The pupillometry of the possible: an investigation of infants' representation of alternative possibilities

Abstract

Contrasting possibilities has a fundamental adaptive value for prediction and learning. Developmental research, however, has yielded controversial findings. Some data suggest that preschoolers might have trouble in planning actions that take into account mutually exclusive possibilities, while other studies revealed an early understanding of alternative future outcomes based on infants' looking behaviour. To better understand the origin of such abilities, here we use pupil dilation as a potential indicator of infants' representation of possibilities. Ten- and 14-month-olds were engaged in an object-identification task by watching video animations where three different objects with identical top parts moved behind two screens. Importantly, a target object emerged from one of the screens but remained in partial occlusion, revealing only its top part, which was compatible with a varying number of possible identities. Just as adults' pupil diameter grows monotonically with the amount of information held in memory, we expected that infants' pupil size would increase with the number of alternatives sustained in memory as candidate identities for the partially occluded object. We found that pupil diameter increased with the object's potential identities in 14- but not in 10-month-olds. We discuss the implications of these results for the foundation of humans' capacities to represent alternatives.

This article is part of the theme issue ‘Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny’.

1. Introduction

A considerable part of human mental life centres around thinking about the ways things might be or what may happen next. To face an uncertain present and an unknown future, we capitalize on an intuitive understanding of the relevant ‘alternatives’, a batch of conceivable states or events that cannot jointly happen, but one of which, we think, must or will occur. Indeed, we learn by contrasting mutually exclusive hypotheses, form predictions about mutually exclusive event outcomes, and make decisions between mutually exclusive actions. Furthermore, ordinary conversations about what ‘may happen’, ‘should be done’ or ‘might be the case’ plausibly require handling multiple, incompatible possibilities as well [1,2]. And, less explicitly, other cognitive capacities central to humans—such as causal and moral judgements—may also depend on computations over alternative possibilities [3]. In summary, we often achieve our goals by facing ‘forking paths’ of alternatives in everyday life and scientific settings.

The cognitive capacity to represent and contrast possibilities¹ is the compass we have to navigate these forking paths. Yet, the developmental origins of this precious resource are uncertain: developmental cognitive science has begun to investigate the foundations of modal cognition with apparently conflicting findings.

On the one hand, infants have been found to be sensitive to the probability of events, which suggests early and rich cognitive resources to handle uncertainty. Whether presented with repeated sequential sampling (resulting in multi-object outcomes; [4–6]) or single events (that lead to single-object outcomes; [7–12]), infants demonstrate early emerging probabilistic intuitions. Such intuitions are supported by flexible inferential mechanisms that can integrate relevant information about the agents who perform the sampling (i.e. intentionality; [5,13]) and about the objects that are sampled (i.e. different physical constraints; [6–10,14]) into their probabilistic expectations [15].

Notably, at least in some cases, these probabilistic intuitions may reflect an early grasp of the possible continuations of simple stochastic processes. For instance, when presented with events randomly generated by a physical lottery device (i.e. four balls—of which three are yellow and one is blue—bouncing inside an urn until one object exits), 12-month-olds look longer at a less probable result (the blue ball exiting) than at a more probable one (a yellow ball exiting; [8,9]). Infants seem to expect the more probable outcome, which may be driven by a computation contrasting predictions of the distinct possible outcomes of the lottery [9,16]. Based on such computations, the yellow ball outcome will become the expected result because it can be realized in more possible outcome events (i.e. three yellow in contrast to one blue). Crucially, this account presupposes that infants predict and keep track of multiple possible lottery results.

On the other hand, more recent [17] and earlier findings [18] suggest that preschoolers have difficulties planning actions that prepare for alternative events. For example, an elegant study by Redshaw and Suddendorf recorded a striking failure in preschoolers' and apes' decision-making. In this task, preschoolers were presented with a forked tube (inverted Y-shaped) with one entrance but two exits. The experimenter dropped a ball in the forked tube, and participants had to catch it by preparing for the two possible outcomes of this event (i.e. the ball falling out from the left or the right branch). Strikingly, only four-year-olds prepared the optimal action reliably and spontaneously (simultaneously reaching for both exits with their hands). Instead, younger children and apes failed to do so, suggesting that they could not optimally prepare for two mutually exclusive outcomes. Interestingly, turning the task into a social game did not improve performance [19], and the challenge children may face seems not to be simply one of manual coordination [20].

To summarize, while infants' probabilistic intuitions point to an early emerging representation of multiple alternative outcomes, the improvement children seem to undergo across the preschool-age years in the forked tube task indicates a protracted development of decision-making processes that take into account mutually exclusive possibilities.

