Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta)

Three rhesus monkeys (Macaca mulatta) were trained to respond to exemplars of 1, 2, 3, and 4 in an ascending, descending, or a nonmonotonic numerical order (1-->2-->3-->4, 4-->3-->2--1, 3-->1-->4-->2). The monkeys were then tested on their ability to order pairs of the novel numerosities 5-9. In Experiment 1, all 3 monkeys ordered novel exemplars of the numerosities 1-4 in ascending or descending order. The attempt to train a nonmonotonic order (3-->1-->4-->2) failed. In Experiment 2A, the 2 monkeys who learned the ascending numerical rule ordered pairs of the novel numerosities 5-9 on unreinforced trials. The monkey who learned the descending numerical rule failed to extrapolate the descending rule to new numerosities. In Experiment 2B all 3 monkeys ordered novel exemplars of pairs of the numerosities 5-9. Accuracy and latency of responding revealed distance and magnitude effects analogous to previous findings with human participants (R. S. Moyer & T. K. Landaeur, 1967). Collectively these studies show that monkeys represent the numerosities 1-9 on at least an ordinal scale.     

Subitizing and similarity: Toward a pattern-matching theory of enumeration

Pattern-matching theories of subitizing claim that subjects enumerate displays with small numerosities by retrieving numerical responses associated with similar displays experienced in the past. Such retrieval implies that displays with small numerosities are similar to other displays of the same numerosity and dissimilar to other displays of different numerosities. These hypotheses were tested by having subjects rate the similarities of displays of dot patterns with numerosities in the range of 1-10. One group of subjects rated patterns of the same numerosity. Their ratings were higher for patterns in the subitizing range (numerosities of 1-3) than for patterns beyond the subitizing range (numerosities of 4-10). Another group rated patterns of different numerosities. Their ratings were lower in the subitizing range than beyond the subitizing range. An analysis based on multidimensional scaling suggested that numerosity could be retrieved accurately for displays of 1-3 dots, but not for displays of 4-10 dots.     

Relative numerosity discrimination by chimpanzees (Pan troglodytes): evidence for approximate numerical representations

Two adult chimpanzees were trained on a relative “numerosity” discrimination task. In each trial, two arrays containing different numbers of red dots were presented on a CRT monitor. The subjects were required to choose the array containing the larger number of dots. In Experiment 1, using numerosities between 1 and 8, 28 different pairs were presented repeatedly, and accuracy scores were analyzed to explore which cues the chimpanzee subjects utilized to perform the task. Multiple regression analyses revealed that the subjects’ performance was (1) not simply controlled by the “numerical” difference between arrays, but that it was (2) best described by Fechner’s Law–that is accuracy increased linearly with the logarithmic value of the numerical difference between arrays divided by the number in the larger of the two arrays. This relationship was maintained when using much larger numerosities (Experiment 3). In Experiment 2, the chimpanzees were tested on the effects of total area and density by manipulating dot size and presentation area. The results revealed that these factors clearly affected the subjects’ performance but that they could not alone explain the results, suggesting that the chimpanzees did use relative numerosity difference as a discriminative cue.     

Baboon (Papio hamadryas) visual preferences for regions of the face

Preferences for regions of the face were examined in four members of a hamadryas baboon (Papio hamadryas) group. Subjects were presented a series of photographic slides displaying various facial regions and combinations of regions of the dominant male in the group with the use of the method of paired comparison. An apparatus consisting of a two-slide screen/two-push-button arrangement permitted the baboons to control slide selection and viewing duration. Both duration and frequency of slide activation were recorded. Correlations of viewing durations among all subjects were significant (p less than or equal to .05). The eye region alone and in combination with other regions received significantly more attention than did all other regions or combinations. Frequency measures were not significant. The results support findings obtained with rhesus monkeys (Macaca mulatta) and suggest that the eye region may provide a primate with an important source of information, possibly information about intent.     

