Edited by: Aaron P. Blaisdell, University of California Los Angeles, USA
Reviewed by: Elizabeth M. Brannon, Duke University, USA; Marcia Spetch, University of Alberta, Canada
*Correspondence: Claudia Uller, School of Psychology, Criminology and Sociology, Kingston University, Penrhyn Road, Kingston-upon-Thames, KT1 2EE, Surrey, UK. e-mail:
This article was submitted to Frontiers in Comparative Psychology, a specialty of Frontiers in Psychology.
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Animals and human infants discriminate numerosities in visual sets. Experiments on visual numerical judgments generally contrast sets in which number varies (e.g., the discrimination between 2 and 3). What is less investigated, however, is set density, or rather, the inter-stimulus distance between the entities being enumerated in a set. In this study, we investigated the role of set density in visual sets by 10-month-old infants. In Experiment 1, infants were offered a choice between two sets each containing four items of the exact same size varying in the distance in between the items (ratio 1:4). Infants selected the set in which the items are close together (higher density). Experiment 2 addressed the possibility that this choice was driven by a strategy to “select all in one go” by reducing the size and distance of items. Ten-month-olds selected the sets with higher density (less inter-stimulus distance) in both experiments. These results, although bearing replication because of their originality, seem consistent with principles in Optimal Foraging in animals. They provide evidence that a comparable rudimentary capacity for density assessment (of food items) exists in infants, and may work in concert with their numerical representations.
From neonates and pre-crawling babies, to toddlers and preschoolers, research indicates that numerical representations may be found early in development. While some researchers reach consensus that numerical understanding exists early in infancy, perhaps even innately (Uller et al.,
Another area of investigation to challenge the perceptual-only hypothesis comes from evidence that infants can approximate the number of items in large sets (e.g., visual objects: Xu and Spelke,
Control experiments contrasting number with variables such as cumulative surface area, perimeter contour, etc., also represent a challenge to perceptual explanations. Most of the number studies with infants control for various continuous variables, and the results suggest that the discriminations infants make are based on number (e.g., Xu and Spelke,
While there is an emerging bulk of evidence for the number argument, contention with regards to variables which confound with number still persists. An aspect of visual sets controlled for is inter-stimulus distance, or set density. The adult visual perception literature on the relation between number and density seems to indicate that, in adults, estimated numerosity and density are negatively correlated (Krueger,
In children, the first observation by Piaget (
Speculations on the basis of experiments with animals, however, are driven by another set of findings. Quantity assessment of food items in patches of potential foraging by animals have been observed and analyzed by theories of optimal foraging (MacArthur and Pianka,
Suppose you are a baboon. You’re hungry. In the Namibian desert, food is scarce. You need to be selective where you forage in order not to waste energy and die. You strike lucky, and find two bushes of edible fruit to be harvested from. It is a simple matter: you’ll go for the bush containing more items. Evidence for non-human animal (monkeys: Hauser et al.,
These two theoretical constructs – theories of numerosity perception in adults and Piagetian assessments in conservation tasks, versus optimal foraging theory – generate conflicting predictions. Optimal Foraging Theory would predict a choice for
It is clear, however, that there may be a difference between the numerical representation of objects (dots on a page/slide) and the numerical representation of edible items, as is the case of optimal foraging. And indeed, research with infants seems to indicate that the domain of food might be uniquely understood (Shutts et al.,
In addition, animals seem to prefer higher density in sets of objects. Stevens et al. (
Twenty (12 ♀) full-term infants participated in the study (Mean age = 10 months, 10 days; range 10;01–10;29). Five additional infants were excluded from the sample because of fussiness, namely, the infants did not make a choice during the familiarization phase. Participants were recruited as volunteers in the Essex/Suffolk/Cambridgeshire area through advertisements and were taken to the baby lab by their parent or caregiver.
The stimuli used for testing were
The more dense array was presented on the left for half the babies, and on the right for the other half. Choice was coded as the set that the infant pointed to or touched. A testing session was considered over when (a) the infant made a choice by either touching one of the four stimuli or the tray on a clear reach to other (rather than the other) side, (b) the infant did not reach for or point to either tray after 60 s, or (c) if the infants choice was unclear, for example, if the infant simultaneously reached for or pointed to both trays. Infants were excluded when (b) and (c) were the case.
The infants sat in the caregiver’s lap facing the experimenter and the stimuli. They were positioned so that their hands rested on the edge of the table. Throughout the experiment, babies were shown toys and edible items. They were allowed to chew on chewable toys shown to them, but they were not allowed to eat the cookies.
The experiment began with a pre-testing familiarization phase. The purpose of this was to (1) get the infant used to reaching for items on a tray and (2) familiarize the infant with the experimental stimuli. The familiarization phase began with the experimenter placing a toy onto an empty tray (identical to the trays the stimuli were presented on) and saying “Look [baby’s name]! Look at this! Would you like to pick it up?” This process was repeated until the infant readily picked up toys (ball, plastic keys, cup) from the tray. Following this, the experimenter hid the toys behind her back and picked and placed one of the cookies onto the tray saying “What’s this? You haven’t seen one of these before! Would you like to have a look?” As soon as the infant picked up the cookie and examined it, the caregiver was instructed to take the cookie from the infant and pass it back to the experimenter. Both cookie and tray were hidden underneath the table immediately thereafter.
If the infant did not respond after 30 s, having made no attempt to reach for the toys, the experimenter provided verbal encouragement: “Here, baby, would you like to grab it for me?” and would simultaneously draw the infant’s attention to the tray whilst speaking. If the infant did not respond after a further 30 s the trial was terminated.
