Perceiving Affordances: Visual Guidance of Stair Oimbing

William H. Warren, Jr.University of Connecticut

How do animals visually guide their activities in a cluttered environment? Gibson(1979) proposed that they perceive what environmental objects offer or qfford foraction. An analysis of affordances in teTms of the dynamics of an animal­environment system is presented. Critical points, corresponding to phase transitionsin behavior, and optimal points. corresponding to stable. preferred regions ofminimum energy expenditure. emerge from variation in the animal-environmentfit. It is hypothesized that these points are constants across physically similarsystems and that they provide a natural basis for perceptual categories andpreferences. In three experiments these hypotheses are examined for the activityof human stair climbing, by varying riser height with respect to leg length. Theperceptual category bauDdary between "climbable" and "unclimbablc" stairs ispredicted by a biomechanical model, and visually preferred riser height ispredicteid from measurements of minimum energy expenditure during climbing..It is ooocluded that pen:::eption for the control of action reftects the uoderlyingdynamics of the animal-envir6nment system.

How do humans and animals visually oon­trol their actions with respect to the surfaces.objects, and events of the local environment?During locomotion, for example, an animalsuccessfully adopts a path through clutteredterrain, selecting surfaces that will supportits weight and posture, avoiding obstacles andprecipitous drops, and tailoring its gait to

The research reported here was performed as part ofa doctoral dissertation at the Uni~ity of Connecticut,with support from a National Science Foundation Grad·uate Fellowship and the Univenity of Connecticut Re­search Foundation. Preparation of this article was wp­ported in pan by a postdoctoral National Research5ervice Award (NS07111~1) from the NationallnstitUtcsof Health, sponsored by the UniYenity of EdinbufJh.

I wookllike to thank,Rober1 Shaw, Michael Tunoey,Jim Todd, Peter Kugler, David Lee, SCott K.ebo.. LenM&I"k, and S¥erter Runeson for their consultatMln andcommenb 011. earlier drafts of the manuscript. My pttitOOealso extends to GeorJe von Cochran for help in seeurill&the rather nOId equipment, ToYa Clayman. Linda. Rieser,and Andy Warner lOr their asaistanoe in the data eoUectiOD.and Linda Ferrell, Jean Sava&e, and Diane Harveaycsfor their aid with the research and prepaia.tion of themanuscript.

Requests for reprinb should be sent to William H.Warren, who is DOW at the Walter S. Hunter laboratoryof Psycholcgy, Brown UnNersity, Providence, Rhode Is1and02912.

uneven (Vound. Recent work by Riccio andE. J. Gibson (1983) has shown that eveninfants who are just learning to walk performdiscriminative actions with regard to travers­ibl.e and nontraversible surfaces. What is therelationship between perception and actionthat makes such oriented activity possible?

Affordances

J. J. G;bson (1958, 1977, 1979, 1983)proposed that animals visually guide theirbehavior by perceiving what environmentalobjects offer or afford fOr action, An afford­ance is the functional utility of an object foran animal with certain action capabilities.Specifically, it is the combination of environ­mental properties that supports some activityfOr a particular animal: "The affordance ofanything is a specific combination of itssubstance and its surfaces taken with referenceto an animal" (1977. p. 67). Affordances arethereby based in material properties of theanimal and the environment and exist whetheror· not they are being perceived.-

, Thus. an affordanoe does not chanae with the needor $lite of the perceiver. This contraslS with yoo UeUuu's(I934/19S7) concept of the UmIW/I, Lewin's (1935)

683

684 WILLIAM H. WARREN, JR.

To determine whether a given path affordslocomotion, the behaviorally relevant prop­erties of the environment must be analyzedin relation to relevant properties of the animaland its action system: surface rigidity inrelation to body mass, surface contours inrelation to gait. passage width in relation tobody dimensions, and so on. Thus, if ananimal guides its activity by perceiving aC­Cordances, it must be capable of perceiv­ing the relationship between environmentalproperties and properties of its own actionsystem. This implies an intrinsic or "body­scaled" metric for the analysis of visualinformation and perceptual-motor control(Fitch & Turvey, 1978; Lee, 1980; Warren &Kelso, 1984; Warren & Shaw, 1981) as 0p­

posed to an. extrinsic or absolute metric.A number of studies in the literature ex­

emplify the perception of affordances by avariety ofspecies. In studies of visually guidedjumping in frogs., for example., Ingle andCook (1917) found that the frequency ofjumping through an aperture dropped from75% to 25% when the width of the openingapproached 1.3 times the width of the frog'shead. Thus, the frog apparently detects a~ertures that afford passage for its specificbody size. In a study of the attack behaviorof the praying mantis, Holling (1964) wasable to predict the prey radius that elicitedthe highest frequency of attack responses,based on an analysis of the grasping capabil­ities of the insect's forelimb. Hence, the man·tis perceives the size of prey that optimallyaffords grasping. A similar result has beenfound for human grasping (Hallford, 1983).

