Affordances and Inertial Constraints on Tool Use

Affordances and Inertial Constraintson Tool Use

Jeffrey B. Wagman and Claudia CarelloCenter for the Ecological Study of Perception and Action

University of Connecticut

Whether an object can be used to satisfy a given tool user’s intention depends on,among other things, the object’s inertial properties. Overcoming an object’s rotationalinertia is key in controlling a handheld object with respect to a given intention. Ma-nipulating an object by means of muscular exertion is the domain of dynamic touch.Thus, the affordances of a given object as a tool should be perceivable by means of dy-namic touch. In 3 experiments, we investigated the inertial variables that support per-ception of 2 potential affordances of handheld tools: hammer-with-ability andpoke-with-ability. The results suggest that ratings of hammers are dependent on thevolume of the inertial ellipsoid in such a way that supports the transference of power tothe struck surface. Ratings of pokers are dependent on the same quantity but in a waythat supports controllability of the poking object. Additionally, results suggest thatminimal experience in a given tool-using task may “tune” tool users to the inertialproperties required of a given tool for a given function.

Tool use is central to the culture of human and nonhuman primates (Berthelet &Chavaillon, 1993; van Lawick-Goodall, 1970). It is an important part of the dailysurvival of many individual animals, as well as of the evolutionary survival of manyspecies (including human and nonhuman primates, other mammals, and somebirds; see Boesch & Boesch, 1983; Hall & Schaller, 1964; McGrew, 1993). The de-velopment of the ability to use tools to achieve a goal is a significant step in the evo-lutionary development of any species and may even serve as a hallmark ofintelligence in an individual or in a species. At the very least, the use of tools is a cri-terion for hominization (Berthelet & Chavaillon, 1993). Furthermore, the evolu-tion of tool use within a species and the evolution of perceiving–acting capabilities

ECOLOGICAL PSYCHOLOGY, 13(3), 173–195Copyright © 2001, Lawrence Erlbaum Associates, Inc.

Requests for reprints should be sent to Jeffrey Wagman, CESPA, Unit 1020, 406 Babbidge Road, Uni-versity of Connecticut, Storrs, CT 06269–1020. E-mail: [email protected]

within that species are symbiotic processes. Because this seems to be especially truein the case of human and nonhuman primates, it seems clear that tools have bothshaped and been shaped by the evolution of the perceiving and acting capabilities ofthese species in particular (Smitsman, 1997).

AFFORDANCES AND TOOL USE

In the ecological approach to perception and action in the tradition of J. J. Gib-son (1966/1983, 1979/1986), affordances are the entry point into the mutualitybetween an animal and its environment. Affordances are real possibilities for ac-tion for a perceiving–acting system (Turvey, 1992), and they are potentialcomplementarity relations between animal and environment (van Leeuwen,Smitsman, & van Leeuwen, 1994). When the environment in question is a de-tached object, rather than an extensive surface, the intrinsic link between theconcept of affordance and the concept of tool use becomes readily apparent.What makes an object a tool is the real possibility of use of that object by an ani-mal so as to supplement the animal’s inherent action capabilities—its effectivityset—in achieving a goal. Thus, tool use can be viewed as a complementary rela-tion between affordance and effectivity (van Leeuwen et al., 1994; cf. Shaw &Turvey, 1981). It has been conjectured, for example, that the design of manymodern tools (e.g., hammers, drills, and utensils) was initially based on the un-aided capabilities of the human hand (Drillis, 1963). In developing from the un-aided hand to the tool, the end effector is displaced from the hand to theimplement (Smitsman, 1997).

In the ecological view, a tool is an object attached to the body in such a way as toextend the organism’s capacity for perceiving and acting. This effectively changesthe boundary between the organism and the environment. Primarily, what a tooldoes for an animal is to enhance the body space or ego field of the operator—thedistance within which the operator can causally affect things. That is, tools extendan animal’s effectivities. A tool, then, is not an object per se. Instead, a tool is thefunction of an object for an agent, and to be considered a tool, the object mustserve to extend the agent’s effectivities (Shaw, Flascher, & Kadar, 1995). Grasp-able, detached objects afford manipulation by an organism with suitable effectors.Such objects can function as tools depending on the particular goals of the organ-ism. The fit between the functionality of a tool and an organism’s action capabili-ties is highlighted by the contribution of “folk norms” in scaling the proportion ofcomponents of tools to the approximate size of the most likely operator (Drillis,1963). In what follows, we consider how some of the research on tool use in bothhuman and nonhuman primates succeeded in formalizing the aforementioned in-tuitions of Drillis (1963; Drillis, Schneck, & Gage, 1963) as well as of J. J. Gibsonand colleagues (see J. J. Gibson, 1966/1983, 1977, 1979/1986; Shaw & Turvey,

174 WAGMAN AND CARELLO

1981; Smitsman, 1997; Turvey, 1992). The potential relevance of research on dy-namic touch is then highlighted, in particular, demonstrations of the constrainingrole played by rotational dynamics in the perception of object properties duringwielding. Finally, we present three experiments in which participants were asked torate unseen handheld objects with respect to their perceived effectiveness as a par-ticular kind of tool. Analyses, focusing on rotational dynamics, are directed at un-covering the physical basis of such perception.

Comment on Previous Research

We begin with Köhler’s (1925) groundbreaking work with chimpanzees. Amongother important observations, Köhler found that chimpanzees spontaneously (i.e.,without explicit training) used tools such as sticks, hooks, or rakes to reach a desired(food) item that would have been out of reach without use of the implement. Al-though Köhler attributed such insightful problem solving to cognitive mechanisms,he commented that for the successful chimp, the stick “has now acquired a certainfunctional or instrumental value in relation to the field of action under certain con-ditions” (p. 36). Clearly, along with Koffka’s (1935) notion of “demand character”and Lewin’s (1935) notion of “invitation character,” this idea was a precursor to J. J.Gibson’s (1977) notion of affordance.