A possible response to these conflicting findings is to question whether infants and young children can actually represent alternative possibilities. Three-year-olds' failure in the forked tube task can be well explained if they fall short of the very capacity of representing two mutually exclusive possibilities at once [21]. According to this proposal, children younger than four years of age can simulate only one possible motion trajectory at once. Therefore, they may plan simple actions that respond to the outcome of that single simulation (e.g. a child might uniquely simulate that the object falls through one exit they randomly select, for instance, the right exit and thus reach only to that side). Likewise, a related account was offered for the findings indicating probabilistic intuitions in infancy [8,9]: infants might generate expectations by simulating only one outcome at a time, focusing on a single object that was randomly selected [21]. On this view, the onset of success in the forked tube task might reflect the emergence of the basic capacity to track the mutually exclusive outcomes of two simulations.

Alternatively, one could argue that three-year-olds' failure may reflect their limitations in decision-making when facing uncertain events. Especially, selecting the best from the potential actions one can perform in the forked tube task (e.g. reaching for the left exit, reaching for the right exit, or reaching for both exits) may require more than just contrasting the two physically possible outcomes defined by the tube's branching structure. Notably, for an optimal goal-directed decision, one has to (i) form a cognitive model of the task by considering the six action-outcome combinations (3 actions × 2 outcomes), (ii) evaluate the expected utility of each action and, finally, (iii) select the appropriate action among the three possible ones. However, such a multistep evaluation and selection process might not be that easy for young children and may mask their ability to represent alternatives. Indeed, the ability to make efficient decisions based on cognitive models of multiple mutually exclusive contingencies seems to depend on cognitive resources that undergo substantial development during and beyond childhood [22,23].

Evidence that may help re-join the apparently conflicting findings and advance our understanding concerning the ontogeny of the representation of possibilities comes from recent studies documenting early emerging logical capacities, like preverbal infants' disjunctive inference [24,25]. In disjunctive inference, two (or more) alternatives are represented in a disjunctive relation such that at least one of them must be correct. Thus, when all options but one are discounted, the remaining one is inferred (e.g. A or B; A is ruled out; therefore, B). Crucially, in common applications of disjunctive reasoning, it is often the case that the disjuncts contrasted in the inference cannot be both true. For example, this is the case when we wonder at which location someone has lost an object (e.g. ‘at the day-care or in the office’), who may be the main culprit of a crime (e.g. ‘the nanny or the butler’), or what could be the referent of an unfamiliar noun. Hence, disjuncts are typically, but not necessarily, alternative possibilities.

Recent findings suggest that infants as young as twelve months spontaneously use a preverbal form of disjunctive inference. In a task that requires neither language nor the production of intentional actions (but is based on subjects' dynamic looking behaviour and pupil dilation), 12-month-old infants were able to disambiguate the identity of a partially occluded object (i.e. an object that could be an umbrella or a puppet) when evidence inconsistent with one alternative was provided (e.g. ‘it must be the umbrella or the puppet’, ‘it is not the umbrella’; ‘therefore it must be the puppet’ [24]). This finding was then confirmed and extended by further data suggesting that infants can readily rely on the disjunctive inference to learn about the social world, and successfully encode the preference of an agent reaching for a goal-object that was ambiguous, and its identity had to be inferred logically [25]. Thus, evidence accumulated by these ‘ambiguous-object’ studies suggests that preverbal disjunctive inference is in place in young infants and can function as a powerful mechanism for knowledge acquisition by making available logical conclusions when more direct evidence is missing.

Hence, well before mastering the logical word ‘or’ (see [26–28] for studies on early production and comprehension of verbal disjunction), infants may spontaneously represent two potential identities of a hidden object in a disjunctive relation (i.e. ‘it must be the umbrella or the puppet’). Importantly, infants have an early understanding that two objects cannot occupy the same region of space at once [29]. Thus, the ambiguous object task may recruit early emerging computations that contrast two mutually exclusive possibilities (i.e. the expectation that the object inside the cup is the umbrella and the one that it is the puppet cannot both be correct).

By contrast to the disjunctive interpretation of the ambiguous-object task, Leahy & Carey [21] have proposed that infants could establish the object's correct identity by arbitrarily mapping one of the two objects' identities onto the hidden object, and revising this first mapping if conflicting evidence is detected. Thus, according to this account, infants never represent a disjunction of two alternatives, but instead waive the ambiguity of the object's identity by randomly picking one possibility and treating it as a fact² (e.g. randomly assuming that the ambiguous object is the puppet). Crucially, Leahy and Carey suggest that guessing serially is sufficient to generate the apparently logical responses recorded in the ambiguous-object task.