concept of ....Ience, and Koffka's (1935) concept ofdemand character. Although alfordanccs themselves donot chan&e with need, an alfordance may be seJectivelyattended to. When a rock of a certain size, shape, andwciaht affords both thl"O'Ning and poundill&o the fact thatI penon in need of a hammer attends to certain aspccuor the rock does not alter iu prqleI'tics or iu utility forboth activities (sec Gibson, 1979, p. 138-139: Gibson.1982, p. 410). Affordances bear a dosa" resemblance toTolman's (1932) concept of sign gestalt, the externalrelatM:lnS amona objects and their properties that supponpurposio.oe behavior. Gibson 1l'Jue5, however; that Suchrelations can be dirmly pe:rt:eived without a prior asso­ciatioa, set, or mcans-eod readiness.. It is inttte:sti1l8 thatboth Gibsorl and Tolman were 51udenu of Holt.

Finally, Branch (1979) has observed thatSouth African east-ooast limpets (clams)shorter than 30 mm in length retreat from apredatory whelk. whereas larger individualsattack the predator by battering it with theirsheU. This boundary shifts to 43 mm forweSt-coa5t limpets, where the whelks arelarger. Thus, the affordances of attack andretreat are determined by the relative size ofpredator and prey.

Such affordances are grounded in materialproperties of the animal and its environment(see Turvey, Shaw, Reed, & Mace, 1981).These properties may be described not onlyby geometric variables. such as the objectsizes and body dimensions required for grasp­ing or passing through apertures, but also bykinetic variables such as mass., force, friction,elasticity, and work, which are relevant tometabolic energy exchanges (Warren, 1983;Winter, 1979). With regard to human I~motion, for example, the elasticity or com­pliance of the surface of locomotion has beenshown to affect energy expenditure and toprunning speed (McMahon & Greene. 1978;Pandolf, Haisman, & Goldman, 1976; Soule& Goldman, 1972). Thus, the dynamics ofthe animal-environment system defined bygeometric and kinetic variableS determine thepossible activities and energetically optimalcourses of action in any situation-I.e., whatthe situation affords for action. A specific setof values of the animal and environmentalproperties that are relevant to a given activitywill be called a dynamic animal-environmentfit. 2 The purpose of the present study is tooffer a precise description of the animal­environment fit for the activity ofstair climb­ing and to determine whether perceptualcategories and preferences relevant to theguidance of this activity reflect the underlyingdynamics of the system.

I An affordance constitutes one pcrspc:cthoe on theorganism-environment fit, construin& environmentalproperties with reference to an orpnism. Tun'e)' andShaw (1979) have introduced the (:OIJlplcmentary term,.ff«1i,ily for the action capabilities of In orpnismwithin a particular environment This provides the rcci~

rocal pcnpcctivc on the orpnism-environmcnt fit, con·struina orpnism propcnic:s with refcrcnoe 10 the envi­~-,

PERCEIVING AFFORJ),t"NCES 685

Stair Climbing

The stairway is a basic modification of thenatural environment to scale it to humanuse. Rights of stairs are found in many earlycultures from neolithic Cyprian vilrages tothe ruins ofearly Egyptian and Mesopotamianbuildlags (see Fitcb, Templer, & Corcoran,1974; and Templer, 1975, for an architecturalsurvey). The activity of stair climbing is aspecial case of human bipedal locomotionthat is metabolically demanding. requiringup to 15 times the energy expended in walkingthe same distance on the level. Unlike simplegrade walking, the stride length and lift workdone on each step are prescribed by thestairway's dimensions, so tbat an optimal gaitcannot be freely adopted. Thus. to a greatextent the metabolic efficiency of climbing isdetermined by lhe fit between the dimensionsof stairway and climber.

The precise formulation of a golden meanfor stairway dimensions bas been a matter ofdispute since the time of the Greeks, withrecommendations offered by Vitruvius in tbe1st cenlury Be (1960), Alberti (1485/1955),and Palladio (I570/l9~5). The first formalmodel was offered by the French architectFran~is Blondel (1675-1683), who reasonedthat SInce a comfortable pace length was 24French royal In. horizontally and 12 in. ver­tically, 2 in. should be subtracted from thetread depth (T) for every inch of riser height(R):

2R + T= 24 in. (1)

This idea was widely adopted and remainsintact in many of hxlay's building codes,such as the National Fire Code (1978; seerelated .versions in National Building Code,1976; Ramsey & Sleeper, 1970). Aside fromtheir dubious biomechanical basis. such rulesare indeterminate, permitting a range of riserand tread combinations that allows the ar­chitect to adapt stair dimensions to the de­mands of the space, but not always to theaction systems of climbers. The dimensionsof actual stairways vary widely, from theshort risers and oversized treads of "monu­ment steps," employed for their sweepingvisual impact, to the high risers and narrowtreads of many basement and attic stairs,

om,l,Et

~

L,..

0 ...L .. R

,I\~.

