5 to 1 was faster than for NR 1 to 10, especially for numerosities four and five. Within NR 1 to 10, in the visual modality the subitizing range was 4, the counting range was from 5 to 9, and there was an end effect of 10 dots. In the tactile modality, when excluding one-hand arrangements, the subitizing range was 2, the counting range was from 3 to 5, there was an acceleration of counting from 5 and on, and there was an end effect for 10 stimuli that was stronger than for 10 visual stimuli. We suggest that NR influences enumeration and that number-hand association (i.e. resulting from finger counting) influences enumeration, resulting in faster counting.

Number As a Primary Perceptual Attribute: A Review

Although humans are the only species to possess language-driven abstract mathematical capacities, we share with many other animals a nonverbal capacity for estimating quantities or numerosity. For some time, researchers have clearly differentiated between small numbers of items--less than about four--referred to as the subitizing range, and larger numbers, where counting or estimation is required. In this review, we examine more recent evidence suggesting a further division, between sets of items greater than the subitizing range, but sparse enough to be individuated as single items; and densely packed stimuli, where they crowd each other into what is better considered as a texture. These two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws and show different dependencies on eccentricity and on luminance levels. But provided the elements are not too crowded (less than about two items per square degree in central vision, less in the periphery), there is little evidence that estimation of numerosity depends on mechanisms responsive to texture. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.

Non-visual numerical discrimination in a blind cavefish (Phreatichthys andruzzii)

Over a decade of comparative studies, researchers have found that rudimentary numerical abilities are widespread among vertebrates. While experiments in mammals and birds have employed a variety of stimuli (visual, auditory and tactile), all fish studies involved visual stimuli and it is unknown whether fish can process numbers in other sensory modalities. To fill this gap, we studied numerical abilities in Phreatichthys andruzzii, a blind cave-dwelling species that evolved in the phreatic layer of the Somalia desert. Fish were trained to receive a food reward to discriminate between two groups of objects placed in opposite positions of their home tank. In Experiment 1, subjects learned to discriminate between two and six objects, with stimuli not controlled for non-numerical continuous variables that co-vary with numbers, such as total area occupied by stimuli or density. In Experiment 2, the discrimination was two versus four, with half of the stimuli controlled for continuous quantities and half not controlled for continuous quantities. The subjects discriminated only the latter condition, indicating that they spontaneously used non-numerical information, as other vertebrates tested in similar experiments. In Experiments 3 and 4, cavefish trained from the beginning only with stimuli controlled for continuous quantities proved able to learn the discrimination of quantities based on the sole numerical information. However, their numerical acuity was lower than that reported in other teleost fish tested with visual stimuli.

The effect of perceptual grouping on haptic numerosity perception

We used a haptic enumeration task to investigate whether enumeration can be facilitated by perceptual grouping in the haptic modality. Eight participants were asked to count tangible dots as quickly and accurately as possible, while moving their finger pad over a tactile display. In Experiment 1, we manipulated the number and organization of the dots, while keeping the total exploration area constant. The dots were either evenly distributed on a horizontal line (baseline condition) or organized into groups based on either proximity (dots placed in closer proximity to each other) or configural cues (dots placed in a geometric configuration). In Experiment 2, we varied the distance between the subsets of dots. We hypothesized that when subsets of dots can be grouped together, the enumeration time will be shorter and accuracy will be higher than in the baseline condition. The results of both experiments showed faster enumeration for the configural condition than for the baseline condition, indicating that configural grouping also facilitates haptic enumeration. In Experiment 2, faster enumeration was also observed for the proximity condition than for the baseline condition. Thus, perceptual grouping speeds up haptic enumeration by both configural and proximity cues, suggesting that similar mechanisms underlie perceptual grouping in both visual and haptic enumeration.

Tactile enumeration of small quantities using one hand

Our study explores various aspects of enumerating small quantities in the tactile modality. Fingertips of one hand were stimulated by a vibro-tactile apparatus (for 100/800 ms). Between 1 and 5 stimuli were presented to the right or the left hand and applied to neighboring (e.g., thumb-index-middle) or non-neighboring (e.g., thumb-middle-pinkie) fingers. The results showed a moderate increase in RT up to 4 stimuli and then a decrease for 5 stimuli. Right hand stimulation evoked more accurate performance than left hand stimulation only under short exposures (100 ms). Importantly, when the stimuli were presented to neighboring fingers, the accuracy rate was higher and the RT was faster than when presented to non-neighboring fingers. We discuss the results and suggest that when the stimuli are presented to one hand the subitizing range is 4 rather than 3. Furthermore, the right hand advantage and the efficiency for neighboring fingers are further support for the association between number and spatial arrangement of the fingers.

