Journal of Experimental Psychology: Human

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Journal of Experimental Psychology: Human Perception and Performance Hierarchical Nesting of Affordances in a Tool Use Task Jeffrey B. Wagman, Sarah E. Caputo, and Thomas A. Stoffregen Online First Publication, June 16, 2016. http://dx.doi.org/10.1037/xhp0000251

CITATION Wagman, J. B., Caputo, S. E., & Stoffregen, T. A. (2016, June 16). Hierarchical Nesting of Affordances in a Tool Use Task. Journal of Experimental Psychology: Human Perception and Performance. Advance online publication. http://dx.doi.org/10.1037/xhp0000251

Journal of Experimental Psychology: Human Perception and Performance 2016, Vol. 42, No. 7, 000

© 2016 American Psychological Association 0096-1523/16/$12.00 http://dx.doi.org/10.1037/xhp0000251

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Hierarchical Nesting of Affordances in a Tool Use Task Jeffrey B. Wagman and Sarah E. Caputo

Thomas A. Stoffregen

Illinois State University

University of Minnesota

In studying the perception of affordances, researchers have typically identified a single affordance and designed experiments to evaluate the perception of that affordance. Yet in daily life, multiple affordances always exist. One consequence of this is that there may be higher order, means-ends relations between different affordances. In 4 experiments, we created situations in which lower order, subordinate affordances could affect the realization of higher order, superordinate affordances, and we asked whether participants were sensitive to these hierarchical, nested relations. Participants wielded tools that varied in length, mass, and mass distribution. In Experiments 1 and 2, we asked them to evaluate these tools in terms of their suitability for executing specific interactions with target objects (striking vs. poking) that were positioned at different distances. In Experiments 3 and 4, we asked participants to select rods and masses and then to assemble them into tools that could be used to execute specific interactions with target objects at different distances. The results were compatible with the hypothesis that participants were simultaneously sensitive to affordances for tool assembly and affordances for tool use. We argue that the nesting of affordances is characteristic of many situations in daily life and that, consequently, sensitivity to hierarchical, means-ends relations among affordances may be an essential characteristic of perceptually guided action. Keywords: affordance, wielding, perception-action, tool use, tool making

about this work is that it not only established that individuals are able to detect whether a given behavior is possible, it also established that individuals are able to detect which of a number of possible behaviors would be most efficient or optimal. To this end, Warren also demonstrated that the energy expended during stair ascent reaches a minimum for stairs that are approximately 25% of an individual’s leg length. Using psychophysical experiments, Warren went on to show that people exhibit precise sensitivity to each of these functional relations: possibility and optimality. To date, research on affordances has typically focused on what we call the “single affordance paradigm”. In this paradigm, researchers select a single affordance as the object of study, and ask whether participants are sensitive to that affordance. The single affordance paradigm is reflected in experimental design and in the instructions that are given to experimental participants. In many studies, participants have been instructed to report, in a yes/no fashion, whether it is possible for them to perform a particular behavior. As described above, Warren (1984, Experiment 1) presented participants with photographs of staircases and asked them to report, yes or no, whether they could ascend each staircase by walking. Similarly, Mark (1987) and Stoffregen, Gorday, Sheng, and Flynn (1999) asked participants to report whether a given seat was low enough to sit upon, and Franchak and Adolph (2014) asked participants to report whether a given doorway was wide enough to squeeze through. In other studies, participants have been asked to indicate when the designated behavior can be performed in an optimal or preferred manner (e.g., Mark et al., 1997; Stoffregen et al., 1999; Warren, Experiment 3). In each of these studies, a logical argument could be made that each of the affordances under study actually consisted of multiple affordances. Sitting on a seat, for example, requires walking to the seat, turning

Affordances are emergent properties of the animal– environment system that constitute opportunities for action. A classic example is walking uphill on a steep, rocky path (e.g., Matthis & Fajen, 2014). Rocks in the path may vary in height; some lower, some higher. A walker may need to consider the height of each rock in choosing a particular path: Is it sufficiently low that it can be stepped upon? Or, does the height of the rock make this behavior impossible? The answer to these questions does not inhere in the metric or extrinsic height of each rock. That is, knowing that a given rock is 0.6 m high is not sufficient to determine whether the rock can be ascended by walking. A tall person might be able to step on this rock, whereas a shorter person might not. Rather, there is a ratio relation between rock height and biomechanical limitations on stepping ability that determines whether any given individual can walk up the rock. This relation was described analytically by Warren (1984), who showed that for healthy adults the maximum riser height that can be ascended by walking is 88% of an individual’s leg length. What is sometimes underappreciated

Jeffrey B. Wagman and Sarah E. Caputo, Department of Psychology, Illinois State University; Thomas A. Stoffregen, School of Kinesiology, University of Minnesota. Portions of these data were presented at the XVIII International Conference on Perception and Action and at the 2015 Meeting of the Psychonomic Society, and appear in the proceedings (Caputo, Stoffregen, & Wagman, 2015; Wagman, Stoffregen, & Caputo, 2015). Correspondence concerning this article should be addressed to Jeffrey B. Wagman, Department of Psychology, Campus Box 4620, Illinois State University, Normal, IL 61790-4620. E-mail: [email protected] illinoisstate.edu 1

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WAGMAN, CAPUTO, AND STOFFREGEN

the body, bending at the knees, and so forth, each of which can be understood as a behavior that is (or is not) afforded. We accept this logical possibility; however, it is important to note that in each study, the authors’ treatment (i.e., motivation, experimental design, data analysis, and discussion) was at the level of a single affordance. Therefore, the single affordance paradigm is not so much a description of actual affordances as it is a description of the approach of the researchers. The single affordance paradigm has provided rich insight into the nature of perception. Yet relative to life outside the laboratory, the single affordance paradigm has an important limitation. Everyday life is characterized by the presence of multiple affordances. In any given situation, relations between properties of the animal (or group) and properties of the environment yield numerous (perhaps, innumerable) available behaviors. That is, many behaviors are possible at any given time. A profound consequence of this fact is that in any real situation we must choose from among numerous available behaviors (Stoffregen, 2003a, 2003b). That is, we must choose which of the numerous possibilities to actualize and how to do so (Turvey, 1992). This choice is influenced by the interplay of intended goals and task constraints (Bingham & Muchisky, 1995; Rosenbaum, Chapman, Weigelt, Weiss, & van der Wel, 2012; Turvey, 2007). The existence of multiple affordances in any given situation, and our consequent obligation to choose among them, gives rise to issues that are important for a theory of affordances. One such issue comprises questions about the relations among the numerous affordances that exist in any situation. Several scholars have suggested that relations among affordances can be conceptualized in terms of nesting (Adolph & Robinson, 2015; Good, 2007; Michaels, 2003; Moore, 2003; Reed, 1996; Stoffregen, 2003a, 2003b; Vicente & Rasmussen, 1990; Wagman & Miller, 2003; Ye, Cardwell, & Mark, 2009). In many cases, these authors have referred to the nesting of affordances but have used the term in an informal or intuitive sense; that is, they have not attempted to formally define nesting. In general, there has not yet been an attempt to provide an account of the nesting of affordances that is systematic or principled. Accordingly, we must infer what is meant from how the term has been used. In this context, one common use of nesting is to refer to the actualization of affordances in temporal sequences. The actualization of one affordance may bring into being another affordance whose actualization may, in turn, bring into existence yet another affordance, and so on. Yet time is not the sole basis for the nesting of affordances. Nesting can also exist across levels that differ in order (Bernstein, 1967; Thelen & Smith, 1994; Turvey, 2007). In fact, the nesting of time scales typically also comprises a nesting at different orders. The swinging of the right leg, for example, is a subordinate behavior that is required for the superordinate behavior of walking, and stabilization of the torso is a subordinate behavior that is required for the superordinate behavior of reaching with the arm and hand. Ye et al. (2009) provided a particularly useful description of affordance nesting, with concrete examples for specific behaviors: [T]he affordance of drinkable from has a nested structure of (component) affordances that include the affordances for pour-in-able, graspable, and liftable. If any of these nested affordances are not present,

then the object does not afford drinking from. (Ye et al., 2009, p. 208, emphasis in the original)