L2 T

Figu'~ J. Variables of the climber-stair system; R - riserheilhl. T" tread deplh. 0" .. stair diapW, a - pitch,g - gm'itational acrelcntion, L - lea IenJth. L 1 - thighkngth.1.J - Iowe1" Ies Jencth. '" - body mass,/-~frequency, E, .. tnetIY tKpenditure per unit time.

used to conserve floor space. HOW' might thelit between stairway and climber be: measured,and how might the limiting and optimaldesigns for stairways be determined? (Thefollowing approach to this problem was in­spired by the work of Kugler, Kelso, & Turvey,1980, 1981; Kugler & Turvey, in press; Iberall,1977, 1978; and Shaw & Cutting, 1980).

The functionally relevant variables of theclimber-stainystem are illustrated in FigureI. A relationship among these variables canbe formalized as an undetermined functionP(cf., Rosen, I978b):

(J(R, D, L, w,f, E,) ~ O. (2)

Rearranged, this equation states that the rateof energy expenditure during climbing (E,) issome function of step frequency (j) and thefour fixed variables of riser height (R), stairdiagonal (D), leg length (L), and bodyweight (W).l

, The other variables in Ftgure 2 can be derived fromthis set: tread deplh (n and stair pitch (a) tfiIonomet­rically from riser height and the stair diapW, and thi&h"""" (L,) ........... """" (i.,) ...... """" byanthrqlOmetric conSWlts (see Expcrimmt I): llfei&bl isrelated to mass by w - mg. The stair diqonal waschosen for its direct relevance 10 tbe stride length of thedimbing gail.

686 WILLIAM H. WARREN, JR.

Such dimensionless ratios of system variablesare called pi numbers and may be derivedusing the methods of dimensional analysis(Buckingham, 1914; Rosen, 1978b; Schuring,1977; Stahl, 1961, 1963).'

The climber-stair system can be describedby finding dimensionless ratios ofthe variablesin EQuation 2 by this method (Warren, 1983).Two ·of these ratios are pertinent to thepresent study:

To formally characterize an affordance,Gibson (1979) suggested that environmentalproperties "have to be measured relative tothe animal," (p. 127-128), rather than mea­sured as neutral properties in arbitrarily de­fined or extrinsic units. This can be achievedby a method of inlrinsic measurement, inwhich one part of a system is taken as a"natural standard" against which a reciprocalpart of the system (having the same dimen­sions) is measured (Bunge, 197~; Warren,1983). Thus, an animal property A may betaken as a standard for measuring an envi­ronmental property E. Procedurally, if A andE aTe measured in the same conventionalunits and are expressed as a ratio. the unitscancel and the result is a dimensionless (Le.,unitless) number that uniquely expresses aparticular animal-environment fit:

11'", "" RIL, (4)

an intrinsic measure of riser height as aproportion of leg length, and

w, = D/L, (5)

an intrinsic measure of the stair diagonal asa proportion of leg length. Specific values ofthese pi numbers capture the geometry of aparticular fit between stairway dimensionsand the climber's body dimensions.

As the animal-environment fit is varied,the affordances of the situation are alteredand qualitative features of behavior emergeat specific values of pi: critical points, c0rre­

sponding to phase transitions in behavior ataffordance boundaries, and optimal poims,corresponding to stable, preferred regions ofminimum energy expenditure, or "best fit"affordances. For example, as riser height isincreased with respect to leg length, a criticalpoint is reached at which the stair is too high

~ = E/A. (3)

to afford bipedal climbing, and the climbermust shift to a quadrupedal (hands--and-knees)gait. Similarly, as riser height is varied withrespect to leg length, an optimal point shouldoccur, yielding minimum energy expenditureper vertical meter_of travel-a candidate forthe best fit between climber and stair. Thus,affordance boundaries and optima are con­densed out of variation in the dynamic fitbetween animal and environment. Theselandmarks may be predicted on the basis ofbiomechanical models, or they may be deter­mined empirically. In the present study, theratio RIL is varied in this way while DIL isheld constant.

To illustrate how optimal and critical pointsemerge from the dynamics of a system, con·sider the occurrence of preferred velocitiesand gait transitions during locomotion. First,Hoyt and Taylor (1981) measured energyexpenditure per meter in horses during forcedlocomotion on a treadmill and found optimalvelocities with minimum metabolic cost forwalking, trotting, and galloping. They thenobserved that these horses adopted preciselythese velocities in each gait during free over­ground locOmotion. Ralston (1958; 2anugh,Todd, & Ralston, 1974) has made the sameobservation for human walking. Thus, pre­ferred behavior tends to correspond to theenergetic optimal point. Second, the trot­gallop transition also occurs at a characteristicvelocity, which can be predicted across speciesas a function of body weight (Heglund, Taylor,& McMahon, 1974; McMahon, 1975). Forthe horses in Hoyt and Taylor's (1981) study,this "allometric" equation yields a value of5 mls for the trot-gallop transition, whichclosely agrees with the empirically determinedvelocity at which galloping became energeti­cally more efficient than trotting (4.7 m/s).These results suggest that both stable gaitsand gait transitions can be accounted for bydynamic optimal and critical points.