Tool use in humans has far surpassed known use of tools in other species, and asa result, the bulk of research on tool use has addressed hypothetical internal cogni-tive mechanisms (e.g., schemas) associated with human tool use. In such research,tool use is usually equated with a logical problem-solving task, rather than with anaffordance-effectivity relation (see, e.g., Birch & Rabinowitz, 1951; Maier, 1931).More in the spirit of Köhler (1925; see also, Birch, 1945) is a study by van Leeuwenet al. (1994) that found the ability of children (9 months old to 4 years old) to use ahook to obtain an attractive toy depended, in part, on the number of transforma-tions of the hook (e.g., turning, flipping, etc.) required to align the crook with thetoy (thereby making it possible for the child to use the hook to draw the toy in-ward). For example, the toy was more likely to be obtained if the hook and toy werein contact than if they were not.

The focus on the geometric fit between an animal’s action capabilities (e.g., thesize, shape, and orientation of the animal’s end effectors) and the correspondingproperties of objects in its environment (e.g., the size, shape, and orientation ofgraspable surfaces) to be used in achieving a goal is an important first step in inves-tigations of the use of tools in goal-directed behavior. However, to investigate per-ception of what a given object affords (which necessarily occurs prior to, orconcurrently with, its actual use as a tool), we may also profit from examining therole played by the rotational dynamics that emerge as a consequence of manipula-tion of the hand-plus-tool system.

AFFORDANCES AND TOOL USE 175

Dynamic Touch as a Setting for the Investigationof Tool Use

The use of most handheld tools (consider, e.g., the use of a hammer, screwdriver, orwrench) often involves firmly grasping an object and manipulating it via musculareffort. The nature of the movements at joints, such as the wrist, elbow, and shoul-der, is rotational. Thus, overcoming the rotational inertia of the hand-plus-tool sys-tem with an appropriate scaling and directing of muscularly generated torques is keyfor an individual to use a given tool to satisfy a given intention (see Drillis et al.,1963; Turvey, 1996). To effectively and efficiently apply such torques requires de-tection of information about the controllability of the hand-plus-tool system; thatis, how much torque is necessary and how should it be directed (Amazeen & Tur-vey, 1996; Shockley, Grocki, Carello, & Turvey, 2001; Turvey, Shockley, &Carello, 1999).

Manipulation of an object by means of muscular effort is known as dynamic touch(J. J. Gibson, 1966/1983). Research over the past decade or so has shown the rele-vance of rotational inertia to characterizing the informational bases for the percep-tion of a multitude of object properties via dynamic touch (for reviews, see Carello &Turvey, 2000; Turvey, 1996; Turvey & Carello, 1995). Given that objects have dif-ferent mass distributions, they will resist differentially being rotated in different di-rections. The quantification of mass distribution in terms of the inertia tensorprovides a basis for distinguishing different object properties. The eigenvalues, Ik, ofthe inertia tensor refer to the resistances to rotational acceleration about thehand–object’s symmetry axes. The eigenvectors, ek, are those symmetry axes. Thegreatest resistance is given by the largest eigenvalue, I1, which has been shown to pri-marily constrain perceived length; the least resistance is given by the smallesteigenvalue, I3, which has been shown to primarily constrain object width (Turvey,Burton, Amazeen, Butwill, & Carello, 1998). The ratio of I1 to I3 is relevant to objectshape (e.g., distinguishing a hemisphere from a cone; Burton, Turvey, & Solomon,1990). Similarly, the orientation of e1, e2, or e3 (depending on which plane of orienta-tion is relevant) has been implicated in the perception of direction-relevant proper-ties such as the orientation of an object in the hand, the orientation of a limb, orwhere the hand is on an object (for a review, see Pagano & Turvey, 1998). Dynamictouch, then, provides a means for an individual to (a) perceive the properties of ahandheld tool and (b) concurrently or subsequently regulate the generation and ap-plication of torques in manipulating that tool so as to satisfy a given intention.

Perception of Affordances by Dynamic Touch

The perception of affordances is often implicit in research on dynamic touch. In themost familiar example, perception of an object’s “reach-with-ability” is addressedthrough a property that stands proxy for it—namely, perception of object length


(see, e.g., Solomon & Turvey, 1988). When the focus moves from an object’s lengthto its sweet spot—the area along the implement one would prefer to contact a tar-get—the affordance context is explicit (Carello, Thuot, Anderson, & Turvey,1999; Carello, Thuot, & Turvey, 2000; Cooper, Carello, & Turvey, 2000). Evalu-ating objects with respect to a specific function (e.g., to produce a maximum dis-tance throw; Bingham, Schmidt, & Rosenblum, 1989; or to displace targets on atable; Bongers, Smitsman, & Michaels, 1999) highlights the capabilities of thehaptic system as a smart perceptual device (cf. Runeson, 1977).

Attempts to characterize the link between rotational dynamics and affordanceshas raised the issue of the ontological status of haptic perception—in essence, askingwhat could be the natural kind descriptors unique to the haptic perceptual system.This emphasis arose from efforts to explain the classic size–weight illusion in whichobjects of a given mass feel heavier the more compact they are (e.g., Charpentier,1891). The solution to this century-old puzzle lies in a particular patterning of an ob-ject’s eigenvalues (Amazeen, 1999; Amazeen & Turvey, 1996). In particular, per-ceived heaviness is a function of resistance to movement, determined jointly by anobject’s mass and the distribution of that mass. The latter is most usefully expressedthrough scalars derived from the object’s inertia tensor, the volume (V) and symme-try (S) of the inertial ellipsoid (Shockley et al., 2001; Turvey et al., 1999):

(1)

and

(2)

These scalars constrain the level and patterning of muscular forces required tomove the object: how much force and how that force should be directed. The rele-vance of movement to perception of objects raises the possibility that a propertysuch as “weight” is ill defined with respect to the perceptual capabilities of thehaptic system. Instead, it seems that words such as “wieldability,” “steerability,” or“controllability” may be more appropriate descriptors for the proper function (cf.Millikan, 1984, 1993) of the haptic system (Amazeen, 1999; Amazeen & Turvey,1996; Bingham et al., 1989; Turvey et al., 1999).

