On the limits of infants' quantification of small object arrays

Recent work suggests that infants rely on mechanisms of object-based attention and short-term memory to represent small numbers of objects. Such work shows that infants discriminate arrays containing 1, 2, or 3 objects, but fail with arrays greater than 3 [Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from infants' manual search. Developmental Science, 6, 568-584; Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological Science, 13(2), 150-156]. However, little is known about how infants represent arrays exceeding the 3-item limit of parallel representation. We explored possible formats by which infants might represent a 4-object array. Experiment 1 used a manual search paradigm to show that infants successfully discriminated between arrays of 1 vs. 2, 2 vs. 3, and 1 vs. 3 objects. However, infants failed to discriminate 1 vs. 4 despite the highly discriminable ratio, providing the strongest evidence to date for object-file representations underlying performance in this task. Experiment 2 replicated this dramatic failure to discriminate 1 from 4 in a second paradigm, a cracker choice task. We then showed that infants in the choice task succeeded at choosing the larger quantity with 0 vs. 4 crackers and with 1 small vs. 4 large crackers. These results suggest that while infants failed to represent 4 as “exactly 4”, “approximately 4”, “3”, or as even as “a plurality”, they did represent information about the array, including the existence of a cracker or cracker-material and the size of the individual objects in the array.     

Quantity-based judgments in the domestic dog (<Emphasis Type="Italic">Canis lupus familiaris</Emphasis>)

We examined the ability of domestic dogs to choose the larger versus smaller quantity of food in two experiments. In experiment 1, we investigated the ability of 29 dogs (results from 18 dogs were used in the data analysis) to discriminate between two quantities of food presented in eight different combinations. Choices were simultaneously presented and visually available at the time of choice. Overall, subjects chose the larger quantity more often than the smaller quantity, but they found numerically close comparisons more difficult. In experiment 2, we tested two dogs from experiment 1 under three conditions. In condition 1, we used similar methods from experiment 1 and tested the dogs multiple times on the eight combinations from experiment 1 plus one additional combination. In conditions 2 and 3, the food was visually unavailable to the subjects at the time of choice, but in condition 2, food choices were viewed simultaneously before being made visually unavailable, and in condition 3, they were viewed successively. In these last two conditions, and especially in condition 3, the dogs had to keep track of quantities mentally in order to choose optimally. Subjects still chose the larger quantity more often than the smaller quantity when the food was not simultaneously visible at the time of choice. Olfactory cues and inadvertent cuing by the experimenter were excluded as mechanisms for choosing larger quantities. The results suggest that, like apes tested on similar tasks, some dogs can form internal representations and make mental comparisons of quantity.     

Number sense in human infants

Four experiments used a preferential looking method to investigate 6-month-old infants' capacity to represent numerosity in visual-spatial displays. Building on previous findings that such infants discriminate between arrays of eight versus 16 discs, but not eight versus 12 discs (Xu & Spelke, 2000), Experiments 1 and 2 investigated whether infants' numerosity discrimination depends on the ratio of the two set sizes with even larger numerosities. Infants successfully discriminated between arrays of 16 versus 32 discs, but not 16 versus 24 discs, providing evidence that their discrimination shows the set-size ratio signature of numerosity discrimination in human adults, children and many non-human animals. Experiments 3 and 4 addressed a controversy concerning infants' ability to discriminate large numerosities (observed under conditions that control for total filled area, array size and density, item size and correlated properties such as brightness: Brannon, 2002; Xu, 2003b; Xu & Spelke, 2000) versus small numerosities (not observed under conditions that control for total contour length: Clearfield & Mix, 1999). To investigate the sources of these differing findings, Experiment 3 tested infants' large-number discrimination with controls for contour length, and Experiment 4 tested small-number discrimination with controls for total filled area. Infants successfully discriminated the large-number displays but showed no evidence of discriminating the small-number displays. These findings provide evidence that infants have robust abilities to represent large numerosities. In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large versus small numerosities.     