In the case of stair climbing, because thepi number RIL expresses an intrinsic ge0­

metric relationship between riser height and

~ Con\lCntly. for elfectivities. environmental propertiesare taken as standards against whidl orpnism propertiesare measured. and the re5ultin& ratios are the in­....me: AlE..

PERCEIVING AFfOROANCES

leg length, these critical and optimal valuesshould be constant regardless of the absolutesize of the climber. That is, for any twophysically similar systems (governed by thesame Equation 2), their critical and optimalpoints occur at equal values of pi, independentof scale (Rosen, 1978a, 1978b). For example,in studies of folk norms for hand tools, Drillis(1963) found that scaling tools as a constantproportion of the user's body dimensions,such as axe handle length equal to the lengthof the user's arm, preserved the most ener­getically efficient design over variations inbody size. In this case, a constant pi valuepreserved the optimal affordance over changesin scale.

L

687

Perception and Action

With this description of an affordance interms of the animal-environment fit and itslandmark critical and optimal points in mind,let us return to the original question aboutperception for the control of action. If thevisual guidance of activity is to be successfuland economical, the perceiver presumablymust be capable of detecting both the limitson action and the most efficient paths ofaction. The central hypothesis of the presentstudy is that perceptual performance reflectsthe underlying dynamics of activity for theanimal--environment system, specifically, thatperceptual category boundaries correspondto critical points and perceptual preferencescorrespond to optimal points in the system,Second, according to the similarity hypothesis,these perceived points are constants over scalechanges in the system. The hypothesized par­allelism between perception and action im­plies that predictions can be made aboutperceptual performance from an analysis' ofaction and vice versa.

In the case of stair climbing, this meansthat the perceptual category boundary be­t\1.ttn bipedally "climbable" and "unclim~

able" risers should correspond to critical riserheight, as estimated by a biomechanicalmodel, and that this value should be thesame for short and tall observers. ExperimentI was designed to test this prediction. Simi­larly, perceptual preferences for riser heightshould correspond to the energetically optimalriser, and again this value should be constant

Fiprt 2. Biomechankal model of critical riser height,showilll idealized maximum Ic& flexion,

for short and tall observers. In Experiment2, optimal riser height was determined em­pirically by measuring the oxygen consump­tion of short and tall climbers during ascenton a motor-driven stairmill, while in Exper­iment 3 visual Preferences for riser heightwere examined.

Experiment I: Visual Perception ofCritical Riser Height

The first experiment examined the hypoth­esis that the perceptual category boundarybetween climbable and unclimbable riserscorresponds to critical riser height.

Maximum or critical riser height Rr canbe estimated from a simple biomechanicalmodel of climbing. To raise the body in agravitational field, a climber must be able toposition his or her center of mass directlyabove the base of support (the top foot). Asriser height increases with respect to leglength, a critical point, 11'c = ReiL, is reachedat which this is no longer possible, and theclimber must shift from a bipedal to a quad­rupedal (hands-and-knees) gait.

This ratio can be approximated by theriser height at which the leg would be com­pletely flexed, with all ,segments vertical (seeFigure 2). Thus,

Rr = L + L. - L2• (6)

688 WILUAM H. WARREN. JR.

NOle. L. leg .. lower ieg length. Measurements are in em.N - 12 per Jl"OOP,

Based on limb segment measurements ofparticipants in the present study (Table I),critical riser height can be calculated for thisgroup as a proportion of leg length:

R< ~ L + .44L - .56L ~ .88L (7)

Table IAfllhropomi!lfic Data for PanicipanlS;11 ExperimRnt J

'""". Hci&bt Eyebei&ht Lq LIq

ShanM 163.61 152.92 76.00 42.98SD 2.SO >7, 2.01 1.22

T>l1M 189.7S 179.13 91.33 50.39SD 3.>6 3.78 3.14 1.41

Because the lower and upper leg proportionsare appro~imately constant over climbers ofdifferent heights, this pi value is constant aswell, reflecting the necessary geometry forraising the body's center of mass in a gravi.talional field.

Thus, the perceptual category boundarybetween bipedaJly climbable and unclimbablerisers., symbolized R~/L, should correspondto .88 for both short and tall observers. Totest this hypothesis, slides of stairs with risersof 20 in.-40 in. (50.8 cm-101.6 cm) werepresented to short and tall observers, andjudgments of climbability were obtained.

Results

Cotegorizationjudgmems. The mean per·centage of "climbable" judgments is plottedas a function of riser height for each groupin Figure 3. The group curves apPear similarin shape, but the Tall curve is shifted to theright of the Short curve. A two-way repeatedmeasures analysis of variance (Riser Height XGroup) was performed on individual scores.A main riser effect showed that the overalldecrease in "climbable" judgments as a func­tion of riser height was significant, Ft4, g8) =

193.14, P < .001, and a main group effectdemonstrated that Tall participants gave sig­nificantly more "climbable" judgments thandid Short participants, fll, 22) - 38.43, p <.00 I. The interaction was also significant,F(4, 88) s 16.85, P < .001.