In the above quotation, the nesting of affordances is not temporal, or sequential. The object can be grasped before or after (or without) pouring into, it can be poured into before or after (or without) being lifted, and so on. A sequence emerges from (or is imposed by) the selection of a superordinate affordance, drinkable from: Grasp, pour into, and lift. That is, graspable, pour-in-able, and liftable are each affordances, but they exist in a subordinate relation to drinkable from, which acts (in this case) as a superordinate affordance. Subordinate and superordinate affordances comprise a means– ends hierarchy (Vicente & Rasmussen, 1990). This hierarchy consists of different levels, with higher levels comprising affordances that exist at higher levels of abstraction and lower levels comprising affordances that exist at lower levels of abstraction. Each level in the hierarchy consists of means to ends that exist at higher levels. Similarly, each level in the hierarchy consists of ends that can be achieved using means that exist at lower levels. Overall, higher and lower levels of the hierarchy relate to each other in terms of why, what, and how (Vicente & Rasmussen, 1990). The why level of the means– ends hierarchy represents an overarching goal to be achieved (e.g., replacing a light bulb), but it does not represent specific behaviors that might be performed to achieve that goal. The what level represents specific behaviors that can achieve the goal represented at the why level (e.g., climbing a ladder to a sufficient height), but it does not represent the means by which to perform such behaviors. The how level represents the various means available for performing the behaviors represented at the what level (e.g., stepping on to the first rung of the ladder; see Figure 1A). In the present study, we sought to understand this hierarchical type of nesting in the context of tool selection and assembly tasks. A critical implication of the abstraction hierarchy is that individual

A WHY?

WHAT?

HOW?

Repair roof

Change light bulb

Climb up ladder

Grasping

Climb out window

Stepping Opening

Reaching

B WHY?

WHAT?

HOW?

Knock over

Displace

Assemble Striking tool

Add multiple masses

Assemble Poking Tool

Choose rod

Add single mass

Figure 1. A. A means– end hierarchy illustrating the nesting of behavior relating to two goals (repairing a roof and changing a light bulb). B. A means– ends hierarchy relating to two of the tasks used in the present study.

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HIERARCHICAL NESTING OF AFFORDANCES

goals, which in the single affordance paradigm appear to exist in isolation, are seen to constitute component affordances that, themselves, satisfy superordinate goals at higher levels of the hierarchy (see Figure 1). Whereas the nesting of affordances is widely assumed to exist, the possibility that people might be sensitive to nesting relations among affordances has not been widely addressed in empirical research. Within the single affordance paradigm, people’s sensitivity to means– end nesting of affordances can be evaluated by asking participants to report on nested affordances as a single unit. For example, Wagman and Morgan (2010) asked participants to report their maximum reaching height; that is, the maximum height to which they could reach while standing. The principal manipulation was to introduce prospective variations in circumstances that would affect actual maximum reaching height. In one condition, participants viewed reaching targets and were asked to report on their maximum reaching height if they were to stand on a visible stepstool. In another condition, participants were asked to report on their maximum reaching height if they were to use a visible handheld stick. As predicted, reports of maximum reaching height were greater in the stool and stick conditions, suggesting that participants judged not what they could do in their current configuration (standing on the ground without a stick), but (as instructed) what they would be able to do if they (first) changed their height (by standing on a stool) or arm length (by picking up a stick). Wagman and Morgan concluded that participants correctly perceived that actualizing a lower order affordance for stepping onto the stool, or for grasping the stick, would change (extend) the higher order affordance of maximum reaching height. Other research has investigated how participants have performed a given behavior when that behavior is nested within different goals to be achieved. For example, participants grasped objects differently depending on where and how those objects were to be moved (Rosenbaum et al., 2012). When participants were to reorient an object, they grasped it so as to allow for a comfortable arm and hand posture at the end of the movement sequence— even at the expense of an uncomfortable posture when initially grasping the object. Similarly, participants grasped a vertical object at different heights depending on whether the purpose of the grasp was to move the object to a higher or lower location. Such studies demonstrate that participants show what Rosenbaum et al. described as “second order planning”—manipulating an object not only on the basis of immediate task demands (i.e., what we are calling subordinate affordances), but also on the basis of future task demands (i.e., what we are calling superordinate affordances). That is, such studies demonstrate that participants can perceive the means by which to achieve an intended end. Importantly, there is evidence for this sort of second order planning in adults, children, and babies, as well as in nonhuman primates (Rosenbaum et al.; see also Kahrs & Lockman, 2014; Mangalam & Fragaszy, 2015). The studies by Wagman and Morgan (2010) and described in Rosenbaum et al. (2012) suggest that participants might be sensitive to nested relations between lower order, subordinate affordances and higher order, superordinate affordances. In the present study, we developed a new method that was intended to permit more direct assessment of participants’ sensitivity to means– ends nesting relations between (and among) lower order and higher order affordances. Our method was based, in part, on the work of

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Bingham, Schmidt, and Rosenblum (1989) and Ye et al. (2009). In those studies, participants were given a goal action, such as throwing an object to a maximum distance, or pouring liquid into a container. They were then presented with an array of objects, and asked to select the one that was best suited to achieving the designated goal. Our study is novel in that we developed an a priori multilevel means– ends hierarchy of nested affordances, and we used it to generate testable hypotheses. In previous research and scholarship, concepts of affordance nesting have been qualitative and post hoc, rather than analytic and a priori. In this sense, our study constitutes a qualitative advance in research on the existence and perception of nesting relations among affordances. We asked whether participants are sensitive to hierarchical relations among affordances. In Experiments 1 and 2, we extended the work of Bingham et al. (1989) and Ye et al. (2009) to the domain of manual wielding (i.e., effortful or dynamic touch; see Turvey & Carello, 2011). We assembled a variety of handheld tools from an assortment of wooden rods and attached masses, such that the tools varied in length, mass, and mass distribution. We presented these tools, one at a time, and we asked participants to categorize each tool as being more appropriate for performing one of two different actions on a target object that was presented at different distances. Manipulations of length, mass, and mass distribution, and rotational inertia (I), have well-documented effects on perception of (a) the distance that can be reached with a handheld object and (b) whether and how the object can be used for a particular purpose. In general, the distance that can be reached with a handheld object scales with object length and (for homogeneous objects) with I (e.g., Solomon & Turvey, 1988). Similarly, Wagman and Carello (2001; Carello & Wagman, 2009) found that objects were perceived to be more appropriate for power tasks (such as striking a large nail or throwing for distance) as mass increased and as the center of mass was located farther from the point of rotation (that is, as I increased), and that objects were perceived to be more appropriate for precision tasks (such as striking a small nail, displacing an object, or throwing for precision) as mass decreased and as the center of mass was located closer to the point of rotation (that is, as I decreased). In Experiments 1 and 2, we asked participants to detect not simply “how far can I reach with this tool,” but “what can I do with it, when it gets there?” That is, we took it for granted that participants could appreciate the immediate affordances relating to the reach-able object and the reach-with-able distance (egocentric distance), and asked whether participants were sensitive to a higher order affordance relating to the behavior to be performed at a given distance. In effect, we asked whether participants were sensitive to the opportunity to use the tool to achieve higher order goals that were not related to egocentric length, as such. In other words, in Experiments 1 and 2 we asked whether participants were sensitive to a means– ends hierarchy consisting of two levels. Their task was to perceive the ends (the appropriateness of the tool for a given task) given the means (a tool of a given length, mass, and mass distribution). In Experiments 3 and 4, we introduced a means– ends hierarchy consisting of three levels, and we asked whether participants could detect affordance relations among these three levels. Rather than asking participants to detect higher order affordances relating to preassembled tools, in Experiments 3 and 4 participants were

WAGMAN, CAPUTO, AND STOFFREGEN

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presented with a selection of rods and masses. We asked them to physically enact means– ends relations by assembling tools that, in their judgment, would enable achievement of designated task goals relating to target objects at different distances. In each of our four experiments, sample sizes were comparable to previous research on manual wielding (e.g., Solomon & Turvey, 1988) and on nested affordances (e.g., Wagman & Morgan, 2010). In the present study, we asked whether participants might be sensitive to the existence of nested means– ends relations between affordances. Our hypotheses pertained to sensitivity to a priori nesting relations among subordinate and superordinate affordances, in the context of variables that influenced the selection and assembly of hand-held tools under task constraints. For this reason, data on judgments (as expressed in the categorization of tools, in Experiments 1 and 2, and in the assembly of tools, in Experiments 3 and 4) were sufficient to evaluate our hypotheses. Consequently, we modeled our experimental design on previous studies on the perception of affordances through effortful touch (Carello, Thuot, Anderson, & Turvey, 1999; Shockley, Carello, & Turvey, 2004; Wagman & Carello, 2001, 2003), and we collected data on tool selection or tool assembly but not on tool use.