One may object to this guessing account that it is unlikely that infants would readily arrive at the correct solution in the ambiguous-object task (therefore, a puppet) by revising their initial guesses whenever they turn out to be wrong (it is not the umbrella), without circumscribing in a disjunctive relation the relevant subset of alternatives for guessing (i.e. ‘the object must be the umbrella or the puppet’—viz. there are no other alternatives). Furthermore, key findings in the targeted studies present challenges for the guessing proposal. First, Cesana-Arlotti et al. [24] found that infants looked at the object hidden inside the cup the first time they saw which object was outside the cup—the point in time infants could draw the disjunctive inferences (i.e. the deduction phase). Crucially, these looks were predictive of the later surprise at the outcomes violating the result of the inference (outcome phase). This relation would be unexpected if infants were guessing.³ Second, the guessing proposal is unlikely to be correct, given recent evidence that infants' can efficiently use the disjunctive inferences to learn [25]. In this study, infants had to learn the preference of an agent that was reaching toward an ambiguous object whose identity had to be inferred by disjunctive inference. Crucially infants successfully encoded the agent's preference after a few demonstrations, which would be unlikely if they were guessing randomly (see [25] for the details of this analysis). Third, it was found that infants' ability to form expectations about probabilistic physical events is impaired in dynamic situations involving a large number of alternative outcomes [10], which is unexpected if each infant generates just a single simulation at the time.

A further crucial question is when infants think about alternative possibilities in situations like the ambiguous-object task. According to one scenario, this may take place early on: when infants see the partially occluded object, they might readily invoke the alternatives responsible for its ambiguity. Conversely, infants might not spontaneously represent the relevant disjunction of possibilities as soon as the partially occluded object appears, but simply represent that there is an object that is not fully visible. In this latter case, the disjunctive representation of the alternatives may be prompted later, when disambiguating information becomes available, allowing infants to work through the steps of the disjunctive inference.

To test the above-mentioned two competing proposals—the guessing account and the disjunction of alternatives—as well as to clarify at which stage of processing infants represent alternatives, if they do it, in the present research, we directly targeted infants' capacity to contrast alternatives. In particular, in an object disambiguation task, we measured the pupillometric indications of the cognitive load induced by the view of an ambiguous object, whose identity was compatible with varying numbers of possibilities.

Since the seminal works revealing the relation between cognitive effort and changes in pupil diameter—as shown by the greater pupil dilation elicited by multiplication tasks [30] or by working memory experiments [31]—there is ample evidence that the size of the pupil is not only influenced by exogenous factors (i.e. light intensity). Since pupil dilation is under the influence of the locus-coeruleus, a nucleus in the brain stem with rich cortical connections that plays a regulatory role in task engagement [32], it can provide a reliable diagnostic measure of cognitive effort [33–35].

Successful exploration of pupil data is responsible for the increasing use of this technique in infant research [36], augmenting the existing repertoire of infant-oriented research methods [37]. Differential pupil dilation can reliably inform theorizing about infants' processing of physically impossible [38–40] and biomechanically implausible events [41], or inefficient actions [42]. Such methods also provide sensitive measures for emotion perception [43] and prosocial motivation [44] at an early age.

Most importantly, task-related pupillary responses are known to correlate with cognitive load across different ages: both in younger and older adults [45] and children [46]. Like every resource-dependent system with capacity limitations, the success of encoding, actively maintaining, and manipulating information is highly dependent on the invested cognitive effort, and infants are not an exception to this phenomenon. In a study targeting infants' visual working memory, Cheng and collaborators [47] demonstrated that cognitive effort (measured by pupil dilation) is a good predictor of 13-month-olds' memory performance.

Building on such findings, we designed a new paradigm to measure infants’ pupil dilation as a potential indicator of the representation of multiple possibilities. In our task (figure 1), infants were presented with three objects that shared a visual feature. After their presentation, the objects were hidden by two lateral screens: two objects behind one screen while the third was behind the other. Finally, one out of the three objects (the target) emerged but remained in partial occlusion, and only the visual features shared by the three objects were revealed. Thus, the visible part was indicative only of the presence of the partially occluded object while its identity was compatible with a varying number of possibilities. In the 1-possibility condition, the object emerged from the screen with one object, while in the 2-possibilities condition, from the one with two objects. We tested 14- (experiment 1) and 10-month-olds (experiment 2), one age at which we know infants pass the ambiguous-object task, and a younger age never tested with it, as contrasting possibilities may be a prerequisite of the disjunctive inference. If infants remember all the objects hidden in the scene, they may identify the correct possible identities of the ambiguous object based on its side of origin. Crucially, we predict that infants will represent a single possible identity when the object emerges from the one-object side (e.g. ‘it must be the toy elephant’), while they will represent two mutually exclusive possible identities when the object emerges from the side with two objects (e.g. ‘it must be either the puppet or the ball’). To test this prediction, we measured infants' pupil diameter change in response to the appearance of the partially occluded object. If infants correctly represent possible identities, their pupils will dilate more when the object is compatible with two possibilities, due to the higher cognitive load of such a more complex representation. The differential pupil dilation should be absent if infants' identification attempts are guided by guessing, or they do not spontaneously form expectations about the identity of the partially hidden object.