The role of pattern recognition in children's exact enumeration of small numbers

Enumeration can be accomplished by subitizing, counting, estimation, and combinations of these processes. We investigated whether the dissociation between subitizing and counting can be observed in 4- to 6-year-olds and studied whether the maximum number of elements that can be subitized changes with age. To detect a dissociation between subitizing and counting, it is tested whether task manipulations have different effects in the subitizing than in the counting range. Task manipulations concerned duration of presentation of elements (limited, unlimited) and configuration of elements (random, line, dice). In Study 1, forty-nine 4- and 5-year-olds were tested with a computerized enumeration task. Study 2 concerned data from 4-, 5-, and 6-year-olds, collected with Math Garden, a computer-adaptive application to practice math. Both task manipulations affected performance in the counting, but not the subitizing range, supporting the conclusion that children use two distinct enumeration processes in the two ranges. In all age groups, the maximum number of elements that could be subitized was three. The strong effect of configuration of elements suggests that subitizing might be based on a general ability of pattern recognition.

Haptic perception

Fueled by novel applications, interest in haptic perception is growing. This paper provides an overview of the state of the art of a number of important aspects of haptic perception. By means of touch we can not only perceive quite different material properties, such as roughness, compliance, friction, coldness and slipperiness, but we can also perceive spatial properties, such as shape, curvature, size and orientation. Moreover, the number of objects we have in our hand can be determined, either by counting or subitizing. All these aspects will be presented and discussed in this paper. Although our intuition tells us that touch provides us with veridical information about our environment, the existence of prominent haptic illusions will show otherwise. Knowledge about haptic perception is interesting from a fundamental viewpoint, but it also is of eminent importance in the technological development of haptic devices. At the end of this paper, a few recent applications will be presented. WIREs Cogn Sci 2013, 4:357-374. DOI: 10.1002/wcs.1238 CONFLICT OF INTEREST: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

Haptic spatial configuration learning in deaf and hearing individuals

The present study investigated haptic spatial configuration learning in deaf individuals, hearing sign language interpreters and hearing controls. In three trials, participants had to match ten shapes haptically to the cut-outs in a board as fast as possible. Deaf and hearing sign language users outperformed the hearing controls. A similar difference was observed for a rotated version of the board. The groups did not differ, however, on a free relocation trial. Though a significant sign language experience advantage was observed, comparison to results from a previous study testing the same task in a group of blind individuals showed it to be smaller than the advantage observed for the blind group. These results are discussed in terms of how sign language experience and sensory deprivation benefit haptic spatial configuration processing.

Subitizing Is Sensitive to the Arrangement of Objects

Subitizing is a fast and accurate enumeration process of small sets of usually less than four objects. Several models were proposed in the literature. Critically, only pattern recognition theory suggests that subitizing performance is sensitive to the arrangement of the array. In our study, arrays of dots in random or canonical arrangements were enumerated. The subitizing range was larger and the reaction time slope was less steep in the canonical arrangements. When noise was added to the canonical pattern, the reaction time slope was proportional to the amount of noise. Moreover, arrangement has a stronger effect on sets with more than four objects. These results support the pattern recognition model of subitizing.

A feeling for numbers: shared metric for symbolic and tactile numerosities

Evidence for an approximate analog system of numbers has been provided by the finding that the comparison of two numerals takes longer and is more error-prone if the semantic distance between the numbers becomes smaller (so-called numerical distance effect). Recent embodied theories suggest that analog number representations are based on previous sensory experiences and constitute therefore a common magnitude metric shared by multiple domains. Here we demonstrate the existence of a cross-modal semantic distance effect between symbolic and tactile numerosities. Participants received tactile stimulations of different amounts of fingers while reading Arabic digits and indicated verbally whether the amount of stimulated fingers was different from the simultaneously presented digit or not. The larger the semantic distance was between the two numerosities, the faster and more accurate participants made their judgments. This cross-modal numerosity distance effect suggests a direct connection between tactile sensations and the concept of numerical magnitude. A second experiment replicated the interaction between symbolic and tactile numerosities and showed that this effect is not modulated by the participants’ finger counting habits. Taken together, our data provide novel evidence for a shared metric for symbolic and tactile numerosities as an instance of an embodied representation of numbers.