Experiment 1 In Experiments 1 and 2, we sought to replicate and expand certain aspects of previous work (Bingham, Schmidt, & Rosenblum, 1989; Wagman & Carello, 2001; Ye et al., 2009; Zhu & Bingham, 2008, 2010). We asked whether participants could use superordinate goals to categorize subordinate affordances. We presented participants with a set of preassembled tools. We allowed them manually to wield each tool, and then we asked them to categorize each tool as being more appropriate for performing one of two different actions under specific constraints. In other words, in Experiments 1 and 2, the participant’s task was to detect affordances of the tools for the accomplishment of superordinate goals—that is, to select the ends that could be achieved using a given set of means (i.e., a given tool). The use of a manual wielding paradigm permitted us to control properties of the tools, such as length, mass, mass distribution, and rotational inertia (I)

that have been shown to influence the perception of affordances through manual wielding (e.g., Solomon & Turvey, 1988; Wagman & Carello, 2001). In Experiment 1, we asked participants to identify tools as being more appropriate for either striking a target object or for poking a target object. We expected that participants would categorize tools with more added mass and with the center of mass located farther from the wrist (i.e., tools with larger rotational inertia) as more appropriate for a striking task than for a poking task (Wagman & Carello, 2001).

Method Participants. Fifteen undergraduate students (3 men, 12 women) at Illinois State University participated in Experiment 1 in exchange for extra credit in a psychology course. All participants were right-handed. Materials and apparatus. The apparatus and experimental setting are illustrated in Figure 2. Participants were seated at the head of a table (180 cm long ⫻ 90 cm wide). A tape mark was placed across the width of the table, 10 cm from the edge closest to the participant. Twelve preassembled tools were placed on a stand on the floor (not visible to the participant) at the far end of the table. Each tool consisted of one wooden dowel (1.3 cm in diameter) and one or more attached plastic masses placed at particular locations along the length of the dowel. Masses were cylindrical, each 5 cm long and weighing 86 g with a 4 cm outer diameter and 1.5 cm inner diameter. Each mass was equipped with a thumbscrew that could be used to secure it to a dowel. A single mass (86 g) was attached to some objects; three masses (totaling 258 g) were attached to others (see Figure 2). Ten cm of tape was wrapped around one end of each dowel, signifying the end to be grasped by the participant. The 12 tools were constructed by completely crossing three levels of dowel length (65 cm, 75 cm, or 85 cm) with two levels of added mass (86 g or 258 g) and two levels of mass placement (1/3 or 2/3 of the length of the dowel). The target object was a PVC pipe, 36.5 cm in height, 16.5 cm in outer diameter, and weighing 675 g, that was placed vertically at the right edge of the table, at one of two

Figure 2. The experimental setting (left) and objects (right) for Experiments 1 and 2. See the online article for the color version of this figure.

Results and Discussion The results are summarized in Figure 3. For each participant, the number of trials in which a given tool was categorized as being more appropriate for striking was converted to a proportion. We compared mean proportions in a 3 (Rod Length: 65 cm vs. 75 cm vs. 85 cm) ⫻ 2 (Added Mass: 86 g vs. 258 g) ⫻ 2 (Mass Placement 1/3 L vs. 2/3 L) ⫻ 2 (Target Distance: 55 cm vs. 65 cm) analysis of variance (ANOVA). The main effect of Added Mass was significant, F(2, 18) ⫽ 5.19, p ⬍ .05, ␩p2 ⫽ .27; tools with more added mass (258 g) were more likely to be categorized as a striking tool (M ⫽ 0.65, SD ⫽ 0.14) than tools with less added mass (86 g, M ⫽ 0.36, SD ⫽ 0.19). The main effect of Mass Placement also was significant, F(1, 14) ⫽ 10.83, p ⫽ .01, ␩p2 ⫽ .44; tools with the mass placed farther from the wrist (2/3L) were more likely to be categorized as a striking tool (M ⫽ 0.65, SD ⫽ 0.19) than tools with the mass closer to the wrist (1/3L, M ⫽ 0.37, SD ⫽ 0.14). There were no other significant effects. As expected, participants preferred tools that were more massive and more top-heavy (yielding tools with larger values of I) in the context of the striking task, relative to choices made in the context of the poking task (see Wagman & Carello, 2001).

p (Categorized for Striking)

A

1.00 0.80 0.60

5

65 cm Rod Length 55cm 65 cm

0.40 0.20 0.00 1/3 L

2/3 L

1/3 L

2/3 L

86 g

86 g

258 g

258 g

B p (Categorized for Striking)

distances from the tape mark (55 or 65 cm; see Figure 2). A measuring tape was secured to the right side of the table so that it was visible to the experimenter, but not to the participant. Procedure. On a given trial, the target object was placed at one of the two different distances from the participant (55 cm or 65 cm). The participant was handed one of the 12 tools such that he or she grasped the taped end in his or her preferred hand with the end of the tool flush with the bottom of the fist. The participant explored the tool by wielding it about the wrist, elbow, and/or shoulder. He or she then indicated whether the tool felt more appropriate for either striking or poking the target object. Striking was defined as knocking the target object over by hitting it from the side, and poking was defined as using the distal end of the tool to contact the target object so as to slide it away from the participant without tipping over. Once the participant provided this response, he or she closed his or her eyes and the experimenter retrieved the tool. The target was then positioned for the next trial and the participant was asked to open his or her eyes. On each trial, the participant was allowed as much time as needed to explore the tool, with the restriction that he or she could not use the tool to touch the target object (cf. Carello, Thuot, Anderson, & Turvey, 1999; Shockley, Carello, & Turvey, 2004; Wagman & Carello, 2001, 2003). Target distances were blocked, and order of distances was counterbalanced across participants. For each target distance, each tool was presented three times in a random order.

1.00 0.80 0.60

75 cm Rod Length 55cm 65 cm

0.40 0.20 0.00

C p (Categorized for Striking)

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HIERARCHICAL NESTING OF AFFORDANCES

1/3 L

2/3 L

1/3 L

2/3 L

86 g

86 g

258 g

258 g

1.00

85 cm Rod Length

0.80 55cm 0.60

65 cm

0.40 0.20 0.00 1/3 L

2/3 L

1/3 L

2/3 L

86 g

86 g

258 g

258 g

Experiment 2

Figure 3. Results of Experiment 1, illustrating the proportion of trials for which an object was categorized as a striking tool as a function of Tool Length, Added Mass, Mass Placement, and Target Object Distance. A. Rod length equals 65 cm. B. Rod length equals 75 cm. C. Rod length equals 85 cm. Error bars indicate standard error.

In Experiment 2, we investigated participants’ sensitivity to hierarchical affordances in a tool categorization task that included an additional set of nested constraints. As in Experiment 1, participants were asked to categorize preassembled tools in the context of performing striking or poking tasks. In a betweenparticipants design, one group of participants categorized tools as being more appropriate for striking the target object either with power or with precision. The other group of participants catego-

rized the tools as being more appropriate for poking the target object either with power or with precision. In both tasks, we expected participants to categorize tools with more added mass and with the center of mass located farther from the wrist (i.e., with larger values of I) as more appropriate for tasks involving power than for tasks involving precision (Wagman & Carello, 2001, 2003). Hove, Riley, and Shockley (2006) implemented a similar

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manipulation by asking participants to use manual wielding to rate how suitable hockey sticks felt for performing power (transferring force) and precision (intercepting a moving object) actions. In this sense, Experiment 2 of the present study was a replication of Hove et al. However, in their experiments, Hove et al. did not vary the length of tools (hockey sticks), such that participants were not required to evaluate relations among weight, mass distribution, and the length of tools. In this respect, Experiment 2 of the present study was an extension of Hove et al.