Our series of experiments examines the properties that make a handheld objectfunctional for particular purposes. In light of the foregoing discussion of dynamictouch, we attempt to uncover the physical bases of the perception of theaffordances of handheld objects for two common functions—hammering (i.e.,pounding) and poking (i.e., displacing)—in the rotational dynamics of thehand–object system. To the extent that the appropriateness of a given object for agiven function is perceived reliably, we investigate whether its appropriateness fordifferent functions is specified by different mechanical quantities.


( ) 1/21 2 34 / 3V I I Iπ −= × ×

3 2 22 /S I I I= +

EXPERIMENT 1

The actions required to use an object as a hammer, versus as a poker, seem to be rea-sonably distinct. Whereas a hammer’s orientation changes throughout the swing, apoker’s orientation must be maintained level as it is pushed. Moreover, hammeringrequires primarily rotational movement, whereas poking requires primarilytranslational movement (which nonetheless entails getting the object’s rotationaldisposition under control to effect the linear translation). A tool user’s selection ofobjects that might best serve these distinct functions is likely to be based on the pres-ence (or absence) of physical attributes of the objects that may promote (or impede)these distinct movements. Given the relevance of rotational dynamics to how ob-jects can be controlled and moved, the affordances of hammering and poking shouldbe distinguishable by dynamic touch. Contrast a paradigmatic hammer with a para-digmatic poker. Whereas the former is a shorter and somewhat top-heavy imple-ment, the latter is an elongated and somewhat bottom-heavy implement. Thepreceding are simply colloquial descriptions of what is more formally captured bymass distributions quantified by the inertia tensor. The suggestion is that not onlyshould these affordances be distinguishd perceptually, but their underlying informa-tional bases should be distinct as well. Previous research has already shown thatperceivers can distinguish between the location of the tip of a handheld object andwhere on the object they would like to strike another object (i.e., the length specifiedby I1 vs. thesweet spot, specifiedby I1/staticmoment,which isaquantity referredtoasthe center of percussion [CP]; Carello et al., 1999; Carello et al., 2000; Cooper et al.,2000). Here we are concerned with what amounts to a value judgment—how wellwould this object serve as a hammer or a poker? Does it, in fact, afford hammering orpoking? We expected that (a) objects rated as being better for hammering would bedistinct from those rated as being better for poking and (b) the properties of goodhammers and good pokers would have distinct physical dependencies.

Method

Participants. Nine introductory psychology students at the University ofConnecticut participated in Experiment 1 in partial fulfillment of a course require-ment. None reported a neurological or skeleto-muscular disorder or recent injury.

Materials and apparatus. Nine objects were constructed from woodendowels (1.0 cm in diameter) with attached masses placed into standardized handles(with a 1-cm inner diameter and a 2.5-cm outer diameter). The lengths and masseswere chosen (see Table 1) so as to achieve three levels of I1:I3 (the inertial propertymost relevant to shape) crossed with three levels of CP ratio (the proportional dis-tance along the object’s length at which the greatest proportion of kinetic energy is


transferred to another object during collision; Brody, 1987). The particular ratioswere chosen to make the objects as distinct as simple exemplars of a hammer (i.e., awooden kitchen mallet) and a standard billiards cue. Inertial values were calculatedrelative to a rotation point about the wrist (for details concerning this convention,see Turvey et al., 1998).

Procedure. A seated participant placed his or her right arm through an occlu-sion curtain. The right forearm was supported on an armrest such that wielding wasonly possible about the wrist. Ratings of hammers and pokers were collected inblocked fashion, and ordering of conditions was counterbalanced across partici-pants. Prior to data collection in each condition, the experimenter demonstratedwhatever function was to be rated in that condition. To demonstrate hammering,the experimenter showed the participants a vertically oriented wooden rod firmlysituated in a wooden block and used the shaft of another rod to pound the rodthrough the wooden block. To demonstrate poking, the experimenter showed theparticipants a horizontally oriented wooden rod loosely situated in a wooden blockand used the tip of another wooden rod to poke the rod through the block. In thehammer condition, the participants were told that they would be rating objects thatthey would use “like they would use a hammer.” In the poker condition, the partici-pants were told that they would be rating objects that they would use “like theywould use a billiards cue” (with the exception that they would only use one hand inmanipulating the experimental object, whereas two hands are typically used in ma-nipulating a billiards cue). Participants were then handed one of the nine objects (inrandom order) by the experimenter such that the participant’s right hand was flushwith the bottom of the attached handle.


TABLE 1Object Characteristics and Ratings for Hammers and Pokers in Experiment 1

I1:I3 CP/L Length (cm) Mass (g) Hammer Ratings Poker Ratings

10:1 .40 75 278 4.0 4.510:1 .67 42 162 2.0 4.610:1 .91a 30 256 4.0 3.920:1 .40 95 288 4.9 4.520:1 .67 53 167 3.2 4.620:1 .91 39 261 4.9 4.430:1 .40b 105 292 5.4 4.630:1 .67 60 271 5.4 4.430:1 .91 47 165 3.6 4.7

Note. I = eigenvalue; CP/L = center of percussion/length.aBased on a standard billiards cue. bBased on a kitchen mallet.