Figure 1.

The structure of the test events in experiments 1 and 2. After infants observed the three fully visible objects (i), the visual access to these objects was blocked by two lateral screens (ii). Then an object emerged and moved behind the horizontal screen while only its identical top part was visible. In the 2-possibilities condition, this object emerged from the side with two objects (iii-1), while in the 1-possibility condition from the side with one object (iii-2). Based on the accessible visual features, these objects were indistinguishable. After some movement (2 s), this partially occluded object settled at the centre of the horizontal screen (iv-1, iv-2) and remained static (3.2 s) till the end of the partial occlusion period. Finally, the object emerged in full view (v-1, v-2), revealing its identity (4.5 s), then the trial ended (marked by arrowhead on the timeline).

2. Material and methods

(a) . Participants

A total of 48 full-term healthy infants were included in the analysis: experiment 1 (N = 24; M_age = 14 m 03 d, range 13 m 13 d–14 m 16 d; 9 girls), experiment 2 (N = 24; M_age = 10 m 21 d, range 10 m 9 d–11 m 01 d; 8 girls). We have complied with all relevant ethical regulations; the United Ethical Review Committee for Research in Psychology (EPKEB) approved the study in Hungary. In experiment 1, 14 additional infants were tested but excluded for not providing enough valid trials, and 12 in experiment 2 (see pupil data analysis). Four infants were excluded for crying during the test trials in experiment 1, and five in experiment 2.

(b) . Materials

Each infant watched three familiarization movies and up to 12 test movies. The movies were presented on a 24-inch Tobii T60XL eye-tracker display (1920 × 1200 pixel resolution) with PsyScope X controlling the experiment, running on an Apple Mac Mini 2,8 GHz Intel Core i5.

In the familiarization trials, identical for both experiments, participants were acquainted with movies where three objects were initially lined horizontally, next to each other, and partially covered by a screen. The three objects (a puppet, a toy elephant and a ball) had identical upperparts. The screen was rectangular and grey, horizontally placed at the centre of the display so that only the identical upperparts of the objects were visible. After about 2.3 s, each object was sequentially revealed, from left to right, rising from behind the screen (see electronic supplementary material, Movie S1). After emerging from behind the screen, each object made its characteristic movement (the puppet smiled, the elephant flapped its ears, the ball bounced) accompanied by a unique sound. Across the three familiarization movies, the initial position of the objects was counterbalanced (i.e. each object appeared at every location).

In the test trials of experiments 1 and 2 (figure 1), infants were shown movies presenting an object identification challenge: an object appeared that was only semi-visible and whose identity was compatible with a varying number of objects seen before (e.g. ‘it must be the puppet or the ball’ versus ‘the object must be the toy elephant’; see electronic supplementary material, Movie S2 and S3). In each movie, two of the objects seen during familiarization were lined up vertically on one side of a central grey screen, one below and one above, and the single remaining object was placed on the opposite side, either above or below the central grey screen, depending on the trial (see the details of the movie counterbalancing in electronic supplementary material, Note S1). In a brief introduction, the objects displayed their characteristic movements accompanied by a unique sound, sequentially in clockwise order, starting from the upper-left position, or the upper-right when the first position was empty.

Afterward, two vertical grey screens simultaneously entered the scene from the sides (0.4 s) and formed with the central screen an H-shape configuration, entirely covering the objects. Then a phase of full occlusion started: all three objects were completely hidden (2.1 s). Pupil diameter recorded in the last 0.8 s of this static scene served as the baseline (i.e. used for baseline correction for our analysis). We allow the pupil to stabilize for 1.3 s before recording its baseline diameter to measure pupil adaptation to the full-occlusion of the three objects.

