Hide and seek: The theory of mind of visual concealment and search

Abstract

Researchers have investigated visual search behavior for almost a century. During that time, few studies have examined the cognitive processes involved in hiding items rather than finding them. To investigate this, we developed a paradigm that allowed participants to indicate where they would hide (or find) an item that was to be found (or hidden) by a friend or a foe. We found that (i) for friends more than foes, participants selected the pop-out item in the display, and (ii) when the display was homogeneous, they selected nearby and corner items. These behaviors held for both hiding and finding, although hide and find behaviors were not identical. For pop-out displays, decision times were unusually long when hiding an item from a foe. These data converge on the conclusion that the principles of search and concealment are similar, but not the same. They also suggest that this paradigm will provide researchers a powerful method for investigating theory of mind in adults.

Many studies have examined search for visual targets when these targets are hidden in plain sight amidst distractor items (see Nakayama & Martini, 2011, for a review). This research has focused almost exclusively on how search performance is influenced by the visual features of either the target or the distractors (e.g., their saliency; Anderson, Heinke, & Humphreys, 2010) or on the relationship between the two (e.g., their visual similarity, Duncan & Humphreys, 1992). Little consideration has been given to the cognitive processes involved in hiding an item. Indeed, researchers have overlooked the idea that, in combination, the study of hiding and finding may create a methodology for investigating “theory of mind” in adults. For example, one can ask whether, and how, one’s hiding behavior is affected by who one believes will be doing the searching, and conversely, whether, and how, one’s search behavior is affected by who one believes has done the hiding.

The present study explores these lines by testing two questions: (1) Are hiding and finding linked, and if so, can the well-established principles of search be extended to the development of a theory of visual concealment? and (2) Can coupling hiding and finding provide a crucible for the manipulation and exploration of theory of mind? Although little previous work exists on these questions, a handful of relevant studies exist, which we briefly review below.

Of relevance to our first question, Smilek, Weinheimer, Kwan, Reynolds, and Kingstone (2009) investigated whether individuals’ intuitions about hiding items matched those influencing search difficulty. Observers arranged an assortment of items so that a target, placed in plain sight, was easy or hard to find amongst distractor items. New observers searched for the target amongst the constructed displays. Comparisons indicated that a target was found more quickly with “easy” than with “hard” search displays, as assigned by the initial observers. These data suggest that the factors considered relevant by individuals when hiding an item match those for finding an item—that is, that the processes underpinning hiding and finding are similar.

Nonetheless, differences between hiding and finding have been observed in more complex environments (Legge et al., 2012; Talbot, Legge, Bulitko, & Spetch, 2009). Talbot et al. asked participants to conceal or find objects in different opaque bins distributed in a room. The first three positions selected for both hide and seek conditions were assessed. Objects were hidden in more dispersed positions, farther away than the place of origin, than those selected when searching. The wider spread for hide locations was amplified when the hiding task was undertaken after the search task, indicating that people’s initial intuitions about hiding were modified after experience with search, as opposed to the two processes naturally tapping into the same strategies.

That hide and find strategies differ suggests that one’s belief in the intents and knowledge of others (i.e., their “theory of mind”) may be critical to hiding and finding behavior; that is, the way that one hides or searches for an object may be affected by who one believes is doing the hiding or doing the finding. Thus, we hypothesized that a hide–find paradigm may represent a new opportunity for researchers to manipulate and explore theory of mind.

The visual environment itself may also be a key factor. Legge et al. (2012) replicated Talbot et al. (2009), but they required individuals to hide and find items in unevenly shaped rooms with darkened areas and windows. The environment interacted differently with hide and find behaviors. When hiding, participants were less likely to place items near windows, though window position had no effect on where people searched. Conversely when searching, participants were less likely to look for items in dark areas, though room luminance had no effect on where items were hidden.