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Method Participants. Twenty-nine undergraduate students (8 men, 21 women) at Illinois State University participated in Experiment 2 in exchange for extra credit in a psychology course. One male participant was excluded from data analysis for failure to understand or follow the instructions. Of the remaining participants, 27 were right-handed, and 1 was left-handed. Half of these participants (n ⫽ 14) were assigned to the striking group, and the other half (n ⫽ 14) were assigned to the poking group. Materials and apparatus. All materials were identical to those in Experiment 1, except for the addition of a red tape mark placed horizontally around the midline of the target object. Procedure. On each trial, the target object was placed at one of two different distances from the participant (55 cm or 65 cm). The participant was handed one of the 12 tools such that he or she grasped the taped end in his or her preferred hand with the end of the tool flush with the bottom of the fist. He or she explored the tool by wielding it about the wrist, elbow, and/or shoulder. Participants in the striking group indicated whether the tool felt more appropriate for striking the target object with power or with precision. Striking with power was defined as knocking the target object over by hitting it from the side; striking with precision was defined as tapping the target object from the side on the red stripe without displacing or tipping it. Participants in the poking group indicated whether the tool felt more appropriate for poking the target object with power or precision. Poking with power was defined as using the distal end of the tool to knock the target object over; poking with precision was defined as using the distal end of the tool to tap the target object on the red stripe without displacing or tipping it over. Participants were permitted as much time as needed to categorize a given tool, but were not permitted to use the tool to touch the target object (cf. Carello et al., 1999; Shockley, Carello, & Turvey, 2004; Wagman & Carello, 2001, 2003). Within each tool-use task condition, target distances were blocked, and order of distances was counterbalanced across conditions. For each target distance, each tool was presented three times in a random order.

Results and Discussion For each participant, the number of trials in which a given tool was categorized as being more appropriate under power constraints for a given tool use task was converted to a proportion. Given that the nesting relationships of interest occurred within a given tool-use task (i.e., within a striking or poking task, respectively), we analyzed the data from the participants assigned to these two tasks separately. In each case, we compared the mean proportions using 3 (Rod Length: 65 cm vs. 75 cm vs. 85 cm) ⫻

2 (Added Mass: 86 g vs. 243 g) ⫻ 2 (Mass Placement 1/3 L vs. 2/3 L) ⫻ 2 (Target Distance: 55 cm vs. 65 cm) ANOVAs. Striking task. The results are summarized in Figure 4. For the striking group, the main effect of Added Mass was significant, F(1, 13) ⫽ 50.7, p ⬍ .001, ␩p2 ⫽ .80: Tools with more added mass were more likely to be categorized as a power tool (M ⫽ 0.71, SD ⫽ 0.15) than tools with less added mass (M ⫽ 0.21, SD ⫽ 0.21). The main effect of Mass Placement was also significant, F(1, 13) ⫽ 12.00, p ⬍ .01, ␩p2 ⫽ .48: Tools with the mass farther from the wrist were more likely to be categorized as a power tool (M ⫽ 0.62, SD ⫽ 0.16) than tools with the mass closer to the wrist (M ⫽ 0.31, SD ⫽ 0.26). In addition, the Length ⫻ Added Mass ⫻ Mass Placement interaction was significant, F(2, 26) ⫽ 5.94, p ⬍ .01, ␩p2 ⫽ .31. To further investigate this interaction, we conducted separate ANOVAs on the mean proportion judged suitable for power at each dowel length, using a 2 (Added Mass: 86 g vs. 243 g) ⫻ 2 (Mass Placement 1/3 L vs. 2/3 L) design. These analyses revealed that 65 cm tools were classified differently than 75 cm or 85 cm tools, as a function of mass and mass placement. For all three tool lengths, there were main effects of Added Mass and Mass Placement: Tools with more added mass and with mass placed farther from the wrist were more likely to be categorized as a power tool than those with less added mass or with the mass closer to the wrist, respectively. However, this was especially so for 65 cm objects. These (shortest) objects were more likely to be categorized as a powerstriking tool than as a precision-striking tool only when the largest mass (258 g) was placed farthest from the hand (2/3 L; see Figure 4A). This was likely because only this configuration of the shortest object provided sufficient rotational inertia to perform the striking task. The omnibus ANOVA also showed a significant Rod Length ⫻ Target Distance interaction, F(2, 26) ⫽ 3.54, p ⬍ .01, ␩p2 ⫽ .21. Follow-up t tests (with Bonferroni corrections) revealed that target object distances affected the likelihood of categorization as power tool only for 75 cm tools. Tools of this length were more likely to be categorized as being appropriate for power when the target object was closer to the participant (55 cm; M ⫽ 0.50, SD ⫽ 0.34) than when it was farther from the participant (65 cm; M ⫽ 0.42, SD ⫽ 0.37), t(13) ⫽ 3.04, p ⬍ .01. There were no other significant effects. Poking task. There were no significant effects (see Figure 5). As expected, in general, participants preferred tools with more added mass and with the center of mass located farther from the wrist (yielding tools with larger values of I) for power-striking tasks than for precision-striking tasks. However, contrary to our predictions, there were no effects of these variables on categorization of tools for use in power- or precision-poking tasks.

Experiment 3 In Experiments 1 and 2, we demonstrated that participants could accurately categorize tools with respect to their utility for achieving higher order affordances relating to designated goal actions. In effect, we investigated participants’ sensitivity to a means– ends hierarchy consisting of two levels. Participants were presented with preassembled tools and were asked to categorize each one as being more appropriate for the achievement of one of two possible ends (i.e., one of two tool-use tasks).

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Figure 4. Results of the Striking Task of Experiment 2, illustrating the proportion of trials for which an object was categorized as a power tool as a function of Tool Length, Added Mass, Mass Placement, and Target Object Distance. A. Rod length equals 65 cm. B. Rod length equals 75 cm. C. Rod length equals 85 cm. Error bars indicate standard error.

Importantly, in Experiments 1 and 2, the tools in question were assembled by the experimenters and were presented to participants only as fully assembled objects. For this reason, participants may have experienced their experimental task as doing only one thing; evaluating (preassembled) tools with respect to the (superordinate) striking and poking tasks. Consequently, it might be argued that Experiments 1 and 2 do not demonstrate sensitivity to nested

relations among subordinate and superordinate affordances. In Experiments 3 and 4, we sought to demonstrate more explicitly the existence of discrete sensitivity to subordinate affordances, as such, and to superordinate affordances, as such. Given existing research (e.g., Bingham et al., 1989; Ye et al., 2009), we felt it was not necessary to demonstrate that our participants were sensitive to the presence or absence of affordances for

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Figure 5. Results of the Poking Task of Experiment 2, illustrating the proportion for which an object was categorized as a power tool as a function of Tool Length, Added Mass, Mass Placement, and Target Object Distance. A. Rod length equals 65 cm. B. Rod length equals 75 cm. C. Rod length equals 85 cm. Error bars indicate standard error.