Next, in the partial occlusion phase, one object slid out from one of the two vertical screens, while remaining partially covered by the central horizontal screen, so that the only fragment visible of the object was the top part, identical for the three objects seen before. This visible part slid toward the centre of the horizontal screen (2 s), where it stopped (3.2 s). In the 1-possibility condition, the object emerged from the screen hiding one item (e.g. the toy elephant), while in the 2-possibilities condition from the screen hiding two items (e.g. the puppet and the ball). Thus, while in the 1-possibility condition, there is only one possible identity for the object (e.g. ‘it must be the toy elephant’), in the 2-possibilities condition, there are two possible identities for it (e.g. ‘it must be the puppet or the ball’). This partial occlusion (5.2 s corresponding to the entire time the object was only partially visible) served as the main window of interest for our data analysis, during which we measured the pupil dilation in response to the detection of the partially occluded object.

Finally, the object emerged fully from behind the screen, revealing its identity and remaining in full sight for 4.5 s, until the trial ended. To draw participants' attention to the events of the movies, these were accompanied by sounds both during familiarization and test. (For detailed movie timing and counterbalancing, see electronic supplementary material, Note S1.)

(c) . Procedure

The experiments took place in a sound-proof room with dimmed lights and followed the same procedure. Participants were seated on their caregiver's lap, at about 650 mm from the display. The caregivers wore opaque glasses that prevented them from seeing the stimuli. They were asked to hold the child seated on their laps and not interact with them. The experimenter sat behind a curtain and monitored infants' behaviour from a separate display via a video camera. A Tobii T60XL eye-tracker recorded participants' looking behaviour and pupil diameter. Before the experiment, participants underwent a 5-point calibration procedure, programmed in PsyScope X. The entire session was video-recorded.

3. Results

(a) . Average pupil change

To calculate the pupil diameter change caused by the appearance of the partially occluded object, for each trial, we computed the average pupil diameter during the baseline phase and subtracted it from each pupil diameter sample collected during the partial occlusion phase. Preliminary analyses verified that the average pupil diameter in the baseline phase was not different between the two test conditions in either experiment (see electronic supplementary material, Note S2 for details about the pupil data preparation and preliminary analyses).

To probe our prediction, we started by comparing the average pupil change across the entire partial occlusion phase in the two test conditions. We averaged the pupil change scores across the test phase for each trial. Preliminary analyses detected neither an effect of the side of appearance of the partially occluded object nor of which two objects were paired behind the same screen for each participant. Thus, we computed an average for each test condition (2-possibilities versus 1-possibility) and ran t-tests to compare the pupil change in the two conditions. The analysis detected an effect of condition on pupil change in experiment 1: 14-month-olds' pupil dilated more in the 2-possibilities condition than in the 1-possibility condition (M_{1-possibility} = 0.102, s.d. = 0.096; M_{2-possibilities} = 0.130, s.d. = 0.090; t₂₃ = 2.799, p = 0.010, two-tailed, d = 0.59; figure 2). By contrast, no significant effect was detected in experiment 2: 10-month-olds' pupil change was not significantly different in the two conditions (M_{1-possibility} = 0.138, s.d. = 0.077; M_{2-possibilities} = 0.152, s.d. = 0.089; t₂₃ = 0.925, p = 0.36, two-tailed; figure 2; more analyses in electronic supplementary material, Note S2).

Figure 2.

Infants' pupil response in experiments 1 and 2. The left panels depict infants' pupil change (baseline corrected) across time during the partial occlusion phase in response to the partially occluded object. The interval before 0 s corresponds to the baseline period preceding the object's partial appearance. The horizontal yellow line represents the temporal window of the effect identified by the permutation test. (a) Fourteen-month-olds' pupil change was higher in the 2-possibilities condition (in red) than in the 1-possibility condition (in blue) between 800 and 2500 ms from the object appearance. (b) No temporal region with an effect was detected for the 10-month-old group. On the right, the comparison of infants' pupil change between the two conditions is presented in difference scores: average pupil change values across the partial occlusion test phase in the 2-possibilities condition minus the values in the 1-possibility condition. Grey dots represent the mean values of individual participants, diamonds mark the mean values of the groups, and error bars represent standard errors of the mean. In experiment 1 (c), 20 out of 24 14-month-olds showed higher pupil dilation in the 2-possibilities condition (binomial test; p = 0.001), a pattern present in only 13 out of the 24 10-month-olds (binomial ns.) in experiment 2 (d).

(b) . Permutation analysis

Next, we investigated the temporal relation between the appearance of the partially occluded object and infants' pupil dilation in the two conditions. We ran a cluster mass permutation test [48–50], to localize the temporal window of the pupil response to the appearance of the object with two potential identities while controlling for multiple comparisons. The permutation analysis, based on two-tailed Wilcoxon sign-rank tests and 10 000 shuffles (see electronic supplementary material, Note S3 for the details of this analysis), revealed in experiment 1 an effect between 0.8 and 2.5 s of the test phase (p = 0.042, figure 2). The onset of this effect closely follows the appearance of the object part and lasts for almost 2 s. By contrast, the same analysis detected no effect in experiment 2.