$i. adjuaablc wooden stairway in fiYe confiJurations:Ib - 20. 25, 30. 35. aDd 040 iD. (SO.8 ern to 101.6 ern),""';th D - 42 in.. (106.7 em); tread depth and pitch l'ViedMXOrdiQlly. The airway bMI two stePS with white ri5asand anY treads; it was pbotoc:rapbed from a distance of14 ft (4.27 m) with camera heighu of 5 ft (1.52 m) and6 ft (1.83 m). c::orrespondilll to the eye heighu of theShort and Tall groups. As $1m eliminaled intrinsicoptical information for the height of stairs relatiYe to theheighl oflhe observer, additional n1ina information wasprovided by placilll a reference object in the slide andin the testing room-in this case a wooden desk chairstanding wilh iu back up against the bottom riser.

The slides were projected from a height of S ft (1.52m) onto a wall in the teslina room. with the referencechair standing to the right of Ihe 4.1\ X 6-1\ (1.22 m X1.83 in) imase. Shorl and Tall parlicipants. run inseparate groups of one to six. viewed the appropriale setof slides while standing al a distance of 14 1\ (4.27. m).This presented approximately the same visual perspectiveon the chair in lhe te:sting room as appeared in the slides.

Procedurt. Five slides of each of the five riser heighuwere arraneed in random order and ~nted once ineach direction. for a total of SO lrials. The test sequencewas preor.ded by two practice slides showirc the tndpoinuof the test series (Rs - 20 in. and 040 iD., or SO.8 ernand 101.6 em). 0I:Jsc:0ers 'IiloUe iDSlrUaCd 10 judaJ:: wbetIxreadl Slairway looked dimbable or unclimbablc Min thenorma1 W'Irf. withoul usina your Iwlds or knees" and 10mart their responses on an answer sheet.. They then raledtheir confidence in the judgment On a scale of I 10 7.whert 1 us IttlSt SlUt and 7 was mosr ~. Theinstructions emphasized the hei&ht of the individual slairsas lhe rdevanl factor and related riser height to chairhei&ht in the two practice slides, which VlUC identifiedas the endpoinu of the series. Each test s1ide....as presentedfor approximately 8 s.. durina which time both a dimb­ability judgment and a confldencc raling were made. Theexperimenllasted aboul 15 min.

(8)T c = RdL = .88.

Method

Subjects. Two groups of male ooIlcF students. selected10 represent !he 2nd and 981h percentiles of normal adullmale heighu (Dreyfuss. 1970). were paid 10 panicipatein the experiment. The Short ItOUP contained 12 partie­ipanu with a mean heiJht of 5 ft <4.4 in. (163.7 em) andthe TaU group contained anothc:f 12 with a mean heightof 6 ft 2.7 in. (189.8 em). After the experimental session.the followilll body measuremenu Mre made UJiIll ametric .mthropomettt (Weiner &. Lourie. 1969): SWldiD&height. silli,. heii/1t. eye height. and knee height (totibial notdl). Les IeniIh was cak:ulated by subtractircsitting height from standina height. yiekfina the distanttfrom the sole of the fOOl to the ischium (bottom of thepelvis). rather than 10 lhe head of the femur. Anthrq»­metric data are presented in Table I.

Displays. Black-and·white slides were taken of a

0'

PERCEIVING AFFQRDANCES 689

..... TAlL

,,,,,

,,,,

0.' 1.0

'"_ SHOllT

I.'I.'

c,I" ,,,,,E

for the Short group, and

R",/L = 81.33 em/91.33 em = .89 (10)

for the Tall group. These values closely cor­respond to the critical ratio of .88 predictedby the biomechanical model (Equation 8).

Confidence ratings. Confidence ratingswere intended to provide a converging mea~

sure of the perceptual category boundary. onthe ~umption that uncertainty about thejudgment would be greatest at or near theboundary, and hence confidence at a mini­mum. Mean confidence ratings for each groupare plotted against riser height in Figure 5.A two-way repeated measures analysis ofvariance revealed a main effect of riser height,R:4, 88) = 57.31, P < .001, no main groupeffect, because the two U·shaped curves coverthe same range of rating values, FlI, 22) =0.87, p > .05, but a significant interaction,

, , , ,

, , ,

....... Tfoll

,,,,,,,,,,,,,,..

"_SHORT

RISER HEIGHT ([H. I"

hn_<,,,,,,,,,,,,,,,,,,,,

..Figurt J. Mean perttn~ of "climbable" jlJd&ments as,a funetKln of riser hei&ht for each &roUP.

The percentage of "climbable" judgmentsdropped from a true ceiling (100%) to a truefloor (0%) for every participant, with a meandrop of 71.5% per series interval across the50% "chance" line. The riser height at whichthe group curve crossed chance was taken toindicate the perceptual category boundary,and was equal to 26.43 in. (67.13 cm) for theShort group and 32.02 in. (81.33 em) for theTall group.