Participants made perceptual reports by means of a 7-point rating scale, rang-ing from 1 (not at all suited for the task of hammering [poking]) to 7 (ideally suitedfor the task of hammering [poking]). This scale was posted on the wall in front ofthem, and only the lowest and highest possible ratings (1 and 7, respectively)were operationally defined for the participants. Participants were allowed towield the object about the wrist in any manner that they felt might best enablethem to rate the object for the particular function. Periodically, before handingthe object to the participant, the experimenter reminded the participant of theirtask by asking, “How good is this object as a hammer (poker)?” Participants wereinstructed to wield objects as long as necessary to achieve an impression of func-tionality. After completion of the first condition, the second function was dem-onstrated, and the procedure continued as in the first condition. The sameobject was wielded three different times by each participant in each condition.

Results and Discussion

Mean ratings are shown in the last two columns of Table 1. A 2 (intentions) × 3 (in-ertial ratios) × 3 (CP ratios) analysis of variance (ANOVA) on object ratings (aver-aged over the three repetitions) showed no main effect of intention, F < 1. Overall,the objects did not differ with respect to their appropriateness for the two functions(as hammers, M = 4.1; as pokers, M = 4.5). Given that hammering and pokingwere expected to show reciprocal dependencies, this was not surprising. The maineffect of inertial ratio was significant, F(2, 32) = 6.24, p < .01, with ratings increas-ing as the ratio increased. The main effect of CP ratio, F(2, 32) = 7.13, p < .01, re-vealed that the middle CP ratio was rated lower than the other two, although theInertial Ratio × CP Ratio interaction, F(4, 32) = 3.66, p < .015, indicated that thiswas not so at the greatest inertial ratio. The significant interactions with intention,Intention × CP Ratio, F(2, 16) = 3.63, p = .05, and Intention × Inertial Ratio ×CP Ratio, F(4, 32) = 4.03, p < .01, revealed that hammer ratings were influencedby the particular combination of CP ratio and inertial ratio, whereas poker ratingsshowed very little modulation (see Table 1). This latter observation was verified in aseparate analysis of the poker ratings, which revealed no significant effects or inter-actions, all Fs < 1.

It is possible that the act of poking is too subtle or ill defined to allow distinctionsamong objects. Analysis of individual participant data, however, revealed that allbut one distinguished among the poker candidates. They simply made those dis-tinctions in different ways that effectively washed out the distinctions in the meandata. The intuition that a good hammer is the inverse of a good poker suggests thathammer and poker ratings should relate negatively. This was, indeed, true for 5participants. For the remainder, this relation was positive, suggesting that they didnot distinguish hammers from pokers.


Regressions of the mean hammer ratings on tensor quantities1 (in log–log coor-dinates) revealed a significant dependence on V, the volume of the inertial ellip-soid, r2 = .94, p < .0001. Regressions of the mean poker ratings for the 5participants who distinguished hammers from pokers also revealed a significant de-pendence on V, along with a contribution of the orientation of e3, r2 = .87, p <.0001. Figure 1 shows that the nature of the dependence on V is reversed for thetwo intentions.

To understand the nature of the relations depicted in Figure 1, refer again toEquation 1, the equation for ellipsoid volume. As noted earlier, V is related to themean level of force needed to move an object. The particular form of this equation(i.e., that it involves the reciprocal of the square root of the product of theeigenvalues)coupledwiththesignof theexponent intheregressions suggests the fol-lowing characterization. Hammers were rated as more effective the greater the levelof force (indexed by a smaller V) needed to move them, whereas pokers were rated asmore effective the less the level of force needed to move them. Additionally for pok-


1A measure of striking tool efficiency has been developed to reflect the proportion of force imparted tothe struck object (Drillis, Schneck, & Gage, 1963). Given the construction of our objects, this measurewas restricted in range (.87 to .97 on a scale ranging from 0 to 1), perhaps accounting for its failure to pre-dict ratings (r2 ≈ 0). Additionally, Drillis et al.’s measure quantified proportional force transferred througha striking implement to a struck surface, and not the amount of force actually applied. It is, therefore,only a measure of hammer efficiency rather than of hammer effectiveness.

FIGURE 1 Implement ratings forthe two intentions have different de-pendencies on inertia ellipsoid volume(V) for pokers, the remainder of thevariance is taken up by eigenvectororientation.

ers, the orientation of e3 was important—presumably for directing the movement byspecifying objects for which the alignment was more nearly horizontal.

In summary, most of the participants showed distinct tensorial dependencies fortheir ratings of the two functions. However, a few participants did not distinguishthese two functions—showing the same negative exponent on V for both functions.The rationale for different poking dependencies remains unclear. It may reflect dif-ferences between poking with precision, in which more control would be desirable,and poking with power, in which the production of force should be maximized. Thisspeculation is at least consistent with the signs on the exponents of V. It may also bethat limitations placed on exploratory behavior (i.e., wielding was restricted to rota-tions about the wrist) affected participant’s ability to rate objects for a poking taskthat entails radial motions. This limitation was eliminated in Experiment 3. Clearly,an object’s appropriateness for hammering can be perceived by dynamic touch, andfor the most part, an object’s appropriateness for poking is distinct from this. Theseaffordances seem to have the same detectable physical basis rooted in the object’s ro-tational inertia. However, as predicted, inertial factors seem to play nearly oppositeroles depending on which function is being evaluated.

EXPERIMENT 2

Experiment 1 demonstrates that participants rated hammers in a systematic fashionprimarily constrained by V. Given the different object configurations, of course,their actual use as hammers would have to reflect differences in how to accomplishthat function. In particular, the best striking location is likely to differ from imple-ment to implement and that should be perceivable as well. Indeed, previous re-search has shown that this location is perceivable for tennis rackets and bats(Carello et al., 1999), and its perception is constrained by CP, a quantity that is an-chored in rotational dynamics. Experiment 2 examines the relation between ratingsof hammer effectiveness and preferred strike location.