Establishing Functional Classes In A Chimpanzee (Pan troglodytes) With A Two-item Sequential-Responding Procedure

A 9-year-old female chimpanzee was trained on a two-item sequential-responding task. Attempts were made with successive-reversal training to establish functional classes. In Experiment 1, the subject was exposed to between-session successive-reversal training in which one of two pairs of stimuli was reversed, and transfer of reversal responding to the other pair was tested with nonreinforcement probe trials. She did not show transfer during the course of reversals. Stimulus control established in the original training was maintained on nonreinforcement probe trials. In Experiment 2, within-session reversals were introduced. She showed transfer from the initially reversed pair to the other. The results were consistent with Vaughan's (1988) results with pigeons on successive discriminations, which indicated the formation of functional classes. In Experiment 3, crossover and wild-card tests were conducted to clarify the stimulus control of sequential responding. The results suggested that the sequential responding was controlled only by the first stimulus of each pair. To establish control by both first and second stimuli, trial-unique stimuli or wild cards were substituted for one of the items of the lists in Experiment 4. Further transfer tests, in which stimuli for the two new pairs appeared, were also given to the subject. She successfully responded to these two merged lists and reversed the order as the result of reversal training.     

SNARC for numerosities is modulated by comparative instruction (and resembles some non-numerical effects)

The spatial–numerical association of response codes (SNARC) effect is observed for both numerical (Arabic digits) and non-numerical stimuli (size, duration, height). However, in a context of comparative judgment, Arabic numbers are mapped onto space differently from sizes and heights: SNARC for Arabic digits is formed consistently in a certain cultural reading direction, whereas SNARC for sizes and heights is additionally modulated by comparative instruction (it reverses when participants choose larger magnitudes). In the present study, we test whether the spatial characteristic of magnitude processing revealed in a context of comparison is determined by a presence or lack of numerical content of the processed information, or it depends on specific directional experience (e.g., left-to-right ordering) associated with the processed magnitude format. We examine the SNARC effect with the pairwise comparison design, by using non-symbolic numerical stimuli (objects’ collections), for which the left-to-right spatial structure is not as exceedingly overlearned as for Arabic numbers. We asked participants from two reading cultures (left-to-right vs. mixed reading culture) to compare numerosities of two sets, choosing either a larger or smaller one. SNARC emerged in both groups. Additionally, it was modulated by comparative instruction: It appeared in a left-to-right direction when participants selected a smaller set, but it tended to reverse when participants selected a larger set. We conclude that spatial processing of numerosities is dissociated from spatial processing of Arabic numbers, at least in a context of comparative judgment. This dissociation could reflect differences in spatial ordering experience specific to a certain numerical input.     

Local rather than global processing of visual arrays in numerosity discrimination by pigeons (Columba livia)

A series of experiments investigated which stimulus properties pigeons use when they discriminate pairs of visual arrays that differ in numerosity. Transfer tests with novel stimuli confirmed that the birds’ choices were based on relative differences in numerosity. However, pigeons differed from other species in the non-numerical cues that affected their choices. In human and non-human primates, numerical discrimination is often influenced by continuous variables such as surface area or overall stimulus brightness. Pigeons showed little evidence of using those cues, even when summed area and brightness had been correlated with numerosity differences and reward outcome. But when array-element sizes were asymmetrically distributed across numerosities, the birds readily utilized information about item sizes as an additional discriminative cue. These novel results are discussed in relation to pigeons’ tendency to focus on local, rather than global dimensions when they process other non-numerical complex visual stimuli. The findings suggest there may be inter-specific differences in the type of perceptual information that provides the input stage for mechanisms underlying numerical processing. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella)

Using techniques established by E. M. Brannon and H. S. Terrace (2000) with rhesus macaques (Macaca mulatta), the authors tested the ability of brown capuchins (Cebus apella) to order arrays of items ranging in quantity from 1 to 9. Three monkeys were trained on a touch screen to select the quantities 1-4 in ascending order. The monkeys exhibited successful transfer of this ability to novel representations of the quantities 1-4 and to pairs of the novel quantities 5-9. Patterns of responding with respect to numeric distance and magnitude were similar to those seen in human subjects, suggesting the use of similar psychological processes. The capuchins demonstrated an ordinal representation of quantity equivalent to that shown in Old World monkeys.     

Dissociation between small and large numerosities in newborn infants

In the first year of life, infants possess two cognitive systems encoding numerical information: one for processing the numerosity of sets of 4 or more items, and the second for tracking up to 3 objects in parallel. While a previous study showed the former system to be already present a few hours after birth, it is unknown whether the latter system is functional at this age. Here, we adapt the auditory‐visual matching paradigm that previously revealed sensitivity to large numerosities to test sensitivity to numerosities spanning the range from 2 to 12. Across studies, newborns discriminated pairs of large numerosities in a 3:1 ratio, even when the smaller numerosity was 3 (3 vs. 9). In contrast, newborn infants failed to discriminate pairs including the numerosity 2, even at the same ratio (2 vs. 6). These findings mirror the dissociation that has been reported with older infants, albeit with a discontinuity situated between numerosities 2 and 3. Two alternative explanations are compatible with our results: either newborn infants have a separate system for processing small sets, and the capacity of this system is limited to 2 objects; or newborn infants possess only one system to represent numerosities, and this system either is not functional or is extremely imprecise when it is applied to small numerosities.     