In the present study, we investigated whether, and how, changes in the visual environment and one’s knowledge about the hider or finder, affects behavior. We exchanged the uncontrolled and complex visual and behavioral environments used by Talbot and Legge for the controlled setting of classic search displays: pop-out displays (one item carries a unique feature) and homogeneous displays (all items are the same). This enabled the manipulation of the complexity of the visual world within which hiding and finding would occur, and eliminated the confounds that exist between behavior and vision when visual changes are introduce by locomotion in a real or virtual environment. Furthermore, and uniquely, we manipulated the participants’ conceptualizations of the hider or the finder, by instructing participants that the person who would be looking for their hidden object, or who had hidden the object that they were now expected to find, was either a “friend” or a “foe.” We anticipated that this would affect the perceived ease of the hide and find conditions (e.g., one might place a house key for a friend in a concealed location that will be easy to discover) and introduce a factor that directly manipulated theory of mind.

In summary, with this study we set out to examine whether search and concealment engage the same or different cognitive processes, and whether our hide–find paradigm can be used to study theory of mind. We explored these issues by manipulating the visual environment for hiding and finding and by varying who participants believed the hider or finder was. If changes in the visual environment and/or a participant’s conceptualization of the hider or finder (friend or foe) have the same impact on search and concealment behavior, then the evidence would be that the two behaviors reflect the same underlying processes (Smilek et al., 2009). A significant change in search and concealment behavior would suggest a very different conclusion. Similarly, if the attribution of the hider and finder as friend or foe were to have a regular and robust effect on hide and seek behavior (e.g., behavioral changes could not be explained entirely by changes in the visual environment), our hide–find paradigm could be an effective tool for investigating theory of mind.

Method

Participants

Thirty-two¹ UBC undergraduates (mean age 21.87 years) took part for either course credit or money. Four of these participants were male.

Design

We manipulated two within-subjects independent variables, partner type (friend or foe) and display type (pop-out or uniform), and one between-subjects variable, task type (hide or seek).

Apparatus

Stimuli were projected by a Dell M410HD projector attached to a Windows 7 PC running MATLAB (using Psychophysics Toolbox, version 3) onto a white tabletop. The projected image of a 1,024 × 768 pixel resolution was 800 × 600 mm. An Optitrack system recorded the time and location of participants’ movements via a marker on the index finger.

Stimuli

Participants viewed a projected image of a 4 × 4 grid of white boxes (each box 94 × 94 mm) on a gray background. Within these squares, blue or green horizontal or vertical bars were presented, each measuring 62.5 × 15.63 mm. A white start bar (78 × 800 mm) was presented below the grid (see Fig. 1).

Fig. 1

Example displays: (a) Pretrial indication as to the nature of the partner on the upcoming trial. (b) Uniform display. (c) Color pop-out display. (d) Orientation pop-out display. Other color and orientation combinations were also displayed

Procedure

The participants were randomly split into two groups, resulting in 17 performing the hide task and 15 performing the find task. Participants sat in front of a table on which the display was projected. The instructions varied depending on task type (hide vs. seek) and the identity of the partner (e.g., whether participants were hiding or finding for a foe or a friend), as is outlined in Table 1. In the hide condition, participants were told to select a location to conceal an item so that a friend could find it or a foe could not find it. In the seek condition, participants were told to select a location where they would look for an object hidden by a friend or a foe. Participants started each trial with their index finger on the start bar at the bottom of the screen and with no items presented in the grid (see Fig. 1a). The start bar indicated whether the trial involved a friend or foe. Once participants had placed their finger in the start bar for a randomized duration between 1,000 and 2,000 ms, a display of 16 items was presented (pop-out or uniform; see Fig. 1b–d for examples). On uniform displays, all items were the same; on pop-out displays, one item differed in either color or orientation.

Table 1 Instructions, split by task type, and type of partner

In all, 12 blocks of 40 randomly ordered trials apiece were presented. Each block contained eight uniform trials (distributed evenly between green/blue and vertical/horizontal items), 16 color pop-out displays (across both orientations), and 16 orientation pop-out displays (across both colors). On pop-out trials, the unique item appeared in each of the 16 possible locations on the table, once per block. Participants undertook six complete blocks with the same type of partner (friend or foe) before reversing the partner (the order was counterbalanced). The item selected by the participant was recorded, as was the time that it took for this selection to be completed.