Method

Participants. Nine introductory psychology students at the University ofConnecticut participated in Experiment 2 in partial fulfillment of a course require-ment. None reported a neurological or skeleto-muscular disorder or recent injury.

Materials and apparatus. The nine objects from Experiment 1 were usedagain. A magnitude production apparatus allowed participants to indicate pre-ferred strike location, using a pulley to adjust the distance of a wooden block with apartially embedded nail as the hammering target (Figure 2).

Procedure. As in Experiment 1, participants sat in a chair and placed theirright arm through a hole in a curtain (which occluded both hand and wielded ob-


jects) and onto the armrest of the chair. They wielded the object in any manner theychose for as long as needed. Once again, two different perceptual reports were ob-tained. The first report was identical to the evaluation of hammers in the first exper-iment. The second report was of the distance at which they would place a nail tomost efficiently strike it with the object in their hand. They were asked to indicatethis location even if the wielded object did not feel like a functional hammer. Peri-odically, before handing the object to the participant, the experimenter remindedthe participant of their task by asking “How good is this object as a hammer andwhere would you place the nail to best use it as a hammer?” Each type of responsewas collected three times for each object.

Results

Ratings data. Mean hammer ratings are provided in Table 2. Ratings of theimplements as hammers in Experiment 2 were highly correlated with hammer ratingsin Experiment 1 (r2 = .93). A 3 (inertial ratios) × 3 (CP ratios) ANOVA on the ham-mer ratings revealed a main effect of inertial ratio, F(2, 16) = 4.50, p < .03, indicatingthat rating increased with an increase in the ratio. The main effect of CP ratio, F(2,16) = 5.45, p < .02, indicated that the middle CP received the lowest rating, al-though the Inertial Ratio × CP ratio interaction, F(4, 32) = 2.59, p = .056, again in-dicated that this was not so at the greatest inertial ratio. As Table 2 shows, this patternis the same as that observed in Experiment 1 (Table 1). The similarity of the mean ob-ject ratings was verified by a regression, in log–log coordinates, which again showed asignificant contribution of V with a negative exponent, r2 = .83, p < .001.

Positioning Data

Mean strike locations (measured from the wrist to the chosen location in centime-ters) are provided in Table 2. An ANOVA on these distances revealed a main effect


FIGURE 2 In Experiment 2, partici-pants adjusted the position of a nail toindicate where they wanted to strikewith the implement they were wield-ing. The implement was wielded out ofview, and the nail’s position wasvisible.

of inertial ratio, F(2, 16) = 18.25, p < .0001, indicating that preferred strike positionincreased with an increase in the ratio. The significant main effect of CP ratio, F(2,16)=6.37,p<.01,andthe interactionofCPRatio×InertialRatio,F(4,32)=2.80,p = .05, were both topologically similar to their counterparts in the ratings data (Ta-ble2).Asimple regressionofmeanstrikepositiononCPlocation(measured incenti-meters) was significant, r2 = .75, p < .03, consistent with previous research (e.g.,Carello et al., 1999). A combination of stepwise and multiple regression, however,revealed that S and V accounted for more variance, r2 = 0.96, p < .0001.

Discussion

The rating data were comparable to those from Experiment 1 in being constrainednegatively by V. The positioning data produced a dependence on V, also negative,togetherwithS,a shapemetric.Shape is aproperty thatmayplayan important role inthe transfer of energy in hammering (Drillis et al., 1963) The positioning results weresomewhat at odds with previous research on perceived strike location in which CPlocationplayedaprimaryconstraining role (Carelloetal., 1999;Carelloetal., 2000).It should be noted that a multiple regression on V and CP location was strong, r2 =.95, p < .0002, but the stepwise regression entered S instead of CP location.

Inspection of Tables 1 and 2 suggests that ratings of hammers and designatedstrike position are positively correlated, r2 = .52, p < .03. This relation may be aconsequence of the inertial constraints on a hammering task. The ratings of bothExperiments 1 and 2 suggest that in rating hammers, participants are placing a pre-mium on the transference of power from striking implement to struck surface (seediscussion of Experiment 1). The further the distance from the wrist to the objectto be struck, the larger the radius of gyration of the striking object, and the moreforce potentially applied per strike (Drillis et al., 1963). Thus, the fact that strike


TABLE 2Object Characteristics, Hammer Ratings, and Strike Position in Experiment 2

I1:I3 CP/L Hammer Ratings Strike Positiona

10:1 .40 4.0 24.010:1 .67 2.7 22.310:1 .91b 3.9 24.120:1 .40 5.1 30.020:1 .67 3.6 25.720:1 .91 5.2 29.330:1 .40c 4.6 37.230:1 .67 5.0 34.830:1 .91 4.2 28.8

aCentimeters from wrist. bBased on a standard billiards cue. cBased on a kitchen mallet.

locations are positively correlated to ratings of hammers further supports this pre-mium placed on transference of power in hammering.

EXPERIMENT 3

Experiment 1 demonstrates that whereas the ratings of hammers (and their physicaldependencies) are systematic across participants, ratings of pokers (and their physi-cal dependencies) are more idiosyncratic for participants, a few of whom did notseem to distinguish good hammers from good pokers. One possible rationale is thatthe act of poking is more varied than the act of hammering. Poking, for example, in-cludes threading a needle, stoking a fire, and jabbing with an épée, which differ intheir needs for precision and power. Furthermore, the restrictions placed on wield-ing in Experiment 1 may have been less appropriate for evaluating pokers, given theabsence of translatory motions. Hammering is somewhat more stereotyped in re-quiring a specific target to be hit with some force. Although options abound here aswell (from the quick blows of stone knapping to the solid strikes of carpentry), par-ticipants’ understanding of what is required in hammering may be more focused.This superior focus may also derive from the relative familiarity with hammeringand poking.