Haptic search for hard and soft spheres

In this study the saliency of hardness and softness were investigated in an active haptic search task. Two experiments were performed to explore these properties in different contexts. In Experiment 1, blindfolded participants had to grasp a bundle of spheres and determine the presence of a hard target among soft distractors or vice versa. If the difference in compliance between target and distractors was small, reaction times increased with the number of items for both features; a serial strategy was found to be used. When the difference in compliance was large, the reaction times were independent of the number of items, indicating a parallel strategy. In Experiment 2, blindfolded participants pressed their hand on a display filled with hard and soft items. In the search for a soft target, increasing reaction times with the number of items were found, but the location of target and distractors appeared to have a large influence on the search difficulty. In the search for a hard target, reaction times did not depend on the number of items. In sum, this showed that both hardness and softness are salient features.

Intentional subitizing: exploring the role of automaticity in enumeration

Subitizing is traditionally described as the rapid, preattentive and automatic enumeration of up to four items. Counting, by contrast, describes the enumeration of larger sets of items and requires slower serial shifts of attention. Although recent research has called into question the preattentive nature of subitizing, whether or not numerosities in the subitizing range can be automatically accessed is yet to be empirically tested. In the current study, participants searched for two pre-defined digits in a circular visual-search array. Distractor dots of various set sizes were placed at the centre of the array. Despite the relevance of the distractor numerosities to the target detection task, the distractors did not influence target detection, thereby suggesting that their numerosities were not automatically accessed in Experiment 1. In Experiment 2, participants were explicitly instructed to enumerate the distractor dots. Here, congruent and incongruent distractor numerosities influenced the target detection task, thereby revealing that the distractor dots were capable of generating interference. Experiment 3 ensured that dots were attended by asking participants to detect the luminance of dots. Data confirmed that subitizing was not automatic. The present study also supported the alleged discontinuity between the subitizing and counting ranges because an examination of reaction time gradients in Experiment 2 found the counting gradient to be significantly steeper than the subitizing gradient. In sum, the results suggest that subitizing is a distinct but non-automatic style of enumeration.

Evidence for a shared mechanism used in multiple-object tracking and subitizing

It has been proposed that the mechanism that supports the ability to keep track of multiple moving objects also supports subitizing--the ability to quickly and accurately enumerate a small set of objects. To test this hypothesis, we investigated the effects on subitizing when human observers were required to perform a multiple object tracking task and an enumeration task simultaneously. In three experiments, participants (Exp. 1, N = 24; Exp. 2, N = 11; Exp. 3, N = 37) enumerated sets of zero to nine squares that were flashed while they tracked zero, two, or four moving discs. The results indicated that the number of items participants could subitize decreased by one for each item they tracked. No such pattern was seen when the enumeration task was paired with an equally difficult, but nonvisual, working memory task. These results suggest that a shared visual mechanism supports multiple object tracking and subitizing.

Haptic subitizing across the fingers

Numerosity judgments of small sets of items (≤ 3) are generally fast and errorfree, while response times and error rates increase rapidly for larger numbers of items. We investigated an efficient process used for judging small numbers of items (known as subitizing) in active touch. We hypothesized that this efficient process for numerosity judgment might be related to stimulus properties that allow for efficient (parallel) search. Our results showed that subitizing was not possible forraised lines among flat surfaces, whereas this type of stimulus could be detected in parallel over the fingers. However, subitizing was possible when the number of fingers touching a surface had to be judged while the other fingers were lowered in mid-air. In the latter case, the lack of tactile input is essential, since subitizing was not enabled by differences in proprioceptive information from the fingers. Our results show that subitizing using haptic information from the fingers is possible only whensome fingers receive tactile information while other fingers do not.