the lifting, manipulation, and combination of rods and masses. That is, in Experiments 3 and 4, we took it for granted that participants could perceive affordances for the manual manipulation of rods and masses, and for the attachment of masses to rods. We treated these as lower order affordances, and we asked whether the exploitation of these lower order affordances (i.e., assembling the tool) might be influenced by logically distinct, higher order

affordances that were related to using tools to accomplish designated interactions with visible targets. In Experiment 3, we investigated the hierarchical nesting of affordances in the context of a means– ends hierarchy consisting of three levels. Rather than asking participants to categorize preassembled tools, we presented participants with a set of rods and masses, and we asked them to assemble tools that would be appropriate for performing given tool-use tasks. In other words, we asked participants to assemble a possible means to achieve a given end. Assembling an appropriate tool required that participants (simultaneously) detect qualitatively different affordances at two higher levels of the means– ends hierarchy. First, participants needed to detect affordances for assembling rods and masses into tools having a particular length, mass, and mass distribution. Second, participants needed to detect affordances for using those self-assembled tools to achieve higher order goals that were related to properties of the tools (in relation to target objects) rather than to properties of the parts. In particular, we presented participants with a selection of rods and cylindrical masses (the “what” level of the means-ends hierarchy) and asked them to use these components to assemble a tool (the “how” level of the hierarchy) that would be useful for either striking or poking a target object that was presented at different distances (the “why” level of the hierarchy). Each tool was required to consist of one wooden dowel and at least one attached mass (secured anywhere along the length of the dowel). Across conditions, we varied the instructions (the tool should be useful for striking vs. poking) and the distance of a target. Assembling an appropriate tool under these conditions required participants to satisfy two nested constraints. First, the tool must be of sufficient length for the participant to reach the target object. Therefore, we expected participants’ choice of wooden dowels would be related to target distance, such that they would choose longer dowels for more distant targets. Second, both the mass and mass distribution of the tool must be appropriate for the task at hand (striking vs. poking). Therefore, we expected that participants would add more mass to the dowel for the striking task than for the poking task. Consistent with the results of Experiment 1, we expected that participants would arrange the added masses such that the center of mass of the tool would be farther from the hand for the striking task than for the poking task. That is, we expected that participants would assemble tools with larger rotational inertia (I) in the striking task than in the poking task (see Wagman & Carello, 2001).

Method Participants. Fifteen right-handed undergraduate students (6 men, 9 women) at Illinois State University participated in Experiment 3 in exchange for course credit. One female participant was excluded from data analysis due to failure to follow instructions. Apparatus. The apparatus and experimental setting are illustrated in Figure 6. Participants were seated at the table described in Experiments 1 and 2. On the left side of the table, there was a cardboard box (40.5 cm long by 30 cm wide). The box contained 8 wooden dowels, varying in length from 30 to 100 cm in 10-cm increments. The near end of each dowel was wrapped in tape, signifying the end to be grasped. The box also contained 8 cylin-

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menter recorded the length of the dowel, the number of attached masses, and the placement of each mass along the dowel’s length. The target object was then moved to the next distance in the sequence, and the tool was disassembled.

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Results and Discussion

Figure 6. The experimental setting and objects for Experiments 3 and 4. See the online article for the color version of this figure.

drical, plastic masses equipped with a thumbscrew. The target object was the same as in Experiment 1. It was placed vertically at the right edge of the table, at one of 8 distances from the tape mark (25–95 cm, in 10-cm increments). Procedure. For each trial, the target object was placed at one of the eight distances. The participant was instructed to assemble a tool consisting of one dowel and at least one mass secured anywhere along the dowel’s length. The participant was instructed that the tool should be appropriate for the designated task when held with one hand grasping the area covered with red tape, and wielded in such a way that the wrist of the grasping hand remained behind the tape line on the table. Trials for assembly of striking and poking tools were completed in blocked fashion, and the order of conditions was counterbalanced across participants. The definitions of the tool-use tasks were the same as in Experiment 1. Within each block of trials, the target object was presented twice at each distance in a random order. Prior to each condition, the experimenter demonstrated the tool-use task by using a preassembled sample tool consisting of one dowel and one attached mass. Participants did not actually perform the tool-use tasks; they assembled tools, but did not use them. Participants were permitted to use both hands during assembly of the tool to explore the various components (e.g., hefting of masses, wielding of rods), and to wield the completed tool about the wrist, elbow, and/or shoulder. The primary limitation was that the participant was not permitted to touch the target object with the tool (cf. Carello et al., 1999; Shockley et al., 2004; Wagman & Carello, 2001). Participants were permitted as much time as necessary to assemble a given tool and could make continual adjustments to the tool (by disassembling and reassembling it) until they were satisfied. Once the participant was satisfied with their tool, he or she closed his or her eyes while the experi-

Rod length. The results are summarized in Figure 7A. We conducted a 2 (Task: Striking vs. Poking) ⫻ 8 (Target Distances) ANOVA on the mean length of participant-selected dowels. The main effect of Target Distance was significant, F(7, 91) ⫽ 464.82, p ⬍ .001, ␩p2 ⫽ .97. Longer rods were chosen when the target was farther away. The main effect of Task was also significant, F(1, 13) ⫽ 29. 95, p ⬍ .001, ␩p2 ⫽ .70. Longer rods were chosen when assembling tools for striking (M ⫽ 75.5 cm, SD ⫽ 20.2 cm) than for poking (M ⫽ 69.1 cm, SD ⫽ 20.9 cm), likely due to differences in where contact would occur in each task, that is, at the tip of the tool in a poking task but at an intermediate distance in a striking task. The Target Distance ⫻ Task interaction was not significant, F(7, 91) ⫽ 1.60, p ⫽ .145. Amount of added mass. The results are summarized in Figure 7B. Mean amounts of added mass (in grams) in each condition were compared in a 2 (Task: Striking vs. Poking) ⫻ 8 (Target Distances) ANOVA. The main effect of Target Distance was significant, F(7, 91) ⫽ 8.39 p ⬍ .01, ␩p2 ⫽ 0.39. Participants added more mass to the tool when the target was farther away, possibly to facilitate transference of sufficient force to a more distant object as well as to reduce the effect of smaller wrist movements on movements of the wrist tip (see Bongers, Michaels, & Smitsman, 2004). The main effect of Task was also significant, F(1, 13) ⫽ 9.13, p ⬍ .01, ␩p2 ⫽ 0.41, revealing that participants added more mass to tools assembled for striking (M ⫽ 149.0 g, SD ⫽ 29.2 g) than to tools assembled for poking (M ⫽ 121.9 g, SD ⫽ 30.0 g). The interaction was not significant, F(7, 91) ⫽ 0.71, p ⫽ .66. Center of mass. The results are summarized in Figure 7C. The center of mass of the tool that was assembled on each trial was calculated (in cm, measured from the end held in the participant’s hand). We evaluated the mean center of mass in each condition in a 2 (Task: Striking vs. Poking) ⫻ 8 (Target Distance) ANOVA. The main effect of Target Distance was significant, F(7, 91) ⫽ 87.21, p ⬍ .001, ␩p2 ⫽ 0.87, revealing that participants assembled tools such that the center of mass was farther from the wrist when the target was farther away, likely a consequence of choosing longer rods for more distant targets. The main effect of Task was also significant, F(1, 13) ⫽ 22.83, p ⬍ .001, ␩p2 ⫽ 0.64. The center of mass was farther from the wrist in tools assembled for striking (M ⫽ 50.5 cm, SD ⫽ 12.7 cm) than in tools assembled for poking (M ⫽ 42.4 cm, SD ⫽ 10.9 cm), again likely due to differences in where contact would occur in each task. The interaction was not significant, F(7, 91) ⫽ 0.71, p ⫽ .66. Rotational inertia. The results are summarized in Figure 7D. For each tool assembled, we determined the rotational inertia (I) in g ⫻ cm2, calculated for rotations about an axis perpendicular to the end of the tool held in the participant’s hand. We divided values by 104 and then compared mean values in a 2 (Task: Striking vs. Poking) ⫻ 8 (Target Distance) ANOVA. The main effect of Target Distance was significant, F(7, 91) ⫽ 43.88, p ⬍ .001, ␩p2 ⫽ 0.77. Values of I increased with target distance, a lawful consequence of choosing longer rods, adding more mass, and assembling tools

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Figure 7. Results for Experiment 3, illustrating properties of assembled tools as a function of the distance of targets and the task for which tools were assembled (striking vs. poking). A. Mean selected rod length. B. Mean mass added to rods. C. Mean location of the center of mass, CM, of assembled tools (from the held end of the tool). D. Mean moment of inertia, I, of assembled tools. Error bars indicate standard error.

such that the center of mass was farther from the wrist for more distant targets. The main effect of Task was also significant, F(1, 13) ⫽ 14.08, p ⬍ .01, ␩p2 ⫽ .52. Values of I were greater in tools assembled for striking (M ⫽ 63.7 g ⫻ cm2, SD ⫽ 38.8 g ⫻ cm2) than in tools assembled for poking (M ⫽ 35.8 g ⫻ cm2, SD ⫽ 38.8g ⫻ cm2). In addition, the Target Distance ⫻ Task interaction was significant, F(7, 91) ⫽ 4.31, p ⬍ .001, ␩p2 ⫽ .25, revealing that the influence of Task on I increased with target distance, a consequence of selecting longer rods for more distant targets. To summarize, consistent with our predictions and with the categorization data from Experiments 1 and 2, participants assembled tools that would be appropriate for performing a striking or poking task on a target object. The tools satisfied two nested constraints. As expected, and consistent with the results of Experiment 1, tools were longer (i.e., participants chose longer dowels) when the target object was farther away, and tools were constructed with larger values of I (i.e., they added more mass, and placed it farther from the hand) when assembling tools for the striking task than when assembling tools for the poking task.