In an effort to better constrain the understanding of both tasks, Experiment 3elicits ratings both before and after a brief tuning task in which the participantsused an implement to hammer or poke in a prescribed way. For hammering, akitchen mallet was used to pound a vertically oriented wooden peg into a tight-fit-ting hole. For poking, a billiards cue was used to push the now horizontally orientedpeg into a looser-fitting hole.

Method

Participants. Fourteen introductory psychology students at the Universityof Connecticut participated in Experiment 3 in partial fulfillment of a course re-quirement. None reported a neurological or skeleto-muscular disorder or recent in-jury. They were assigned randomly to the hammer or poker groups.

Materials and apparatus. The same nine objects were used. As in Experi-ment 1, participants were seated while wielding and rating objects. However, to al-low for a more natural range of motion in wielding, participants placed their armaround (vs. through) an occlusion curtain. Furthermore, in this experiment, wield-ing motions were not restricted to the wrist. Participants were instructed to wieldwith any movements of their right arm (including their right wrist, elbow, or shoul-der, or all of these). The manner of reporting object ratings was identical to that inExperiment 1.


Procedure. Given the difficulties some participants had in evaluating pok-ers in Experiment 1, wielding was relatively unrestricted in Experiment 3. In par-ticular, the restraining armrest was removed, which allowed participants to movethe objects in any direction and about any of the arm joints. Prior to data collec-tion, the experimenter verbally explained the function that was to be rated. Thepretest conditions were identical to Experiment 1. After each pretest, the occlu-sion curtain was opened, and participants completed a brief training task. Forhammering, they used a wooden kitchen mallet to pound a tightly fitting woodendowel (1.25 cm in diameter) through a predrilled hole in a wooden block (1.35cm in diameter). After performing this task three times, the occlusion curtainwas closed, and participants again rated the objects as hammers. For poking, thetraining consisted of using a billiards cue to poke or push a loosely fitting woodendowel (1.25 cm in diameter) through a predrilled hole in a wooden block (1.5cm in diameter) using only one hand. Participants then proceeded to the pokerposttest. Periodically, before handing an object to the participant, the experi-menter reminded the participant of the task.

Results

Meanratings for the two intentionsare showninFigure3.A2(intentions)×3(iner-tial ratios) × 3 (CP ratios) × 2 (training) ANOVA on object ratings (averaged overthe three repetitions) reveals that the contribution of training did not reach signifi-cance,F(1,12)=3.61,p=.08(ratingsbefore training=4.1; ratingsafter training=4.5),andnointeractions involvingtrainingweresignificant,F<1.As inExperiment1, the objects did not differ with respect to their appropriateness for the two func-tions, F < 1 (as hammers, M = 4.4; as pokers, M = 4.3). The inertial ratio,F(2, 24) =2.20, p > .10; CP ratio, F(2, 24) = 2.69, p < .09; and their interaction, F < 1, did notreach significance. However, each of these interact significantly with intention. TheIntention×InertialRatio interaction,F(2,24)=3.45,p<.05, reveals thathammerratings increase with ratio but poker ratings do not. The Intention × CP Ratio inter-action, F(2, 24) = 14.18, p < .0001, reveals that the middle CP received the lowesthammerratingsbut thehighestpoker ratings. Intention×InertialRatio×CPRatio,F(4, 48) = 16.48, p < .0001, indicates that this pattern changed for the largest iner-tial ratio. Figure 3 shows that hammer and poker ratings are reciprocals of one an-other both before and after training. This reciprocity, which had characterized thewithin-subjects design of Experiment 1, was obtained in Experiment 3, although theratings of the two intentions were obtained from two different groups of participants.Ratings of hammers before and after experience in a hammering task are highly cor-related with each other (r2 = .96) as well as with ratings from the first two experi-ments (r2 = .90 to .99). Ratings of pokers before and after experience in a poking taskare highly correlated with each other (r2 = .91) as well as with ratings from Experi-ment 1 (using the 5 participants of Experiment 1 who had differentiated hammersfrom pokers, r2 = .91 and r2 = .86, with pre- and posttraining, respectively).


A parallel 2 (intentions) × 3 (inertial ratios) × 3 (CP ratios) × 2 (training)ANOVA was conducted on the average deviation of the ratings across the threerepetitions of an object to assess whether the minimal training served to focus re-sponses. The main effect of training, F(1, 12) = 8.70, p < .015, indicates that thevariability of ratings before training (20.55) was higher than the variability of rat-ings after training (14.90). This was so for both hammers and pokers; the Training× Intention interaction was not significant, F < 1. The significant interactions ofCP Ratio × Intention, F(2, 24) = 7.70, p < .003, and CP Ratio × Intention × In-ertia Ratio, F(4, 48) = 5.74, p < .001, both show patterns that complement thepatterns from the implement ratings. In particular, objects that were highly ratedshowed less variability. Moreover, the least consistently and lowest rated hammerswere the most consistently and highest rated pokers.


FIGURE 3 Mean implement ratings before and after training as a function of CP/L (center ofpercussion/length) and I1:I3 for hammers (top) and pokers (bottom) in Experiment 3.