(c) . Looking-proportion analysis

To identify the role of the objects' representation in the pupil dilation pattern, next, we analysed its potential signature, namely, higher attention toward the screen where two objects were hidden, in the different phases of the test trial.

First, we checked whether infants looked more toward the 2-object screen during the baseline. For this analysis, we defined two 710 × 1045 pixel areas of interest (AOI), surrounding each lateral screen. For each trial, we computed the proportion of looking at the 2-objects screen as the looking time at the AOI of the 2-objects screen divided by the total looking time at both 1-object and 2-objects screen AOIs. Looking proportions to the 2-objects screen during the baseline were not significantly different in the two conditions, neither in experiment 1 (M_{1-possibility} = 59%; M_{2-possibilities} = 52%; t₂₃ = 0.99, p = 0.33), nor in experiment 2 (M_{1-possibility} = 56%; M_{2-possibilities} = 49%; t₂₃ = 1.36, p = 0.18). Furthermore, subjects' looking proportions toward the 2-objects screen during the baseline phase were not significantly different from chance in either experiment (both one-sample t-tests: p > 0.1), suggesting that having more occluded objects at one side does not seem to bias infants' attention at this phase.

Second, we analysed the partial occlusion phase. To compare infants' visual attention to the location where two objects were hidden versus where one object was hidden, we restrained our analysis to a time window that started after the ambiguous object had stopped at the centre of the scene (to exclude possible biases induced by directional movement) and examined the distribution on their fixations. This window started 2 s after the beginning of the partial occlusion phase till the end of this phase. Two participants were excluded from this looking proportion analysis in each experiment since they lacked looking proportion data in one of the experimental conditions (i.e. they did not look at any of the lateral screens). In experiment 1, 14-month-olds' proportion of looking at the 2-objects screen was higher in the 2-possibilities condition than in the 1-possibility condition (M_{1-possibility} = 46%; M_{2-possibilities} = 61%; t₂₁ = 2.16; p = 0.041, d = 0.68, two-tailed). By contrast, in experiment 2, the analysis detected no difference (M_{1-possibility} = 65%; M_{2-possibilities} = 55%; t₂₁ = 1.25; p = 0.22, two-tailed; see electronic supplementary material, figure S1). Averaged across conditions, 10-month-olds’ proportion of looks at the screen hiding two objects was higher than chance (M = 60%; t₂₁ = 2.8; p = 0.01, two-tailed).

Next, we checked whether infants' larger pupil change in the 2-possibilities condition was determined by their representation of the two objects at the screen from which the partially hidden item was sampled, rather than being a consequence of the representation of the ambiguous object's possible identities. If the object representations invoked by the 2-possibilities condition are the primary cause of both the higher pupil change and more attention to the 2-objects screen, then these two indexes should be positively correlated. To probe this possibility, we calculated the pupil dilation difference between the two experimental conditions and the difference in looking at the 2-objects screen. Crucially, we found no significant correlation between these indexes (experiment 1: Pearson's r₂₀ = 0.23, p = 0.299, two-tailed; experiment 2: Pearson's r₂₀ = −0.05, p = 0.796, two-tailed).

To corroborate the absence of a relation between infants' attention at the 2-objects screen and their pupil change, we fitted mixed-effects linear regression models to infants' pupil change (using the lm4 package for R, [51]). Each model had a random intercept for participants and an effect for conditions (2-possibilities versus 1-possibility). The ‘null-hypothesis’ model had no effect for the proportion of looking at the 2-objects screen, while the ‘alternative-hypothesis’ model had such an effect. To compare the two models, we used the Bayes Information Criteria of the models to approximate their Bayes factor [52,53], which is the ratio of the likelihoods of the observed data under the two different models (see electronic supplementary material, Note S4 for details about this analysis).

This analysis of experiment 1 revealed that the data are four times more likely (BF₀₁ = 4.27) under the ‘null-hypothesis’ than the ‘alternative-hypothesis’: that is, in the 14-month-old group, there is evidence of no linear relation between looking more at the 2-objects screen and higher pupil change. The same analysis of experiment 2 revealed that the data are five times more likely (BF₀₁ = 5.30) under the ‘null-hypothesis’ than the ‘alternative-hypothesis’: also in 10-month-olds, there is evidence of no linear relation between the proportion of looking at the 2-objects screen and pupil change.