Core information processing deficits in developmental dyscalculia and low numeracy

There are two different conceptions of the innate basis for numerical abilities. On the one hand, it is claimed that infants possess a 'number module' that enables them to construct concepts of the exact numerosities of sets upon which arithmetic develops (e.g. Butterworth, 1999; Gelman & Gallistel, 1978). On the other hand, it has been proposed that infants are equipped only with a sense of approximate numerosities (e.g. Feigenson, Dehaene & Spelke, 2004), upon which the concepts of exact numerosities are constructed with the aid of language (Carey, 2004) and which forms the basis of arithmetic (Lemer, Dehaene, Spelke & Cohen, 2003). These competing proposals were tested by assessing whether performance on approximate numerosity tasks is related to performance on exact numerosity tasks. Moreover, performance on an analogue magnitude task was tested, since it has been claimed that approximate numerosities are represented as analogue magnitudes. In 8-9-year-olds, no relationship was found between exact tasks and either approximate or analogue tasks in normally achieving children, in children with low numeracy or in children with developmental dyscalculia. Low numeracy was related not to a poor grasp of exact numerosities, but to a poor understanding of symbolic numerals.     

Do infants have a sense of numerosity? A p‐curve analysis of infant numerosity discrimination studies

Research demonstrating that infants discriminate between small (e.g., 1 vs. 3 dots) and large numerosities (e.g., 8 vs. 16 dots) is central to theories concerning the origins of human numerical abilities. To date, there has been no quantitative meta‐analysis of the infant numerical competency data. Here, we quantitatively synthesize the evidential value of the available literature on infant numerosity discrimination using a meta‐analytic tool called p‐curve. In p‐curve the distribution of available p‐values is analyzed to determine whether the published literature examining particular hypotheses contains evidential value. p‐curves demonstrated evidential value for the hypotheses that infants can discriminate between both small and large unimodal and cross‐modal numerosities. However, the analyses also revealed that the published data on infants’ ability to discriminate between large numerosities is less robust and statistically powered than the data on their ability to discriminate small numerosities. We argue there is a need for adequately powered replication studies to enable stronger inferences in order to use infant data to ground theories concerning the ontogenesis of numerical cognition.     

The interaction between time and number in a temporal bisection task: a reply to Vicario (2011)

Abstract. We discuss the results of Vicario (2011, Perception 40 23-29), in the light of an experiment designed to bypass some of the limits of that study. There, participants were asked to perform a temporal bisection on numerical stimuli (small or large digits) presented either for 700/900 ms or 2000/2200 ms. For the two longest durations only, bisections of larger digits occurred later than those of smaller digits. Here, subjects judged the temporal position of a flick occurring during the visual presentation of a digit (1, 5, or 9) which lasted on the screen for either 700 ms or 2000 ms. Results revealed no difference in the perceived temporal midpoints of large compared to small digits. In contrast, they showed a response bias: only with the shortest-duration stimuli the digit's magnitude affected the subject's response.     

Do fish count? Spontaneous discrimination of quantity in female mosquitofish

The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.     

Influence of physical and semantic information in a categorisation task of fragmented forms.

Two experiments were carried out to investigate the influence of structural and semantic information in the categorisation of visual forms. In experiment 1 the stimuli were pairs of 'well structured' or 'poorly structured' fragmented forms differing in structural properties including convexity, collinearity, and closure of the elements, and in their 'nameability'. The influence of structural and semantic information was tested by means of a task involving the presentation to both visual hemifields separately of stimuli having within-category physical similarity. For well structured forms, subjects were asked to judge if two sequentially presented forms belonged to the same semantic category. For poorly structured forms, subjects were required to decide if two stimuli belonged to the same previously learnt category of forms. For the two types of stimuli, one category was composed of physically similar items, and the other was composed of physically dissimilar items. The results show a marked advantage for the category composed of physically similar forms when the stimuli are well structured but no differences between the two categories when the stimuli are poorly structured. This suggests a facilitation in the computation of global shape information for forms having collinear and closed elements. The only effect of semantic information was a tendency towards a right visual field advantage for same-category pairs of well structured forms. The pattern of results for well structured fragmented forms (experiment 1) and forms in which fragments had been joined in order to complete the contour (experiment 2) were similar, suggesting that structured incomplete forms can be processed in the same way as forms having a continuous contour. Hypotheses about the organisational processes of forms are proposed in the discussion.     