Inhibitory control and response selection in problem solving: how cotton-top tamarins (Saguinus oedipus) overcome a bias for selecting the larger quantity of food

When presented with a choice between 1 and 3 pieces of food in a type of reversed contingency task, 4 cotton-top tamarins (Saguinus oedipus) consistently chose the 3 pieces of food and received nothing, even though the choice of 1 piece would have yielded 3. However, in a task in which the tamarins received the 1 piece of food when they chose it, all subjects learned to select 1 over 3. Thus, the tamarins' prior failure on the reversed contingency task did not result entirely from an inherent inability to suppress the prepotent response of reaching to the larger of 2 quantities of food. After the experience of selecting the smaller quantity and receiving it, all of the tamarins solved the version of the reversed contingency task that they failed initially. These results suggest that the tamarins' initial failure may have reflected a difficulty with selecting an alternative response option.     

Event-related potential (ERP) indices of infants' recognition of familiar and unfamiliar objects in two and three dimensions

We measured infants' recognition of familiar and unfamiliar 3-D objects and their 2-D representations using event-related potentials (ERPs). Infants differentiated familiar from unfamiliar objects when viewing them in both two and three dimensions. However, differentiation between the familiar and novel objects occurred more quickly when infants viewed the object in 3-D than when they viewed 2-D representations. The results are discussed with respect to infants' recognition abilities and their understanding of real objects and representations. This is the first study using 3-D objects in conjunction with ERPs in infants, and it introduces an interesting new methodology for assessing infants' electrophysiological responses to real objects.     

A double-dissociation in infants' representations of object arrays

Previous studies show that infants can compute either the total continuous extent (e.g. Clearfield, M.W., & Mix, K.S. (1999). Number versus contour length in infants' discrimination of small visual sets. Psychological Science, 10(5), 408-411; Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: evidence from infants' manual search. Developmental Science, 6, 568-584) or the numerosity (Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: evidence from infants' manual search. Developmental Science, 6, 568-584) of small object arrays. The present experiments asked whether infants can compute both extent and number over a given array. Experiment 1 used a habituation procedure to show that 7-month-old infants can compute numerosity when the objects in the array contrast in color, pattern, and texture. Experiment 2 revealed that, with these heterogeneous arrays, infants no longer represent the array's total continuous extent. Since previous work shows that infants compute continuous extent but not numerosity when objects have identical rather than contrasting properties, these results form a double dissociation. Infants computed number but not extent over representations of contrasting objects, and computed extent but not number over representations of identical objects.     

Why additional presentations help identify a stimulus

Nosofsky (1983) reported that additional stimulus presentations within a trial increase discriminability in absolute identification, suggesting that each presentation creates an independent stimulus representation, but it remains unclear whether exposure duration or the formation of independent representations improves discrimination in such conditions. Experiment 1 replicated Nosofsky's result. Experiments 2 (masking the ISI between two-presentations) and 3 (manipulating stimulus duration without changing number of presentations or overall trial duration) ruled out an explanation in terms of extended opportunities for stimulus sampling, from either a sensory buffer during additional ISIs or increased stimulus exposure, respectively. Experiment 4 (comparing two and three-presentations, other factors controlled) provided some limited additional support for Nosofsky's original claim that additional stimulus presentations can create either independent or duplicate representations. Experiments 5 and 6 (both manipulating ISI) demonstrated that a key factor in the additional stimulus presentation effect is the overall trial duration. We discuss the results in relation to models of absolute identification, their relative emphasis on stimulus sampling versus response selection, and the mechanisms by which duplicate representations could be created.     