Experiment 4 In Experiment 4, we investigated the hierarchical nesting of affordances in the context of a tool assembly task with an additional set of nested constraints. Whereas in Experiment 3, participants were given only a tool use task as an intended end, in Experiment 4, participants were given both a tool use task (striking or poking) and a specific constraint on that task (power vs. preci-

sion). Again, participants were asked to assemble a means given these ends. As in Experiment 3, assembling an appropriate tool under these conditions required satisfying a number of nested constraints. First, the tool must be of sufficient length for the participant to reach the target object. Therefore, as in Experiment 3, we expected that participants’ choice of wooden dowels would be related to target distance, such that they would choose longer dowels for more distant targets. Second, both the mass and mass distribution of the tool (quantified by I) must be appropriate for both the task at hand and the specific constraints on that task. Therefore, we expected that participants would add more mass to the dowel, and that the center of mass would be located farther from the hand, in the striking task than in the poking task, and more under power constraints than under precision constraints. That is, we expected that participants would assemble tools with larger rotational inertia (I) in the striking task than in the poking task, and under power constraints than under precision constraints (see Wagman & Carello, 2001, 2003).

Method Participants. Twenty-four undergraduate students (7 men, 14 women) at Illinois State University participated in Experiment 4 in exchange for extra credit in a psychology course. Two participants (both male) were excluded from data analysis due to failure to understand or follow instructions. Of the remaining participants, 20 were right-handed and two were left-handed.

Materials and apparatus. All materials were identical to those in Experiment 3, except that a red tape mark was placed horizontally around the midline of the pipe. Procedure. The procedure was similar to that of Experiment 3. On a given trial, the target object was placed at one of the eight distances. The participant was instructed to assemble a tool, consisting of at least one dowel and at least one mass secured anywhere along the dowel’s length, such that it would be appropriate for the designated task. The designated tasks were striking with power, striking with precision, poking with power, and poking with precision, each of which was defined as in Experiment 2. Trials for assembly in the four tasks were completed in a blocked fashion and in a random order for each participant. Within each block, the target object was presented once at each distance, in a random order. As in Experiment 3, prior to each condition, the experimenter demonstrated the tool-use task by using a preassembled sample tool consisting of one dowel and one attached mass.

Results and Discussion

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poking (M ⫽ 70.3 cm, SD ⫽ 19.4 cm), again likely because of difference in where contact would be made in each of these tasks. However, these effects were qualified by a Target Distance ⫻ Task interaction, F(7, 147) ⫽ 3.72, p ⬍ .001, ␩p2 ⫽ 0.15. Follow-up t tests (with Bonferroni correction) revealed that longer rods were chosen in the striking task than in the poking task only at target distances of 35 cm, 65 cm, or 75 cm (each p ⬍ .006). This interaction may suggest that, consistent with subsequent analyses, the distinction between power and precision tasks was more salient to participants than the distinction between striking and poking tasks. The main effect of Constraint was significant, F(1, 21) ⫽ 10.71, p ⬍ .01, ␩p2 ⫽ 0.34: Longer rods were chosen under the Power constraint (M ⫽ 74.4, SD ⫽ 18.2 cm) than under the Precision constraint (M ⫽ 72.2 cm, SD ⫽ 19.4 cm), likely because shorter tools facilitate better control when a tool-use task is performed under precision constraints (see Bongers, Michaels, & Smitsman, 2004). There were no other significant effects. Amount of added mass. The results are summarized in Figure 8B. We evaluated mean amounts of added mass using a 2 (Task: Striking vs. Poking) ⫻ 2 (Constraint: Power vs. Precision) ⫻ 8 (Target Distances) ANOVA. The main effect of Target Distance was significant, F(7, 147) ⫽ 5.71 p ⬍ .01, ␩p2 ⫽ 0.21: More mass was added to the tool when the target object was farther away, likely to facilitate transference of sufficient force to a more distant object as well as to dampen the effect of small wrist movements on movements of the tip of the tool (see Bongers et al., 2004). The main effect of Constraint was also significant, F(1, 21) ⫽ 23.12, p ⬍ .001, ␩p2 ⫽ 0.52: More mass was added to the

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Figure 8. Results from Experiment 4, illustrating properties of assembled tools as a function of the distance of targets, the task for which tools were assembled (striking vs. poking), and the task constraints (power vs. precision). A. Mean selected rod length. B. Mean mass added to rods. C. Mean location of the center of mass, CM, of assembled tools (from the held end of the tool). D. Mean moment of inertia, I, of assembled tools. Error bars indicate standard error.

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tool under the Power constraint (M ⫽ 152.9 g, SD ⫽ 14.9 g) than under the Precision constraint (M ⫽ 101.9 g, SD ⫽ 13.4 g). There were no other significant effects. Center of mass. The results are summarized in Figure 8C. We evaluated the mean center of mass using a 2 (Task: Striking vs. Poking) ⫻ 2 (Constraint: Power vs. Precision) ⫻ 8 (Target Distances) ANOVA. The main effect of Target Distance was significant, F(7, 147) ⫽ 194.02, p ⬍ .001, ␩p2 ⫽ 0.90: Participants assembled tools such that the center of mass was located farther from the wrist when the target object was farther away. The main effect of Task was significant, F(1, 21) ⫽ 23.16, p ⬍ .001, ␩p2 ⫽ 0.52: The center of mass was located farther from the wrist in tools assembled for striking (M ⫽ 49.0 cm, SD ⫽ 12.2 cm) than in tools assembled for poking (M ⫽ 43.5 cm, SD ⫽ 11.8 cm), again likely reflecting a difference in where on the tool contact would be made in each task. The main effect of Constraint was significant, F(7, 147) ⫽ 24.63, p ⬍ .001, ␩p2 ⫽ 0.54: The center of mass was located farther from the wrist under the Power constraint (M ⫽ 50.6 cm, SD ⫽ 12.1 cm) than under the Precision constraint (M ⫽ 42.0 cm, SD ⫽ 10.9 cm), allowing for the transference of greater force in a power task than in a precision task. In addition, the Target Distance ⫻ Constraint interaction was significant, F(7, 147) ⫽ 2.38, p ⬍ .05, ␩p2 ⫽ .10. Follow-up analysis of difference scores calculated at each target distance revealed that the influence of Constraint was more pronounced when the target was farther away (e.g., 75 cm) than when it was closer (e.g., 25 cm), t(21) ⫽ 3.66, p ⬍ .01, likely reflecting a concern for controllability of the object tip while under precision constraints. There were no other significant effects. Rotational inertia. The results are summarized in Figure 8D. Rotational inertia (I) values were calculated and transformed as in Experiment 3 and then compared in a 2 (Task: Striking vs. Poking) ⫻ 2 (Constraint: Power vs. Precision) ⫻ 8 (Target Distances) ANOVA. The main effect of Target Distance was significant, F(7, 147) ⫽ 60.63, p ⬍ .001, ␩p2 ⫽ 0.73: Participants assembled tools with larger values of I when the target was farther away. There was also a main effect of Task, F(1, 21) ⫽ 10.29, p ⬍ .01, ␩p2 ⫽ 0.33: Values of I were larger in tools assembled for striking (M ⫽ 53.8 g ⫻ cm2, SD ⫽ 33.6 g ⫻ cm2) than in tools assembled for poking (M ⫽ 42.9 g ⫻ cm2, SD ⫽ 30.0 g ⫻ cm2). The main effect of Constraint was significant, F(1, 21) ⫽ 23.84, p ⬍ .001, ␩p2 ⫽ 0.53: Values of I were larger under the Power constraint (M ⫽ 63.4 g ⫻ cm2, SD ⫽ 34.7 g ⫻ cm2) than under the Precision Constraint (M ⫽ 33.3 g ⫻ cm2, SD ⫽ 20.0 g ⫻ cm2). In addition, the Target Distance ⫻ Constraint interaction was significant, F(7, 147) ⫽ 8.05, p ⬍ .001, ␩p2 ⫽ 0.28: The influence of Constraint was more pronounced when the target object was farther away, again a consequence of selecting longer tools for more distant targets. To summarize, and consistent with our predictions and consistent with results of Experiments 1, 2, and 3, participants assembled longer tools (i.e., they chose longer dowels) when the target object was located farther away. In addition, participants added more mass, placed that mass farther from the hand, and consequently created tools with larger values of I when assembling tools for striking rather than poking, and when assembling tools to be used under power constraints than under precision constraints.