Enumeration of small and large numerosities: the effect of element visibility

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1-8) or by tens (10-80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.     

Male chacma baboons (Papio hamadryas ursinus) discriminate loud call contests between rivals of different relative ranks

Males in multi-male groups of chacma baboons (Papio hamadryas ursinus) in Botswana compete for positions in a linear dominance hierarchy. Previous research suggests that males treat different categories of rivals differently; competitive displays between males of similar rank are more frequent and intense than those between disparately ranked males. Here we test whether males also respond differently to male–male interactions in which they are not directly involved, using playbacks of the loud wahoo calls exchanged between competing males in aggressive displays. We played paired sequences of vocal contests between two adjacently ranked and two disparately ranked males to ten subjects, half ranking below the signalers in the call sequences and half above. Subjects who ranked above the two signalers showed stronger responses than lower-ranking subjects. Higher-ranking subjects also responded more strongly to sequences involving disparately ranked, as opposed to adjacently ranked opponents, suggesting that they recognized those individuals relative ranks. Strong responses to sequences between disparately ranked opponents might have occurred either because such contests typically involve resources of high fitness value (defense of meat, estrous females or infants vulnerable to infanticide) or because they indicate a sudden change in one contestants condition. In contrast, subjects who ranked lower than the signalers responded equally strongly to both types of sequences. These subjects may have been able to distinguish between the two categories of opponents but did not respond differently to them because they had little to lose or gain by a rank reversal between males that already ranked higher than they did.     

The development of ordinal numerical competence in young children

Two experiments assessed ordinal numerical knowledge in 2- and 3-year-old children and investigated the relationship between ordinal and verbal numerical knowledge. Children were trained on a 1 vs 2 comparison and then tested with novel numerosities. Stimuli consisted of two trays, each containing a different number of boxes. In Experiment 1, box size was held constant. In Experiment 2, box size was varied such that cumulative surface area was unrelated to number. Results show children as young as 2 years of age make purely numerical discriminations and represent ordinal relations between numerosities as large as 6. Children who lacked any verbal numerical knowledge could not make ordinal judgments. However, once children possessed minimal verbal numerical competence, further knowledge was entirely unrelated to ordinal competence. Number may become a salient dimension as children begin to learn to count. An analog magnitude representation of number may underlie success on the ordinal task.     

Understanding of the concept of numerically "less" by bottlenose dolphins (Tursiops truncatus)

In 2 experiments, bottlenose dolphins (Tursiops truncatus) judged the ordinal relationship between novel numerosities. The dolphins were first trained to choose the exemplar with the fewer number of items when presented with just a few specific comparisons (e.g., 2 vs. 6, 1 vs. 3, and 3 vs. 7). Generalization of this rule was then tested by presenting the dolphins with all possible pairwise comparisons between 1 and 8. The dolphins chose the exemplar with the fewer number of items at levels far above chance, showing that they could recognize and represent numerosities on an ordinal scale. Their pattern of errors was consistent with the idea of an underlying analog magnitude representation.     

An effect of linguistic experience: The discrimination of [r] and [l] by native speakers of Japanese and English

To test the effect of linguistic experience on the perception of a cue that is known to be effective in distinguishing between [r] and [l] in English, 21 Japanese and 39 American adults were tested on discrimination of a set of synthetic speech-like stimuli. The 13 “speech” stimuli in this set varied in the initial stationary frequency of the third formant (F3) and its subsequent transition into the vowel over a range sufficient to produce the perception of [r a] and [l a] for American subjects and to produce [r a] (which is not in phonemic contrast to [l a ]) for Japanese subjects. Discrimination tests of a comparable set of stimuli consisting of the isolated F3 components provided a “nonspeech” control. For Americans, the discrimination of the speech stimuli was nearly categorical, i.e., comparison pairs which were identified as different phonemes were discriminated with high accuracy, while pairs which were identified as the same phoneme were discriminated relatively poorly. In comparison, discrimination of speech stimuli by Japanese subjects was only slightly better than chance for all comparison pairs. Performance on nonspeech stimuli, however, was virtually identical for Japanese and American subjects; both groups showed highly accurate discrimination of all comparison pairs. These results suggest that the effect of linguistic experience is specific to perception in the “speech mode.”