4. Discussion

In our study, 14- and 10-month-old infants saw a partially occluded object compatible with various possible identities. We predicted that if infants represent the possibilities compatible with the object's appearance, their pupils may dilate more in the 2-possibilities condition than in the 1-possibility one due to the higher cognitive load of a more complex representation.

Our prediction was confirmed for the 14-month-old infants. Infants were exposed to visually identical events, also matched in terms of the hidden objects to be remembered. However, their pupils increased more at the appearance of the partially occluded object when there were two possible identities. A temporal analysis confirmed that 14-month-olds' pupillary response was locked to the appearance of the partially occluded object, with an effect window between 0.8 and 2.5 s after the object's appearance. Crucially, such a differential pupillary response would be unexpected if infants simulated only one identity in both conditions (e.g. ‘the hidden object must be the puppet face’) or represented an object without spontaneously tracking its possible identities (i.e. ‘there is an object that is partially occluded’). Thus, our findings support the proposal that infants contrasted the two mutually exclusive identities of the ambiguous object.

Across trials, the side of appearance—whether the partially occluded object will emerge from the left or the right screen—was counterbalanced. Not knowing the side of their appearance in advance required infants to remember all objects on the scene. When the partially occluded object moved to the centre, 14-month-olds spent more time visually exploring the screen that initially hid two objects in the 2-possibilities condition than in the 1-possibility condition. This pattern of visual exploration was absent in 10-month-olds. However, the looking preference of the 14-month-olds was not related to their pupil dilation, suggesting that these indexes do not express the effects of a common cause. This is not surprising, as the locus of ambiguity is the partially occluded object, not the lateral screens. Instead, orientations toward the side with two objects may signal the representations of those objects and not the one that is partially occluded.

Importantly, however, when infants represent possibilities, they should represent valid possibilities, alternatives that are correctly derived from the objects that were involved in the sampling. For this, object representations have to be accessed. While reliable object representations are the preconditions for infants' success, identifying the contribution of the different factors (memory for objects, representation of alternatives) to infants’ pupil pattern may reveal important characteristics of the cognitive processes involved in the ambiguous object experiments. In the present study, we held constant the total number of occluded objects—i.e. three—while we varied the number of possibilities—i.e. two versus one. Future research with a dedicated experimental design, different from the one presented here, is required to further dissociate these factors and their contribution to pupil dilation.

Unlike in older infants, we found no difference in 10-month-olds' pupil dilation between the 1- and 2-possibilities conditions. This lack of differentiation might reflect a failure to represent the alternative identities of the ambiguous object. If so, why might 10-month-olds have failed? One should note that in the pupillometric task used here, infants may rely on the categorical attributes of the objects to represent the alternative identities (e.g. ‘the ball or the elephant’). Then, it is possible that some of the items used in the present task do not embody a category contrast typically available at 10 months. Consistently with this hypothesis, an exploratory analysis indicated that 10-month-olds' pupil diameter increases above the 1-possibility condition level when the ambiguous object's alternative identities could be construed as ‘the human or the non-human object’ ([54–56]; see electronic supplementary material, Note S2).⁴ In interpreting this finding, one must be cautious and take into account the exploratory character of this analysis. Nevertheless, future research can further investigate this pattern, as it suggests that tracking sets of occluded objects without conceptual representations (e.g. [57]) might be insufficient to represent one object's alternative identities at this age.

In summary, the higher cognitive load induced by the partially occluded object appearance in the 2-possibilities condition shows that 14-month-old infants are not simply generating a single simulation and assuming its result to be actual, regardless of the number of alternatives compatible with the scene. Instead, this result is predicted by the proposal that infants contrast the two alternative identities of the ambiguous object. Previous studies found that infants can infer the partially occluded object's true identity based on evidence inconsistent with one of the competing possible identities [24,25]. Thus, together with previous findings, the present results point to a representation of the object's alternative identities connected in a disjunctive relation (e.g. ‘it must be the puppet or the ball’).

Alternatively, infants may instead guess a single possibility but also track its epistemic status (i.e. its uncertainty), either with an operator of possibility (e.g. ‘maybe the ball’) or with a finer-grained representation of uncertainty (i.e. the subjective probability that the guess is correct). According to this ‘modal guessing’ account, higher pupil dilation to the partially occluded object in the 2-possibilities condition than in the 1-possibility condition would reflect the representations of uncertainty/certainty (i.e. ‘maybe the ball’ versus ‘certainly the ball’). Such capacity to mark the modal (i.e. epistemic) status of a simulation may reflect a preverbal form of modal representation of possibility [21].