Results

The position selection and timing data were analyzed separately, with the former analysis being based on the normalized frequency data. All analyses of variance (ANOVAs) below report the partial eta-squared (η _p ²) statistic, which describes the proportion of total variability attributable to the particular factor (Olejnik & Algina, 2003). Huynh–Feldt adjustments were used on the probabilities, where necessary, and all post hoc pairwise comparisons included Bonferroni adjustments and were measured as significant at the p < .05 level.

Pop-out displays: how often do hiders and seekers select the unique item?

To investigate whether selection was biased toward visually unique items, we analyzed pop-out trials,² calculating the relative frequency with which the unique item was selected. The data were split by task type (hide or seek) and partner type (friend or foe). The group means are shown in Fig. 2.

Fig. 2

Mean relative frequencies with which the unique item was selected (±1 standard error), split by type of partner (friend vs. foe) and task type (hiding vs. seeking)

We found a main effect of partner type [F(1, 30) = 87.187, p < .001, η _p ² = .744]: The unique item was selected more frequently on friend than on foe trials (.726 vs. .071). No other effects were significant (all ps > .1).

Homogeneous displays: are some spatial positions selected more often than others?

To investigate item selection in the absence of visual biases, we analyzed which items were selected on homogeneous displays.

Near versus far

Reaching for closer items required less effort and energy than does reaching for items at the back of the display. Would such “embodied” considerations have an impact on the locations selected when hiding and finding for a friend or a foe?

We collapsed item selections across the four items in each row, collapsing further the top two and bottom two rows. These data are shown in Fig. 3, from which an overall bias is clear toward participants selecting items closer to themselves. One-sample t tests indicated that the relative frequencies of selecting bottom items were above chance (.5) for all conditions (all ps < .01). A mixed-design, two-factor ANOVA (Partner × Task Type) revealed a main effect of partner type, F(1, 30) = 4.741, p = .037, η _p ² = .136), so that participants were more likely to select items closer to themselves on friend than on foe trials (.836 vs. .704). No other effects were significant (all ps > .4).

Fig. 3

Relative frequencies with which the top and bottom two rows were selected on homogeneous displays, split by partner type (friend vs. foe) and task type (hiding vs. seeking)

Center versus corners

Past studies have revealed a tendency to attend, look, and reach toward the middle of displays (e.g., Prime & Marotta, 2013). We compared the numbers of times the center four items were chosen with the numbers of times the four corner items were chosen (see Fig. 4). A three-factor ANOVA (on task type, partner type, and item position) indicated main effects of item position [center vs. corner: F(1, 30) = 9.875, p = .004, η _p ² = .248], partner type [friend vs. foe: F(1, 30) = 4.535, p = .042, η _p ² = .131], and task type [hide vs. seek: F(1, 30) = 5.742, p = .023, η _p ² = .161]. Items in the corner were more likely to be selected than central items (.352 vs. .189), whereas the selection of both types of items was increased on friend as compared with foe trials (.316 vs. .225), and was increased on hide as compared with seek trials (.302 vs. .239). We also found a Partner Type × Item Position interaction [F(1, 30) = 29.209, p < .001, η _p ² = .493]: Corner items were more likely to be chosen on friend than on foe trials (a difference of .329, p < .001), whereas central items were more likely to be chosen on foe than on friend trials (a difference of .165, p = .002). No other effects were significant (all ps > .05).

Fig. 4

Relative frequencies with which center and corner items were selected on homogeneous displays, split by partner type (friend vs. foe) and task type (hiding vs. seeking)

Do the times taken to hide and seek differ?

The time from the start of the trial until participants had selected an item was recorded (completion time). Median completion times were calculated for each participant within each condition (display type + type of partner) and split by task type (hiding, seeking). The group means are shown in Fig. 5.

Fig. 5

Means of median completion times (±1 standard error), split by display type (uniform vs. pop-out), partner type (friend vs. foe), and task type (hiding vs. seeking)

Uniform displays

On trials with no unique items, a borderline interaction emerged between partner type and task type [F(1, 30) = 3.941, p = .056, η _p ² = .116]. When hiding, no difference was observable between friend and foe (p = .719), but when seeking, a difference of 268 ms emerged (p = .017). No other main effects or comparisons were significant (all ps > .1).