TQ examine the similarity hypothesis, thedata are replotted on an intrinsic R/L axisin Figure 4, where L is the" mean leg lengthfor the corresponding group. The resultingcurves are nearly congruent, the intrinsicscaling of riser height eliminating group dif­ferences. The category boundaries are alsoequivalent, yielding

p

ic ,E,T

C,I" ,•,•,E

R,.-/L = 67.13 cm/76.00c~ = .88 (9)Figurt 4. Intrinsic plot: mean perttn~ of "climbable"judgments as a function of RIL for each &roUP.

690 WILLIAM H. WARREN, JR.

F(4, 88) = 24.65, p < .001, demonstrating anonparallelism between the group curves.

The precise locations of the minima of thecurves in Figure 5 are obscured by thecoarseness of the riser height series used inthe experiment. To obtain a more preciseestimate. an average of each participant'slowest rated riser was calculated, yieldingmeans of 26.25 in. (66.68 em, SD = 5.74em) for the Short group and 31.67 in. (80.44em, SD = 8.28 em) for the Tall group-verynear the judgment boundaries of 26.43 in.and 32.02 in. (67.1 em and 81.3 em), respec­tively, lending further support to these valuesas perceptual category boundaries.

Plotting the confidence ratings on an in·trinsic R/L axis in Figure 6 yields nearlycongruent curves, as with the categorization

1

•

e ,,,fIoE,.eE,,TI ,,,

•,,,,,,,,,,,,,,,,,,,

1 ,

,,,,,

Figure 6. Intrinsic plot: mean confidence ratings as afunction of RIL for each g.roup.

,....,..,'.,'IC

_ SHORT

,..

data. The minima may also be expressedintrinsically:

R,,/L ~ 66.68 em/76.00 em ~ .88 (II)

for the Short group, and

Rc*/L = 80.44 cm/91.33 cm = .88 (12)

for the Tall group. These values correspondto the critical value of .88 predicted by thebiomechanical model.

•,,,,,,,,,,,,,,,,,,, ,'- .J\)y~~ .. .,,,

,,,,,,,,,,,,

"

,

•

"o,fIoE

"eE,,TI,,

Figure 5. Mean confidence ratings as a function of riserheight for each group.

RISER HEIC~tT IIM.l

~SHORT

" " " "6-6-. TALL

Discussion

The results demonstrate that both shortand tall observers judge stairways as unclimb­able at a riser height that is a constantproportion of their leg lengths. Categorizationjudgments and confidence ratings convergeon a perceptual category boundary of K./

PERCEIVING AFFOR~NCES 691

L = .88, the value predicted by the biome­chanical model. These results lend strongsupport to the hypothesis that perception isanchored in the biomechanics of activity andto the similarity hypothesis that functionalcategory boundaries are constant over changesin scale. Thus, a general critical pi value forperception and action in stair climbing ap­pears to be justified:

11'(= .88. (13)

The affordance boundary between climb­able and unclimbable stairways and the ac­companying perceptual category boundarycan thus be seen to emerge from the dynamicsof the animal--environment system. Analyzingthe biomechanical basis for critical riser heightand identifying intrinsic optical informationspecific to RIL (see General Discussion)would provide the makings of a lawful ac­count of perceptual categories without anappeal to mediating constructs such as mentalcategories or concepts.

The view that perceptual categories have anat.ural basis in critical points of dynamicsystems may be generalized to other studiesof categorization. Some research on "mental"or linguistic categories is directly related tothe affordances of objects for certain aetivitte:s.For example, Labov (1973) varied the height­to-width ratio in drawings of cuplike objectsand obtained categorizations of bowl, cup,and vase. These judgment boundaries mayhave a perceptual rather than conceptualbasis, because the categories are intrinsicallydefined by the ratio of container dimensionsthat is required to hold a flower upright orto permit a spoon to hold food or liquid.These functional requirements have conse­Quences for the shape and formal similarityof category members and, hence, for theirvisual specification.

Other research has focused on the catego­rization of natural objects, such as species ofplants and animals. In such cases, the criticalpoint occurs in the dynamics of an evolvingspecies, leading to speciation and leaving itsmark in the distinctive morphology and for­mal similarity of species members (cf. Ghi­selin, 1981). For example, CereUa (1979)studied abstract concepts of leaf patterns inthe pigeon, and found Quickly learned and

highly reliable discrimination of oak leavesfrom those of other species. Rather thanascribing such categorization behavior to apriori concepts or classification strategies, theinformational basis for categorization yieldedby the critical point must be sought: thehigher order invariant pattern that underliesthe staggering variety of oak leaves, whichpigeons can apparently detect in a singleexemplar. In sum, many category boundariesmay be perceptual in origin, having a basisin information that specifies critical pointsin affordances and other natural systems.

The first experiment provided evidencethat the perceptual category boundary cor­responds to critical riser height; the remainingexperiments go on to examine optimal riserheight.