Crucially, there are reasons to favour the account in terms of a disjunction of multiple alternatives over a single simulation marked by a modal representation. First, while at one point in time, one can represent ‘maybe the ball’ without simultaneously representing other alternatives, to assign less than certainty to such a hypothesis, one must have, at a former step, contrasted it with the alternative that the object might be something else. Thus, the computation of uncertainty presupposes the representation of at least two alternatives, even if construed in abstract terms such as ‘the ball or something else that is not the ball’. Second, the modal guessing account seems to suffer from the same explanatory challenges as the basic guessing account. It is unclear how it can account for some of the existing results (e.g. the predictive power of infants' oculomotor markers of inference drawing [24], the efficiency of infants' learning based on the disjunctive inference [25]).

Our disjunctive account is consistent with multiple proposals for the format of the representations used by infants to track extensionally distinct alternatives framed in a disjunctive relation. These are few, not exhaustive options. A disjunction of alternatives might be represented via a mental operator of disjunction, linked to domain-general deductive rules, analogous to one of formal logic [58,59]. Alternatively, a disjunction of alternatives might be encoded as a batch of multiple models, each corresponding to a possibility incompatible with the others. These mental models might be generated in working memory as a set of two or more alternative possibilities, sustained and pruned as new evidence is acquired [60,61]. Or else, there may be domain-specific solutions, where the alternative identities of an object's identity may be stored via mutually exclusive mental files linked to the same object representation (cf. [62,63]).

The current experiments introduce a new pupillometric paradigm to study the preverbal representation of alternatives, in line with recent studies that recruited pupillometry to investigate the precursors of logical operations in infancy (e.g. alternative elimination [24]; the negation of the abstract relation ‘same’ [64]). This approach opens new opportunities to test competing proposals about the representational format and computational mechanisms underlying infants' capacity to track possibilities. For example, future pupillometric research may ask whether preverbal disjunction of possibilities displays or not the signature limit of infants' working memory—i.e. no more than three discrete items can be maintained in parallel [65].

Finally, our findings invite new questions about young preschoolers' difficulties in making optimal decisions facing alternative outcomes (cf. [21]). If infants can track incompatible possibilities in basic scenarios, why do three-year-olds fail in other tasks, like the forked tube [17], that require the production of goal-directed actions? While future research is needed to address this question fully, we propose two tentative answers.

First, it is possible that the preverbal understanding of alternative possibilities hereby recorded has limited flexibility and a narrow range of application restricted to the representation of surrounding objects and occurring events under epistemic uncertainty [66]. In this case, the preverbal representation of alternatives may not be best suited to contrast mutually exclusive predictions about events that have yet to happen, like the future dropping of an object through a bifurcating tube.

Alternatively, young preschoolers may already understand the space of possible outcomes of the forked tube task. Still, their ability to plan actions and make decisions may not yet capitalize on such understanding. Consistent with this second interpretation, complex decision-making that can also integrate mutually exclusive contingencies may emerge gradually through a protracted development of executive functioning and other cognitive capacities [22,23]. Future investigations are needed to shed light on the developmental changes required to integrate the representation of alternative outcomes in weighting the expected utilities of alternative goal-directed choices.

We learn, predict, and decide by conceiving small arrays of possibilities that cannot jointly happen but one of which we assume must occur. The developmental foundations of our intuitive sense of the relevant alternatives are, however, unknown. Our pupillometric tests indicate that one milestone of such cognitive resources, the capacity to represent multiple mutually incompatible possibilities, is in place in humans at least from the second year of life. This finding is in line with the proposal that infants can spontaneously react to ambiguous events with the representation of a disjunction of alternatives that they can readily update in response to new evidence. This basic logical representation may be one building block of the developmental processes that, through learning, maturation and language acquisition, result in human-unique forms of reasoning and planning.

Ethics

We have complied with all relevant ethical regulations; the United Ethical Review Committee approved the study for Research in Psychology (EPKEB) in Hungary.

Data accessibility

The data and code that support the findings of this study are available in the OSF repository: https://osf.io/j3ybx [67].

The data are provided in electronic supplementary material [68].

Authors' contributions

N.C.: conceptualization, data curation, formal analysis, investigation, methodology, visualization, writing—original draft, writing—review and editing; B.V.: data curation, formal analysis, methodology, visualization, writing—original draft, writing—review and editing; E.T.: conceptualization, funding acquisition, investigation, methodology, project administration, resources, supervision, validation, visualization, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work was supported by a European Union's Horizon 2020 Research and Innovation Programme ERC Starting grant no. 639840 (PreLog), and by funds for a postdoctoral fellowship from the James S. McDonnell Foundation.