As in previous experiments, regression of the mean pretraining hammer rat-ings on tensor quantities (in log–log coordinates) revealed a significant depend-ence on V with a negative exponent, r2 = .93, p < .0001. Regression of themean posttraining hammer ratings revealed the same dependence on V, r2 =.89, p < .0001. For poker ratings, the dependencies were on V (with a positiveexponent) and e3 (with a negative exponent), r2 = .93, p < .001, for pretrainingand, r2 = .85, p < .001, for posttraining. Although the specific dependencies didnot change after training, for both functions the posttraining regressions accountfor slightly less variance than the pretraining regressions. Figure 4 also showswhat may be a subtle shift and suggests an intriguing, albeit highly speculative,possibility. The panels on the left (pretraining) show the objects to be evenly andcontinuously distributed on the regression line. The panels on the right, in con-trast, show groupings of objects in which the ratings are more nearly equivalent.Certain objects form a group of better hammers (ratings = 5.5 to 5.8), whereasother objects form a group of middling hammers (ratings = 4.1 to 4.5), and oneobject was not considered much of a hammer at all (rating = 2.6). Similarly,there were groupings of good pokers and mediocre pokers. The less continuouschange in ratings resulted in a decrease in the amount of variance accounted forby the power functions. In some sense, as participants developed their ability todifferentiate good tools from mediocre and poor tools, object ratings convergedinto fairly distinct groups. Of course, methodological concerns (particularly themodest amount of practice that the participants received in the hammering andpoking tasks) limit the force of this speculation.

Discussion

The pretuning phase of Experiment 3 replicates the results for hammer ratings ob-tained in the comparable conditions of Experiments 1 and 2 (cf. Tables 1 and 2 andFigure 3). The same physical basis was implicated in each experiment: a depend-ency on V with a negative exponent. Similarly for pokers, the dependency apparent(at least for the majority of participants who differentiated hammers and pokers) inExperiment 1 was replicated: a dependency on V and e3 with positive and negativeexponents, respectively. The fact that the participants in Experiment 3 were al-lowed to wield in a range of motion that was more reminiscent of ordinary hammer-ing and poking may account for this increased ability (relative to Experiment 1) todifferentiate hammers from pokers.

The experiments were consistent in showing reciprocity between hammeringand poking. Across all relevant conditions, the same four objects were rated highlyas hammers and poorly as pokers. Both conditions in Experiment 3 revealed the av-erage deviation for these particular objects to be relatively low when they wererated as hammers and relatively high when they were rated as pokers. Similarly,three other objects were consistently rated highly as pokers (with low average devi-


ation) and poorly as hammers (with high average deviation). Thus, an object thatis suitable for a function is rated more consistently than one that is unsuitable. Notsurprisingly, the objects identified previously are the same objects that form thegroupings in the posttraining regressions of Experiment 3.

GENERAL DISCUSSION

This series of experiments suggests that the affordance of “hammer-with-able” isperceptible via dynamic touch and that there is a natural basis for the perception ofthis affordance. Similar to the perception of many properties of handheld objects, itseems to be dependent on a particular parsing of the object’s inertia tensor—specifi-cally, the eigenvalues of the inertia tensor, I1 and I3, as configured in V, the volumeof the inertial ellipsoid. Ratings of objects as hammers increased as V decreased.Thus, as an object shows increasing resistance to rotational acceleration about its


FIGURE 4 Implement ratings as a function of inertial constraints for hammers (top panels)and pokers (bottom panels). Before training, the fits are tighter and use the ratings range morecontinuously (left). After training, the fits are not as good and the ratings tend to cluster around afew values (right).

major and minor axes (i.e., as the object becomes thicker with the mass concen-trated farther from the hand), that object is perceived as a better hammer. This pat-tern suggests that participants were rating objects as hammers in a way that places apremium on transference of power from the implement to the struck object.

Experiments 1 and 3 further suggest that the affordance of “poke-with-able” isperceptible via dynamic touch, and there is a natural basis for the perception of thisaffordance as well. Perception of appropriateness for poking is also based on theeigenvalues of the inertia tensor configured in V, this time with a positive coeffi-cient. This indicates that ellipsoid volume is playing a different (possibly opposite)role in constraining the two intentions. Ratings of objects as pokers increased asthe V increased. Thus, as an object shows decreasing resistance to rotational accel-eration about its major and minor axes (i.e., as objects become thinner with themass concentrated nearer the hand), it is perceived as being a better poker. Theangle of e3 also played a role in these ratings, such that a more nearly horizontal ori-entation of the object’s longitudinal symmetry axis promoted better poker ratings.Presumably, such an orientation allows for better controllability of an object—aproperty that may be important in a precision poking task. This finding is consis-tent with research that has suggested that eigenvector angle underlies perceptionof object orientation (Pagano & Turvey, 1992).

This link between haptically perceived affordances and the inertia tensor of ahandheld object is a logical extension of recent attempts to rationalize the inertialcharacterization of the information of relevance to perception by dynamic touch(Shockley et al., 2001; Turvey et al., 1999). What is it about dynamic touch thatmakes the inertia tensor useful? One conjecture is that it fits with the ways inwhich we use objects (Carello & Turvey, 2000; Kreifeldt & Chuang, 1979). Whenwe grab objects—be they hammers and pokers or tennis rackets, coffee cups, brief-cases, and so on—we translate and rotate them. These interactions involve therigid body laws of motion, requiring forces proportional to an object’s mass andtorques scaled to an object’s inertia tensor. The sensitivity of the haptic perceptualsystem to the inertia tensor is a sensitivity to information required for the control ofmovement. How an object can be moved is clearly relevant to how it may be usedand, therefore, to its affordances.

Perceptual Learning

Experiment 3 provides participants with minimal training to tune them to the task.The nature of the change in performance after such training was, in some sense, notdramatic. The overall ratings did not change, and their particular inertial depend-encies did not change. Qualitative distinctions among the objects seemed toemerge, however. One speculation is that these qualitative distinctions may be ex-emplary of perceptual learning. Perceptual learning involves an increasing ability todifferentiate aspects of the flux of stimulation. Successful perceptual learning must


result in the ability to differentiate invariants (those variables in the flux of stimula-tion that do not change over transformation) from variants (those variables in theflux of stimulation that do change over transformations; E. J. Gibson, 1969). Thus, ahallmark of perceptual learning is the sharpening of a perceiver’s ability to differen-tiate among increasingly subtle (and complex) aspects of structured energy arraysthat were indistinguishable previous to an appropriate degree of practice (E. J. Gib-son, 1969; J. J. Gibson & Gibson, 1955; Pick 1997).