General Discussion In four experiments, participants demonstrated a robust ability to detect the task-specific utility of objects in a manner consistent with the hypothesis that they were sensitive to hierarchical, meansends relations between lower-level and higher-level affordances. Our findings extend the work of Wagman and Morgan (2010) and described in Rosenbaum et al. (2012) to the domain of manual wielding, and to functional (i.e., affordance) relations between tasks, target distance, and the rotational inertia of wielded tools. Our results provided quantitative support for the general hypotheses that multiple affordances exist in any given situation, that these affordances exist in nested relationships, and that perceivers are sensitive to hierarchical, means– ends nesting of affordances (e.g., Adolph & Robinson, 2015; Reed, 1996; Stoffregen, 2003a, 2003b; Vicente & Rasmussen, 1990; Wagman & Miller, 2003; Ye et al., 2009). In Experiments 1 and 2, we asked whether participants were sensitive to hierarchical nesting of affordances in two levels: the higher level of using a manual tool to achieve defined interactions with a target at different distances, and the lower level of manual tools that could be used to reach to different distances in different ways. In Experiment 1, we presented participants with preassembled tools and asked them to categorize each tool as being more appropriate for performing one of two actions (striking vs. poking) on targets that were presented at different distances. We varied the length of tools, their mass, and the location of the center of mass (nearer to vs. farther from the hand). In Experiment 2, separate groups of participants categorized tools for striking or poking tasks, in each case categorizing tools as being more appropriate for performing the task with either power or precision. Particularly in the striking task, the pattern of categorization judgments was consistent with the hypothesis that participants were sensitive to a hierarchical, nested relation between lower level affordances relating to the arm-tool system (which could be detected through wielding) and higher level affordances relating to the arm-tool-target system (which could not be detected solely on the basis of wielding). In the poking task, none of the manipulated variables influenced categorization judgments. Although this was unexpected, previous research has shown that participants have stronger preferences for configurations of a striking tool than of a poking tool (Wagman & Carello, 2001). To the extent that such preferences do exist, objects are perceived to increasingly afford poking-with as the tip of the object is easier to control in a task-specific manner and as the mass distribution is more aligned with the long axis of the arm. In addition, as shown in Experiment 4, the distinction between striking and poking tasks was not as salient to participants as the distinction between power and precision tasks. Whether or not these preferences for configurations of poking tools would emerge in tool assembly may require a more defined poking task (as in Wagman & Carello, 2001). This may be a topic of future research. In Experiments 3 and 4, we expanded the hierarchical nesting of affordance to three separate levels. The highest level (“why”) consisted of the goal of using a manual tool to achieve defined interactions with a target at different distances; the middle level (“what”) consisted of manual tools that could be used to reach to different distances in different ways; and the lower level (“how”) consisted of rods and weights that could be assembled to create

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HIERARCHICAL NESTING OF AFFORDANCES

manual tools that differed in length and rotational inertia. However, rather than asking participants to categorize preassembled tools (in terms of their appropriateness for interacting with the targets), we asked them to assemble tools that would be appropriate for performing striking or poking tasks on the target at that distance. In Experiment 3, participants assembled tools that they judged to be appropriate for striking versus poking that target object. In Experiment 4, participants assembled tools that they judged to be appropriate for the striking and poking tasks, with precision and power constraints, respectively. In both experiments, the results were consistent with our hypothesis that participants simultaneously detected hierarchical, means– end relations between higher level affordances (relating to goal tasks and target distances), intermediate level affordances (relating to the rotational inertia and length of tools), and lower level affordances (relating to the selection of rods and masses for tool assembly). In addition, the results of Experiments 3 and 4 suggest that participants’ awareness of nested, means– ends relations was prospective insofar as, at the beginning of each trial, the assembled tools did not yet exist. For this reason, our results demonstrated an understanding of affordance nesting in a way that qualitatively differs from previous research (e.g., Bingham & Muchisky, 1995; Bingham et al., 1989; Solomon & Turvey, 1988; Wagman & Miller, 2003; Wagman & Morgan, 2010; Ye et al., 2009; Zhu & Bingham, 2008, 2010). The pattern of results differed across experiments. For example, whereas target distance did not influence the categorization of tools in Experiment 1, it did influence the categorization of striking tools in Experiment 2, and also the assembly of tools in Experiments 3 and 4. In addition, the categorization of poking tools was not affected by any of the experimental manipulations in Experiment 2, but assembly of tools differed for striking and poking tasks in Experiments 3 and 4. These differences, although real, do not imply that there was any inconsistency (across experiments) in the extent to which the results supported our hypotheses regarding the perception of hierarchical, nested relations among affordances. The four experiments differed substantially with respect to design (e.g., categorization vs. assembly), the number and type of independent variables (e.g., the inclusion or exclusion of precision constraints), and other factors. For example, in Experiments 1 and 2, the task of the participant was to categorize existing tools, and there was a single discrete dependent variable. In addition, in Experiment 1, the within-participants variation in categorization tasks was with respect to whether the tool was more appropriate for a striking or poking task, whereas in Experiment 2, the withinparticipants variation in categorization tasks was with respect to whether the tool was more appropriate for a power or precision task. In Experiments 1 and 2, the dependent measures were categorical, whereas in Experiments 3 and 4 the dependent measures were continuous. Moreover, in Experiments 1 and 2, participants were asked to categorize tools that already existed, as opposed to Experiments 3 and 4, in which participants were asked to create (assemble) tools. Finally, in Experiment 3, the within-participants variation in tasks was with respect to assembly of tools appropriate for a striking or poking task, whereas in Experiment 4, the withinparticipants variation in task was with respect to assembly of tools appropriate for a power or precision task. It is to be expected that these substantial differences in experimental design would lead to differences in results across experiments. Yet at the same time, the results of each experiment are consistent with our general hypoth-

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esis that participants were sensitive to hierarchical, means– ends nesting of subordinate and superordinate affordances, and that they used this sensitivity in performing the different tasks in each experiment.