Cohesion as a constraint on object persistence in infancy

A critical challenge for visual perception is to represent objects as the same persisting individuals over time and motion. Across several areas of cognitive science, researchers have identified cohesion as among the most important theoretical principles of object persistence: An object must maintain a single bounded contour over time. Drawing inspiration from recent work in adult visual cognition, the present study tested the power of cohesion as a constraint as it operates early in development. In particular, we tested whether the most minimal cohesion violation - a single object splitting into two - would destroy infants' ability to represent a quantity of objects over occlusion. In a forced-choice crawling paradigm, 10- and 12-month-old infants witnessed crackers being sequentially placed into containers, and typically crawled toward the container with the greater cracker quantity. When one of the crackers was visibly split in half, however, infants failed to represent the relative quantities, despite controls for the overall quantities and the motions involved. This result helps to characterize the fidelity and specificity of cohesion as a fundamental principle of object persistence, suggesting that even the simplest possible cohesion violation can dramatically impair infants' object representations and influence their overt behavior.     

When representations conflict with reality: the preschooler's problem with false beliefs and "false" photographs

It has been argued that young preschoolers cannot correctly attribute a false belief to a deceived actor (Wimmer & Perner, 1983). Some researchers claim that the problem lies in the child's inadequate epistemology (Chandler & Boyes, 1982; Wellman, 1988); as such, it is specific to the child's theory of mind and no such problem should appear in reasoning about nonmental representations. This prediction is tested below in the "false photograph" task: here an actor takes a photograph of an object in location X; the object is then moved to location Y. Preschool subjects are asked: "In the picture, where is the object?" Results indicate that photographs are no easier to reason about than are beliefs. Manipulations to boost performance on the photograph task proved ineffective. Further, an explanation of the failure as a processing limitation having nothing to do with the representational nature of beliefs or photographs was ruled out. It is argued that young children's failure on the false belief task is not due to an inadequate epistemology (though they may have one) and is symptomatic of a larger problem with representations.     

Dissociations between featural versus conjunction-based texture processing in infancy: analyses of three potential contributing factors

Many models of object perception posit that adults encode individual features in visual scenes before processing the conjunction relations among these features to generate holistic representations. Prior research suggests that infants detect textural discrepancies based on individual features more readily than those based on feature conjunctions. While these results suggest adult-like qualitative differences in infants' processing of features versus conjunctions, there are potential alternative explanations. We examined three such explanations: (1) failure to process one of the features that constitute the conjunction, (2) failure to encode and remember conjunction information that is necessary to detect conjunction-based textural discrepancies, and (3) the fact that conjunction-based discrepancies involve stimuli that are more similar to original stimuli than those involving feature-based discrepancies. None of these factors could explain 5.5-month-olds' superior processing of featural than conjunction-based textural discrepancies. Thus, in infancy, as in adulthood, features and conjunction relations appear to be processed by qualitatively different mechanisms.     

Comparing choice and questionnaire measures of the acceptability of a staff training procedure

We compared questionnaire and choice measures of acceptability while evaluating effects of staff familiarity versus unfamiliarity with the system used to monitor performance during a training program. Staff members rated both monitoring formats equally favorably on the questionnaire, whereas when given a choice, they frequently chose the familiar format and never chose the unfamiliar format. These results suggest that traditional questionnaire evaluations may not be sufficiently sensitive measures of acceptability relative to choice measures.     

Imprinted numbers: newborn chicks’ sensitivity to number vs. continuous extent of objects they have been reared with

Newborn chicks were tested for their sensitivity to number vs. continuous physical extent of artificial objects they had been reared with soon after hatching. Because of the imprinting process, such objects were treated by chicks as social companions. We found that when the objects were similar, chicks faced with choices between 1 vs. 2 or 2 vs. 3 objects chose the set of objects of larger numerosity, irrespective of the number of objects they had been reared with. Moreover, when volume, surface or contour length were controlled for using sets of 1 vs. 4, 1 vs. 6 or 1 vs. 3 objects, chicks resorted to choosing the larger object, rather than the familiar numerosity. When, however, chicks were reared with objects differing in their aspect (colour, size, and shape) and then tested with completely novel objects (of different colour and shape but controlled for continuous extent), they chose to associate with the same number of objects they had been reared with. These results suggest that identification of objects as different and separate individuals is crucial for the computation of number rather than continuous extent in numerical representation of small numerosities and provide a striking parallel with results obtained in human infants. Early availability of small numerosity discrimination by chicks strongly suggests that these abilities are in place at birth.     