Pop-out displays

A main effect of partner type was apparent [F(1, 30) = 8.124, p = .009, η _p ² = .213], in which responses were longer for foes than for friends (1,129 vs. 980 ms), as well as an interaction [Task Type × Partner: F(1, 30) = 7.299, p = .011, η _p ² = .196]. The interaction was driven by hiding a target for a foe taking far longer than both hiding a target for a friend (290 ms, p = .001) and seeking an item hidden by a foe (a difference of 290 ms, p = .031). No other comparison reached significance (all ps > .9).

Discussion

We addressed two broad theoretical issues: (1) Do the principles of search apply also to concealment? and (2) Does a hide–find paradigm allow for one to examine theory of mind in adults?

On the first count, the data revealed that the underlying cognitive processes for search are similar to, but not the same as, those for concealment. When presented with pop-out displays, participants in both the hide and find groups selected the unique item for friends but not for foes. In other words, they opted for the item that is known to attract attention automatically only when they understood that the hider or the finder was a friend. We propose that this reflects the fact that participants appreciate that a friend would conceal an object or search for an item at a location that would attract attention. This is similar to the finding that participants infer what is salient to another person when interpreting language (see Clark, Schreuder, & Buttrick, 1983). Importantly, hide and find behaviors also diverge in at least one respect: When a unique pop-out item is present, participants take longer to decide where to hide an item from a foe than to search for a target hidden by a foe (see Fig. 5).

The latter finding points to the conclusion that our hide–find paradigm engages processes relating to theory of mind. We propose that participants, when faced with a visual item that pops out, accurately intuit that a searcher will be attracted to the pop-out location. A hider thus needs to “simulate” where a foe’s attention will go next after the pop-out location, and hide it elsewhere. This process is likely to be time consuming and risks becoming a recursive problem, akin to the “prisoner’s dilemma.”³ This explains why decision time is delayed. In contrast, when searching for a target hidden by a foe in such a situation, the task of selecting the target location will quickly be learned to be relatively insurmountable (15 possible locations, if the pop-out location is excluded from consideration) and a rapid guess is as likely to succeed as a slow and considered response. A critical question for future investigation will be to examine the level of theory of mind that is (or can be) engaged by our novel paradigm. Specifically, it is very much an open question whether participants were basing their decisions on (i) a fairly simple strategy, (ii) their current situation and what they themselves would think and do, or (iii) what another person is thinking and how they are likely to act.

In short, our study suggests not only that hiding and finding engage different cognitive processes, but it raises the possibility that the hide–find paradigm can serve as a tool for examining theory of mind. Indeed, the theory of mind in our study extends beyond the visual to the embodied environment. When displays were uniform, participants in both the hide and find groups selected items that were physically closer, suggesting that embodied cues were used to determine an easy (friend) and a hard (foe) search. Participants also selected corner positions on friend trials and more central items for foe trials. The placing of easy targets in corner positions of the display and hard targets more centrally converges with the notion that edges are a salient feature that supports pop-out in a variety of domains (e.g., texture, motion, and disparity), whereas a target is well camouflaged when surrounded by like items. Our finding that participants have accurate and natural intuitions of these facts dovetails with Smilek et al. (2009).

We have introduced a novel hide–find paradigm to study theory of mind, in general, and the cognitive processes of hiding and finding, in particular. This paradigm provides the opportunity to answer a wide range of research questions of both empirical and theoretical import. Some issues are natural follow-ups to the present investigation. Only homogeneous and pop-out visual situations had previously been compared. What happens in more realistic, nonuniform, and spatially jumbled displays, with different luminance values scattered somewhat randomly across the visual field (e.g., Legge et al., 2012), or with feedback regarding the success of one’s behavior? The “mind game” underlying our deceptively simple paradigm therefore not only is of theoretical interest itself, but is an invaluable starting point for an exciting array of future research.