Experiment 2: Energetics ofOptimal Riser Height

As riser height is varied with respect. to leglength, an optimal point should occur, yieldingminimum energy expenditure per verticalmeter of travel. In Experiment 2 I sought todetermine this optimal riser height empiricallyby measuring energy expenditure duringclimbing.

Optimal riser height Ro is a consequenceof two factors: First, as risers become lower,more step cycles are required to ascend agiven distance; hence total muscle activityand energy expenditure increase. On the otherhand, as risers become higher relative to leglength, energy expenditure increases due togreater Oexion at the knee and hip, andconsequently, there is greater initial musclelength (Hill, 1930; Morrison, 1970), greaterco-contraction for joint stabilization (Joseph& Watson, 1967; Morrison, 1969; Townsend,Lainhart, Shiavi, & Caylor, 1978), and higherraising of tbe lower limbs during the swingphase (Cappozzo & Leo, 1974). The combi­nation of these two factors should yield anoptimal ratio of R.,/L with minimum energyexpenditure.

A number of studies have compared themetabolic cost of climbing on stairways withdifferent dimensions, by means of either ox­ygen consumption (Bruce, Aoyd, & Ward,1967; Corlett, Hutcheson, DeLugan, & Ro-

692 WlLUAM H. WARREN, JR..

Table 2AnlhrO{JOl7letric DaJa 1m Panicipanu in Experimmr 2

weiaht HeiJht Eyebeiiht Ua LIq vo,muSubjea ... (q) (=l (=) (em) (=l (rnJlk&·min) Percentile /(JL

ShonRW 18 63.8 160.9 150.1 73.3 42.7 S7.6 90 .26AD 18 ".7 161.0 150.6 1$.7 43.6 55.9 8S ~7

LS " .n.l 159.8 !<d.9 7•.S 43.2 47.S 00 ~6

M 160.57 14'J.1I1 74.50 43.11

T>11DB 19 7lS 193.1 182.3 95.3 53.1 59.3 " .25EF 18 89.6 196.7 181.5 93.9 53.3 52.5 '" .32TC 18 84.9 191.S 171.4 92.7 S1.6 57.6 90 .24M 193.17 180.40 93.97 52.67

NOit. L. Iq; - lower lei lencth; VG.tnw. - muimal aerobic power; RJL - optimal riser height 10 leg!ength ratio.

gozensJci. 1972; Hirschberg & Ralston, 1965;Keiser, 1960; Richardson, 1966; Shinno,1971) or heart rate (Corlett el al., 1972; Ward& Beadling, 1970; Ward & Randall, 1967).The average optimal stairway·over these stud­ies had dimensions of R - 6.8 in. (17.4 em),D = 13 in. (32.8 em), T = II in. (21.8 em),and a = 32°. However, these investigators ranrelatively few (two to six) conditions withoutsystematically varying stair dimensions, oftenconfounded ascent and descent in the sametest trials. and did not report the body di·mensions of subjects.

The most complete study was performedby Lehmann and Engelmann (1933), whoran 15 conditions and found a well-definedminimum of 10 cal/kg-m on a stairway withR = 7.1 in. (18 cm), D "'" 13.4 in. (34 cm),T = 11.4 in. (29 cm), and a = 290

• However,ascent and descent were again confounded,and body dimensions were not reported.Templer (1975) employed a large multipleregression approach but obtained rather un­systematic results with no clearly definedminima. This could be due to his variationof both vertical velocity and step frequencyacross conditions. the measurement of netinstead of gross energy expenditure (see Ral­ston, 1976), or allowing climbers to use ahandrail. The only known study to reportbody heights is that of Benedict and Parmen­ter (1928), from which the leg lengths of theirfemale subjects can be estimated using an­thropometric norms (Dreyfuss., 1970). Opti­mal leg length for the one stairway tested

(R = 8.2 in. or 21 cm, D = 13.8 in. or 35.1cm) was approximately 83 em, suggesting anoptimal ratio of RJL - .25.

In Experiment 2, optimal riser height wasdetermined empirically by measuring the ox­ygen consumption of short and tall climbersduring ascent on an adjustable motor-drivenstairmill. The similarity bypothesis predictsthat RJL should be a constant over climberswith different leg lengths, because withinlimits, any similar limb systems progressingthrough the samt geometric configurationsshould require tht same energy expenditure,given that body rrtass and step frequency areequated. This optimal point was then usedto predict perceptual preferences -ror riserheight in Experiment 3.