Active navigation and orientation-free spatial representations

In this study, we examined the orientation dependency of spatial representations following various learning conditions. We assessed the spatial representations of human participants after they had learned a complex spatial layout via map learning, via navigating within a real environment, or via navigating through a virtual simulation of that environment. Performances were compared between conditions involving (1) multiple- versus single-body orientation, (2) active versus passive learning, and (3) high versus low levels of proprioceptive information. Following learning, the participants were required to produce directional judgments to target landmarks. Results showed that the participants developed orientation-specific spatial representations following map learning and passive learning, as indicated by better performance when tested from the initial learning orientation. These results suggest that neither the number of vantage points nor the level of proprioceptive information experienced are determining factors; rather, it is the active aspect of direct navigation that leads to the development of orientation-free representations.     

Confidence in Personal Preferences

The first aim of this study was to test the self‐consistency model (SCM) of subjective confidence as it applies to personal preferences. According to SCM, participants presented with a two‐alternative forced‐choice (2AFC) item draw a small sample of representations of the item. Their confidence reflects the extent to which the choice is representative of the population of representations associated with the item, and the likelihood of making that choice on subsequent occasions. The second aim was to use confidence judgment as a clue to the dynamics of online preference construction. Participants were presented with 2AFC items measuring everyday personal preferences. The task was presented five times. In line with SCM, (i) when participants changed their preferences across presentations, they were systematically more confident when they made their more frequent choice; (ii) confidence in a choice in the item's first presentation predicted the likelihood of repeating that choice in subsequent presentations; (iii) despite the idiosyncratic nature of personal preferences, confidence was higher for consensual than for nonconsensual preferences; (iv) when participants predicted the preferences of others, they were also more confident when their predictions agreed with those of others; and (v) the confidence/accuracy correlation for predictions was positive for consensually correct but negative for consensually wrong predictions. These results suggest that confidence in preferences can help separate between the stable and variable contributions to preference construction in terms of the population of representations available in memory and the representations that are accessible at the time of preference solicitation, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Superior performance of blind compared with sighted individuals on bimanual estimations of object size

Five preliminary experiments on sighted individuals revealed marked overestimation on an object size-estimation task using a bimanual response. These experiments ruled out the possibility that overestimation was due to the mode of visual presentation (whether two-dimensional or three-dimensional), the input modality (visual or kinesthetic), or the influence of other visual cues. The main experiment then investigated whether these distortions are due to visual experience by using a variant of the same task to test 24 blind and 24 sighted control participants. Remarkably, the sighted control participants overestimated object size, on average, but the blind participants did not. A follow-up experiment demonstrated that visual memory was the primary influence causing the size over-estimations. We conclude that blind individuals are more accurate than sighted individuals in representing the size of familiar objects because they rely on manual representations, which are less influenced by visual experience than are visual memory representations.     

Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations

Two rhesus monkeys selected the larger of two sequentially presented sets of items on a computer monitor. In Experiment 1, performance was related to the ratio of set sizes, and the monkeys discriminated between sets with up to 10 items. Performance was not disrupted when 1 set had fewer than 4 items and 1 set had more than 4 items, a critical trial type for differentiating object file and analog models of numerical representation. Experiment 2 controlled the interitem rate of presentation. Experiment 3 included some trials on which number and amount (visual surface area) offered conflicting cues. Experiment 4 varied the total duration of set presentation and the duration of item visibility. In all of the experiments, performance remained high, although total set presentation duration also acted as a partial cue for the monkeys. Overall, the data indicated that rhesus monkeys estimate the approximate number of items in sequentially presented sets and that they are not relying solely on nonnumerical cues such as rate, duration, or cumulative amount.     