Means–End Nesting of Affordances The corpus of existing research and theory relating to affordances conforms primarily to what we have called the single affordance paradigm. This approach has been very productive. It has demonstrated that a wide variety of individual affordances can be perceived by adults (e.g., Chang, Wade, & Stoffregen, 2009; Ramenzoni, Riley, Davis, Shockley, & Armstrong, 2008; Stoffregen et al., 1999), children and infants (e.g., Adolph, 1995; Yonas & Hartman, 1993), and other animal species (e.g., Branch, 1979; Irschick & Losos, 1999; Reed, 1982; Tarsitano & Andrew, 1999; see Turvey, 2013). However, we argued that this paradigm may not be representative of everyday life situations. We pointed out that multiple affordances exist in any given situation, that is, in any given situation there are multiple (perhaps innumerable) opportunities for action. The existence of multiple opportunities for action raises questions about relations among them (see Bingham & Muchisky, 1995). We argued that one type of relation among affordances is that of a means-end hierarchy. In the present study, our main purpose was to evaluate the hypothesis that humans may be sensitive to means– end relations among multiple affordances at multiple levels. Our results suggested that, without training, practice, or detailed instruction, participants were sensitive to the existence (and utility) of means– ends relations among affordances that were nested in three logically distinct levels in a means– ends hierarchy. In this sense, our results resemble those of Warren (1984), whose participants exhibited robust sensitivity to means– end relations between properties of their own bodies and properties of the environment: that is, to individual affordances. If it is accepted that multiple affordances exist and that means– ends relations among affordances exist, then the present study can be taken as an empirical demonstration of a novel category of perceivables, and in that sense is similar to Warren’s original demonstration of the perception of individual affordances. Many studies have focused on the perception of a single affordance (e.g., Mark, 1987; Stoffregen et al., 1999; Warren, 1984). In the Introduction, we pointed out the logical possibility that in those studies it might also be possible to interpret the “single affordances” within the concept of nested, means– ends relations. The results of the present study provided empirical support for this logical possibility. Accordingly, it seems both possible and useful to offer an example derived from what we have referred to as the single affordance paradigm. In Warren’s (1984) study, the “affordance for stair climbing” can be understood as the assembly or organization of a specific set of nested affordances. This is because stair climbing entails a number of actions, each of which can be performed independent of the others and outside the context of stair climbing. Examples of such actions include maintaining balance, lifting one leg while standing on the other, bending a lifted leg at the knee, positioning a raised foot over a stair, and straightening a bent leg so as to raise the entire mass of the body (see

WAGMAN, CAPUTO, AND STOFFREGEN

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Figure 9). Note that these (and other) component actions need not be solely sequential. It might be argued that participants in our experiments were not sensitive to relations among affordances, but were instead exclusively sensitive to a single higher order affordance. In fact, any relation among affordances can be described as a single higher order affordance, and vice versa. In large part, this is the claim being made by scholars who argue that affordances are nested within one another (Reed, 1996; Stoffregen, 2003a, 2003b; Wagman & Miller, 2003). The value of an analysis of such nestedness as a hierarchical means– ends relation among affordances is that it provides “a generic framework for describing goal-oriented systems with many degrees of freedom” (Vicente & Rasmussen, 1990, p. 208), which respects the goal-directedness and flexibility of perception and behavior. In the present study, the perception of nested affordance relations was implicit in Experiments 1 and 2, in which participants exploited (and, therefore, presumably perceived) affordances for the wielding of tools, so as to support the explicit task of judging the suitability of tools for higher order tasks. Experiments 3 and 4 were designed so as to make concrete the logical distinction between lower order and higher order affordances. In Experiments 3 and 4, participants were asked to judge the suitability of tools for the accomplishment of higher order goals (striking and poking, with power or precision). However, unlike Experiments 1 and 2, in Experiments 3 and 4 participants were asked to make these judgments about tools that did not (yet) exist. They exploited affordances for (lower order) manual manipulation of rods and masses in the context of creating tools that would (prospectively) be suitable for the accomplishment of (higher order) affordances for striking or poking. As noted in the introduction to Experiment 3, we took as given participants’ ability to detect (lower order) affordances for the manual manipulation of rods and masses. The results of Experiments 3 and 4 demonstrated that participants accurately detected these lower order affordances (as demonstrated by their ability actually to assemble tools). More importantly, the results of Experiments 3 and 4 demonstrated that participants’ exploitation of these lower order “affordances for object assembly” were guided by logically distinct, higher order affordances relating to how the assembled tools might be used.

Relations to Research on Manual Wielding A major inspiration for our experimental design was the large body of literature demonstrating that manual wielding of unseen rods is sufficient for perception of length-related affordances of the rod (for reviews see Carello & Wagman, 2009; Turvey & Carello,

WHY?

Ascend Stairs

WHAT?

Step on surface

HOW?

Lift one foot

Tie shoes

Crawl on surface

Bend knee

Adopt prone posture

Figure 9. A means– end hierarchy illustrating the nesting of behavior relating to two goals (ascending stairs and tying shoes).

2011). In particular, people can perceive how far they could reach with a given unseen wielded rod (e.g., Solomon & Turvey, 1988) and where along the length of the rod they would choose to strike a target object (Carello et al., 1999; Wagman & Carello, 2001; Wagman & Taylor, 2004), and they can do so without feedback or opportunities to perform the relevant behavior. Our method differed from earlier studies of manual wielding in several ways. First, in our study wielded tools (and their components) were always visible. Second, in our study length (or reachwith-able distance) was subordinate to the superordinate affordances that participants were asked to detect, in that we varied the nature of interactions with target objects (striking, poking, with power, or with precision). These variations gave importance to the overall mass of the tools and to their rotational inertia. The results of all four experiments indicated that participants were sensitive to affordances of the tool-target system. Together, the mass and mass distribution of an object determines its rotational inertia: its resistance to rotational acceleration about an axis. An object’s rotational inertia determines the direction and scaling of muscular forces required to control that object. That is, it determines how (and how easily) that object can be used, and consequently, it affects the affordances of the object (Carello & Wagman, 2009). In the present study, for both categorization and assembly tasks, participants’ selection of tools was influenced by relations between rotational inertia and task constraints. This result is consistent with research showing that perception of the utility of a tool reflects the rotational inertia of that tool in a task-specific manner (Wagman & Carello, 2001, 2003) and extends it to the domain of hierarchically nested affordances. The previous comments refer to judgments that we asked participants to make in each of our four experiments. In addition, in Experiments 3 and 4 certain judgments about subordinate affordances were implicit in the choices that participants made during tool assembly (i.e., judgments about the suitability of rods and masses for the assembly of tools). We provided masses that might be added to rods, and we invited participants to heft the masses in making their decisions about how much mass to add to rods, as well as the placement of added mass. This portion of the method resembled the study of Bingham et al. (1989) in the sense that participants were invited to heft objects that differed in mass, as a means to obtain information about the suitability of the objects for the actualization of affordances. In Bingham et al., hefting occurred in the context of the single affordance paradigm: participants hefted each object so as to determine how far they could throw it. In Experiments 3 and 4 of the present study, hefting could provide information that was relevant to a higher order affordance for the construction of tools, but also for superordinate affordances for the use of tools to interact with the target objects. In the present study, we asked whether participants might be sensitive to the existence of nested means– ends relations between affordances. This is, in part, why we modeled our experimental design on previous studies that have collected data only about affordance judgments (e.g., Carello et al., 1999; Shockley et al., 2004; Wagman & Carello, 2001, 2003). Researchers have occasionally evaluated hypotheses about relations between the judgment of an affordance and the ability to actualize that affordance (e.g., Adolph, 1995; Bingham et al., 1989; Zhu & Bingham, 2008, 2010): in effect, about the accuracy of affordance judgments. The results of the present study, demonstrating that participants were

HIERARCHICAL NESTING OF AFFORDANCES

sensitive to the existence of nested, means– end relations between affordances, can be used, in future research, to motivate testable predictions about the accuracy of such sensitivity, and about how judgment accuracy might be influenced by variations in means– ends relations among nested affordances.

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Conclusion Affordances are opportunities for action by a given individual (or group) in a given environment. Particular affordances do not exist in isolation; rather, many affordances exist in any given situation. In this article, we argued that relations between affordances comprise a nested, means– end hierarchy. In four experiments, we asked whether participants were sensitive to nested, means– ends relations among affordances. The results of the present study provided explicit empirical evidence for the hypothesis that humans are sensitive to the existence of affordances in a nested, means– ends hierarchy, and that they can use this knowledge of these hierarchical relations, in effect, to create higher– order affordances by exploiting extant affordances at lower levels of the hierarchy.

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Received December 22, 2015 Revision received April 5, 2016 Accepted April 12, 2016 䡲

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