The test phase began directly after the removal of the cookie. The experimenter would say to the infant “Here, baby, we have some more cookies to play with!” The experimenter then uncovered both trays simultaneously. Following this, the experimenter simultaneously displayed both trays in a vertical position before pushing them within reaching distance of the infant. The experimenter and the caregiver would immediately avert their gaze downwards with a neutral facial expression until the infant reached for one of the trays. This method is generally used in infancy research (e.g., Feigenson et al.,
The trial was terminated as soon as the infant hand made contact with one of the cookies on either tray. All trials were recorded with a
Data from 17 infants who reached for either the more dense (1) or less dense (4) set were coded as choice. Thirteen infants selected the more dense set and four infants selected the less dense set. A binomial test revealed a significant difference between the two choices,
The results of this experiment indicate that 10-month-old infants preferred to select the more dense set of four items. There are two interpretations for this finding. One is that human babies have an intrinsic natural propensity to go for more (density) in sets, namely, babies, like other non-human animals, prefer sets that are more compact, in which items are closer together.
Another interpretation is that 10-month-old infants prefer the more dense set because they equated the greater inter-stimulus distance in the less dense display with the impossibility of getting all the cookies at once with one hand (“all in one go” hypothesis), which could easily be done in the more dense set. Although we see this alternative too as part of the intrinsic preference to “go for more dense,” it could also be considered a strategy. To test the latter hypothesis, we decided to run another group of 10-month-old infants in Experiment 2.
The aim of Experiment 2 was to investigate whether the result of Experiment 1 was due to (1) an intrinsic preference to “go for more dense,” or (2) a strategy to select the set with items closer together (select all in one go hypothesis).
In order to address this possibility, we reduced the size of the stimuli while keeping inter-stimulus distance the same. By reducing the size of the stimuli we enable both sets to be kept within grabbing distance for a 10-month-old. That is, a 10-month-old hand would be able to grab all four stimuli at once whether the intra-stimulus distance was small or large. The inter-stimulus distance ratio (1:4) was kept the same.
The method was the same as in Experiment 1, except as follows.
Eighteen (8 ♀) full-term infants participated in the study (Mean age = 10 months, 16 days; range 10;03–10;28). Four additional infants were excluded from the sample due to fussiness/no reach. Participants were recruited in the Essex/Suffolk/Cambridgeshire area through advertisements and were taken to the Lab by their parent or caregiver.
The food stimuli used were
Side of density ratio (1-L, 1-R) was counterbalanced across participants. The infant’s choice recorded as one level of density or the other (1 or 4). A testing session was considered over when the infants had made a choice. If the infant did not reach for or point to either tray, or if the infants choice was unclear (e.g., if the infant simultaneously reached for or pointed to both trays), this was coded as “no choice” and the participant was excluded.
Data from 16 infants who reached for either the more dense (1) or less dense (4) set were coded as choice. Thirteen infants selected the more dense set and three infant selected the less dense set. A binomial test revealed a significant difference,
The findings in Experiment 2 supports the proposal that infants selected the more dense set because there is some mechanism at play that makes them prefer higher density than lower density. There is no evidence for the strategy explanation, whereby infants in Experiment 1 selected the more dense set because it was the set that enabled them to grab all four items at once as opposed to the less dense set, in which the four cookies were too far apart to grab all at once. Together, the results from Experiments 1 and 2 suggest that density assessment of sets of equal numerosity may be determined by a preference for things that are closer together.
The present experiments were developed to start to address questions involving a variable that is generally conflated with numerical assessment and controlled for – set density. We contrasted two hypotheses in the fields of human perception and development (theories of numerosity perception in adults and Piaget’s number conservation ideas) and animal behavioral ecology (optimal foraging ideas). Evidence with children (Piaget’s conservation tasks) and adults (literature on numerosity perception) suggests that we tend to equate more as “more length” or “more space” in between items, while Optimal Foraging Theory predicts that patches of food containing items more packed together yield a better rate of return: animals seem to engage in evaluative computations which enable them to maximize profit and minimize cost. Although tentative and speculative at this stage, we pitted these two frameworks against each other because they predict opposite behaviors – children may prefer more as in
We set out to test these alternatives with two experiments addressing the question of inter-stimulus assessment in visual displays. Our results in Experiment 1 showed that, at 10 months, infants selected the more dense set by touching the chosen set. That is, infants reached and made a choice for the set in which elements were displayed closer together at the ratio of 1:4. Infants at 10 months make use of the variable “density” to make a numerical choice. This evidence supports preliminary evidence to show that infants have the ability to assess and compare quantities of a food substance (Van Marle and Wynn,
The alternative interpretation for the results of Experiment 1, that 10-month-old infants preferred the more dense set because they equated the smaller inter-stimulus distance in the more dense display with the possibility of getting all the cookies at once with the hand was addressed in Experiment 2. Two sets holding a 1:4 ratio between them, both with close enough items to be grabbed with one hand at once, were used in Experiment 2. Ten-month-old infants showed a preference for the more dense set, even though both sets could be grabbed with one hand at once. The preference observed in Experiment 1, therefore, cannot be attributed to a preference based on a “grab all in one go” strategy. Altogether, our results provide novel evidence that infants make decisions on numerical choices taking into account inter-stimulus distance (set density). The fact that the infants were not random in their choices means that this variable plays a role in numerical assessment.
A second conclusion stemming from these experiments is that there is a predisposition in young infants to select sets that contain items closer together. The data suggest that, at 10 months, infants are equipped with a capacity to discriminate two sets of equal number. What is even more extraordinary is that not only do infants detect the differences in density, but also make a particular choice, and reach for it. It is possible that these choices may apply uniquely to “foraging” situations, and indeed, the domain of food (Shutts et al.,
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.