Thus, perceptual learning results in the differentiation of affordances subse-quent to a sufficient degree of experience. Affordances, of course, are properties ofthe environment with respect to the animal. For a given animal, with a particulareffectivity set, any given object or situation either affords a particular behavior or itdoes not. For example, for a given animal, a staircase is either climbable or not(e.g., Warren, 1984), an aperture is either “pass-through-able” or not (e.g., Warren& Whang, 1987), or an object is either reachable or not (e.g., Carello, Grosofsky,Reichel, Solomon, & Turvey, 1989).

An individual can come to discover what opportunities for action are affordedin a given situation through exploration of a given object or event. When oppor-tunities for exploration are restricted, the ability of individuals to discover theaffordances of their environment is similarly restricted (J. J. Gibson, 1962; Pick,1997). In this way, exploration (visual, haptic, etc.) aids perceptual learning inthat it serves to tune participants to those variables that specify limits on actioncapabilities in a given situation (Mark, Balliet, Craver, Douglass, & Fox, 1990;Mark, Young, King, & Parsche,1999). Exploration, resulting in perceptual learn-ing, may aid a perceiver in distinguishing those objects that afford a given actionfrom those that do not. Although two objects may differ in some respects, theymay in fact be functionally equivalent given a particular animal’s actioncapabilities.

Likewise, even though objects may be similar in some respects, they may in factbe functionally distinct given the animal’s action capabilities. Thus, perceptuallearning may result in an increased ability to determine whether objects are func-tionally equivalent (and which are not) for a given purpose. The grouping shownby the power equations for both hammering and poking in all three experiments isan example of the former phenomenon: They show a differentiation of objectaffordances given modest exploration of, and experience with, those objects. Inthis particular case, participants learned to differentiate objects that afford ham-mering from those objects that afford poking through haptic exploration. It is inter-esting to note that participants seem to show an increased ability to differentiateobjects given enhanced opportunity for exploration (cf. methodologies of Experi-ment 1 and Experiment 3; see also Pick, 1997).

The groupings observed in the postconditions of Experiment 3 are an exampleof the latter phenomenon: They suggest that sets of implements had become func-tionally equivalent (and, thus, received highly similar ratings) after experience inthe task. That objects are clustered in terms of perceived affordances allows an eco-


logical take on the issue of categories with respect to “ecologically reliablepartitionings” of substances, surfaces, places, objects, or events (Turvey & Shaw,1999).

The type of abstraction achieved via perceptual learning may underlie the moretraditional notion of concept formation in both infants and adults (Pick, 1997).Similar to the more traditional notion of concept formation, successful perceptuallearning yields a generalized ability to solve a wide range of problems. Additionally,just as the relative effect of a single trial on learning is vastly more effective after thedevelopment of the appropriate abstraction or generalization, a single trial is alsovastly more effective after the acquisition of the appropriate learning set via per-ceptual learning (Epstein, Hughes, Schneider, & Bach-y-Rita, 1989; Harlow,1949). This may have been the effect (albeit a very limited one) of very few trainingtrials in Experiment 3.

When One Affordance Becomes Another

Not only is the affordance of an object or event dependent on the action capabilitiesof a particular organism (i.e., effectivities; see Shaw & Turvey, 1981; Turvey &Shaw, 1979), but it is also dependent on subtle variations in properties of the objector event in question. For example, slight increases in the grade of a slope will even-tually transform a surface of support into either an obstacle to locomotion or a dan-gerous falling-off place (Fitzpatrick, Carello, Schmidt, & Corey, 1994; J. J. Gibson,1977; Kinsella-Shaw, Shaw, & Turvey, 1992). This generalization applies equallywell to the properties of graspable, detached objects in the environment as it does tosurfaces of support. Thus, subtle variations in any tool alter the functionality of thattool for a particular purpose.

J. J. Gibson (1977) elucidated this concept by describing what seemed to be theminimum requirements for an object to afford various functions. He pointed outthat whereas an elongated object of moderate size and weight affords wielding,hammering, or raking, a rigid object with an edge affords cutting or scraping, and agraspable rigid object of moderate size and weight affords throwing (for a similartaxonomy, see Reed, 1996, p. 120). Of course, any given object affords many func-tions, but a given object may be better suited for one particular purpose than for an-other. Slight changes to the properties of the object may make it even better suitedfor a particular purpose. This shift in perceived object affordances with subtlechanges in object properties is made explicit in the experiments presented here byshifts in ratings of functional utility with changes in inertial properties. The factthat the functions evaluated here were, in some sense, opposites makes such shiftsespecially evident.

A central tenet of the ecological approach to perception is that the properties ofan object structure energy distributions lawfully, thereby providing informationspecific to those properties. This lawfulness holds even when the property in ques-tion is as rich as the suitability of an object for a particular function (J. J. Gibson,


1977; Turvey, 1992). Information specifying environmental properties can be de-tected provided that (a) the properties structure energy media reliably and (b) suchstructure is resonant with the perceptual capabilities of the organism (J. J. Gibson,1977; Turvey, Shaw, Reed, & Mace, 1981). These requirements can be seen as an“ecologized” version of Drillis’s (1963) claim that efficient tools must be “adaptedto the senses of the operator.”

ACKNOWLEDGMENTS

This research was supported by National Science Foundation Grant SBR97–09678. We thank Robert Shaw for helpful discussions on intentional dynamics,Leonard Katz for assistance with statistical analysis, and the staff of T&M Distribu-tors in Willimantic, CT, for providing us with information concerning the physicalmagnitudes of billiard cues. We also thank Claire Michaels and John Pittenger fortheir helpful comments on an earlier draft of this article.

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Affordances and Inertial Constraints on Tool Use

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