Continuous visual properties of number influence the formation of novel symbolic representations

Numerical symbols are thought to be mapped onto preexisting nonsymbolic representations of number. A growing body of evidence suggests that nonsymbolic numerical processing is significantly influenced by the associated visual properties of continuous quantity (e.g., surface area, density), but their role in the acquisition of novel symbols is unknown. Forty undergraduate students were trained to associate novel abstract symbols with numerical magnitudes. Half of the symbols were associated with nonsymbolic arrays in which total surface area and numerosity were correlated (“congruent”), and the other symbols were associated with arrays in which total surface area was equated across numerosities (“incongruent”). As numbers are represented in multiple formats (words, digits, nonsymbolic arrays), we also tested whether providing auditory nonword labels facilitated symbol learning. Following training, participants engaged in speeded comparisons of the newly learnt symbols. Comparisons were affected by the ratio between the numerosities associated with each symbol, a characteristic marker of numerical processing. Furthermore, comparisons were hardest for large-ratio comparisons of symbols associated with incongruent area and numerosity pairing during learning. In turn, these findings call for the further investigation of visual parameters on the development of numerical cognition.     

More or less: spontaneous quantity discrimination in the domestic cat

We examined spontaneous quantity discrimination in untrained domestic cats in three food choice experiments. In Experiment 1, we presented the cats with two different quantities of food in eight numerical combinations. Overall, the subjects chose the larger quantity more often than the smaller one, and significantly so when the ratio between the quantities was less than 0.5. In Experiment 2, we presented the cats with two pieces of food in four different size combinations. Again, subjects chose the larger piece above chance, although not in the combination where the largest item was presented. In Experiment 3, a subset of the cats was presented multiple times with two different quantities of food, which were hidden from view. In this case, the cats did not choose the larger quantity more often than the smaller one, suggesting that in the present experiments they mainly used visual cues when comparing quantities. We conclude that domestic cats are capable of spontaneously discriminating quantities when faced with different numbers or sizes of food items, and we suggest why they may not always be motivated to choose the larger quantity. In doing so, we highlight the advantages of testing spontaneous choice behavior, which is more likely to reflect animals’ everyday manner of responding than is the case when training them in order to test their absolute limits of performance which may not always coincide with their daily needs.     

THE EFFECTS OF CHOICE ON SELF‐CONTROL

Three adolescents with traumatic brain injury performed a physical therapy task in the absence of programmed consequences or duration requirements. Next, the experimenter gave the participants the options of a smaller immediate reinforcer with no response requirement or a larger delayed reinforcer with a response requirement. Self‐control training exposed participants to a procedure during which they chose between a smaller immediate reinforcer and a progressively increasing delayed reinforcer whose values varied and were determined by a die roll. The participants chose whether they or the experimenter rolled the die. All participants initially demonstrated low baseline durations of the physical therapy task, chose the smaller immediate reinforcer during the choice baseline, and changed their preference to the larger delayed reinforcer during self‐control training.     

Behavioral economic analysis of activity choice in obese children

Evaluated children's choice for sedentary versus vigorous activity. Experiment 1 assessed the influence of percent overweight (less than 20%, 20% to 80%, greater than 80%) on choice of a moderately liked vigorous activity at a constant variable ratio (VR) 2 reinforcement schedule versus a highly liked sedentary activity with the schedule varied from VR2 to VR32. All children chose the sedentary choice when the schedules were VR2. As the cost for sedentary activity increased, lean and moderately obese children switched to the vigorous activity, but the very obese children still chose the sedentary activity. Experiment 2 compared moderately obese children's choice between easily accessible, highly or least liked vigorous activities (VR2) and highly liked sedentary activity with the schedule varied from VR2 through VR16. When the reinforcement schedules were equal, and sedentary activity and vigorous activity were rated as equally linked, children chose the sedentary activity. All subjects switched from the sedentary to the vigorous activity, but there were no differences in choice as a function of liking for vigorous activities.