The effect of feature saliency on haptic subitizing

'Subitizing' refers to fast and error-free numerosity judgment for small (<4) sets of items. For larger sets, the slower process of 'counting' is used. Counting has a serial character, whereas subitizing is believed to have a parallel character. While subitizing was initially found in vision, it has been shown to exist in touch as well. In vision, it has been demonstrated that adding distractor items to a set of target items influences numerosity judgment of the target items. Subitizing was in this case only possible if the distractor item is highly salient among the targets. In the present study, we investigated the effect of adding a distractor item on haptic judgement of a set of target items. To this end, we asked subjects to judge the number of spheres grasped in their hand. Either a cube or an ellipsoid could be added to the set. A cube among spheres has been shown to be highly salient, while an ellipsoid among spheres is not. Our results show that adding a distractor item led to an increase in the response time slopes regardless of the distractor shape. Subitizing was, however, only possible in the case of a salient distractor. This is in agreement with results from vision.

Figure/Ground Segmentation via a Haptic Glance: Attributing Initial Finger Contacts to Objects or Their Supporting Surfaces

The current study addresses the well-known "figure/ground" problem in human perception, a fundamental topic that has received surprisingly little attention from touch scientists to date. Our approach is grounded in, and directly guided by, current knowledge concerning the nature of haptic processing. Given inherent figure/ground ambiguity in natural scenes and limited sensory inputs from first contact (a "haptic glance"), we consider first whether people are even capable of differentiating figure from ground (Experiments 1 and 2). Participants were required to estimate the strength of their subjective impression that they were feeling an object (i.e., figure) as opposed to just the supporting structure (i.e., ground). Second, we propose a tripartite factor classification scheme to further assess the influence of kinetic, geometric (Experiments 1 and 2), and material (Experiment 2) factors on haptic figure/ground segmentation, complemented by more open-ended subjective responses obtained at the end of the experiment. Collectively, the results indicate that under certain conditions it is possible to segment figure from ground via a single haptic glance with a reasonable degree of certainty, and that all three factor classes influence the estimated likelihood that brief, spatially distributed fingertip contacts represent contact with an object and/or its background supporting structure.

Haptic Object Individuation

Item individuation, i.e., how we decide which parts belong to one object and which to another, is an important aspect of haptic perception and may be important for design of interfaces in which different buttons have to be distinguished. We daily hold several objects in our hand. Somehow, we decide that we are holding several small objects instead of one large object. We aim to provide insight into how it is decided that some parts belong to the same object and others to a different object, i.e., object individuation. This process may be influenced by heterogeneity of size or shape of the handled objects. To investigate this, subjects were asked to grasp varying numbers of shapes together in the hand and respond fast and accurately the number of shapes. We compared performance for a set of homogeneous objects (Experiment 1) to performance for sets of objects heterogeneous in size (Experiment 2) or shape (Experiment 3). It was found that numerosity judgments in terms of response times, error rates, and object handling were similar in all three experiments. We conclude that size and shape features that are used for object recognition do not play a role in item individuation.

Range dependent processing of visual numerosity: similarities across vision and haptics

'Subitizing' refers to fast and accurate judgement of small numerosities, whereas for larger numerosities either counting or estimation are used. Counting is slow and precise, whereas estimation is fast but imprecise. In this study consisting of five experiments we investigated if and how the numerosity judgement process is affected by the relative spacing between the presented numerosities. To this end we let subjects judge the number of dots presented on a screen and recorded their response times. Our results show that subjects switch from counting to estimation if the relative differences between subsequent numerosities are large (a factor of 2), but that numerosity judgement in the subitizing range was still faster. We also show this fast performance for small numerosities only occurred when numerosity information is present. This indicates this is typical for number processing and not magnitude estimation in general. Furthermore, comparison with a previous haptic study suggests similar processing in numerosity judgement through haptics and vision.

Grabbing subitizing with both hands: bimanual number processing

Visual judgment of small numerosities (<4) is generally assumed to be done through subitizing, which is a faster process than counting. Subitizing has also been shown to occur in haptic judgment of the number of spheres in the hand. Furthermore, interactions have been shown to exist between visually perceived numbers and hand motor action. In this study, we compare enumeration of a set of spheres presented to one hand (unimanual) and enumeration of the same total number of spheres presented divided over the two hands (bimanual). Our results show that, like in vision, a combination of subitizing and counting is used to process numbers in active touch. This shows that numbers are processed in a modality-independent way. This suggests that there are not only interactions between perception of numbers and hand motor action, but rather that number representation is modality-independent.