Method

Subj«u. Sill male coIlqe students. none of whom~ in the perceptual studies. were paid to participatein this experiment. The three Short participants ~ I

mean hei&hl of ~ It. 3.2 in. (160.6 em). and the threeTall participants~ a mean height of 6 ft 4.3 in. (193.8em). Maximal aerobic power I'VOJ mall) was estimatedfrom retO'lIUy heart Rle usi.. I steP test (McArdle,KItch. &. Kitch, 1981); the participants rar.,cI from the60th 10 the 95th male populatiOll perttntiks. None ofthe participants 'iloCI"e smokers or team athletes. Anthro­pometric dati appear in Table 2.~ipmm. Test triall were run on an adjUSUlble

slairmiU driven by. variabl~motor (the same onecbcribed in Richardson. 1966, and Fitch, Templer, &.Corcoran, 1914). A panicipant could climb Min p1aoe"It a specified step frequc:nc:y for an indefinite period oftime and perform an amount of work equal to that 01'1 afixed stairway. Sill'. stairway conditions were designed to

PERCEIVING AFFORDANCES 693

aM:l' the typical uchi.UlCturaJ ranee of riser heiabts: Rs •S. 6. 7, 8. 9, and 10 in. (12.7 em 10 2S.4 em), with D.14 in. (34.3 em); tread Ind pileh Ylried accordinsIy. Stepfrequency was Iixed II f - SO steps/min, based on thestandard practice of usina constanl frequencies. and onTempler's (197S) empirica1 equation shoowina lhat 5lepfrequency is approximalely constant in free dimbilll0Ytf this r&IlF of Rairqy conditions (see Warren, 1983,for a diJclw,ion). Identical values of D lad/for the two1fOUP5 introduced sliJht violations of F<JII'lC'I.rlc andkinematic similarity. which will ~ consida'ed in thisexperiment's Discussion.

Gas samples were collected in • DouaJas bag mounledal head level, the dimbtr breathina throuah a rubbermouthpiece with a modil\cd two-way Qtis.-McKerrowvalue. The volume or upiml air was mel$UmI with aPRcition wet-test meter. and O:! and~ analyses wereperformed with I 8edman &2 oX)'lm anal)'7.c:r equippedwith Dricrite and soda-lime circuits. Ambienl temperatureand p«:s.sun: were monilored with a Wekh lhermomelerlbarometer. The tlte of OX)'Itn uptake (Ii ten/min STPO)was calculated by computer and converted 10 rllte ofeneJl)' upendilure (kc:ablmin) by multiplyina by 4.82S.the caloric equiYllmt for a mixed fat and carbohydratemetabolism.

Pro«du,~. Testina involved dally l-hr sessions for 19consecutive weekdays. The first was • practice session;!hen panicipants rca:ived two lest Irials per session forthe remainder of the uperimcnl. The six stairway con­ditions wen: 1'\10 in I ra.ndom order, with six ronsecuilioetest trials in each condition.

The tests empk))oed a acady-sute ooI.lel:tic.l method.A test session consisted or I 2O-min rest period followedby • S·min exercise bout, including 4 min of warm-upexercise and a I·min sample ofexpired •.ir. After another20-min rest period. a second ttst trial was run. Pilot testshad indicated thai a metabolic ~eady-state was reachedwithin 2-4 min ofexcn:ise in all uperimental conditions.It !lad abo been determined thai a ~ep frequency or SOa1Jowed an Xl"Obic metabolism to be maintaiDed in themost stfeDuous (R - 10 in.) cooditioD, ensurilll thaiOlYltn uptake M:IIIld ~ratdy rellect tota1 energy ex­penditure. A eheclc was provided by rnonitorill& thew:ntilatory equivalent (ratio of expired air to oxygenconsumed), whtch remained within a f'allIIC of 19.4 to26.7 for all participants,. indicatirc that an aerobic mo­tabolism was maintained in all uials.

Participants wore gym dothe5 and tennis shoes anddid nOl eat, exercise, or drink coffee. alcohol. or dairyproduC15 for 2 hr prior to lestina. They were in5lruetedto climb normally withoul touching the stairmill handrails.Body ~ight without shoes was measured in each sessionon • balancc ICale.

Results

Metabolic rate is plotted as a function ofriser height in Figure 7. Each data pointrepresents the mean of six trials for eacbparticipant.) In accordance with acceptedassumptions for the analysis ofenergetic data(see Ralston, 1976), the data for each group

were fit with a quadratic equation by least·squares multiple regression, and the resultingcurves are also shown in Figure 7. Theregression equation for the Short group is

E, - U81R' - 10.680R + 106.420, (14)

where E, is caI/kg-min and R is riser heightin inches. This equation fit the data with amultiple correlation of R = .994, and an Ftest was significant, F{2, 12) ,. 501.95, p <.00 I. For the Tall group the regression equa­tion is

E, - .110R' + 1.391R + 49.870, (II)

with, a correlation of R = .992, F{2, 15) =461.168, p < .001.

The data were transformed to energy ex­penditure per vertical meter (dividing E, by fand multiplying by the number of risers permeter), and the fining equations and groupmeans are replotted in Figure 8. The resultingvalues were comparable to those found inother studies under similar conditions ofcon­tinuous asoent.6 A twc>way repeated measuresanalysis of variance (Riser Height X Group)was performed on the transformed data.,1

yielding a significant main effect of riserbeight, F{5, 20) E 57.87, p < ,001, a signifi­cant group effect. F{I, 4) ::: 14.44, p < .05,and a significant interaction. F{S, 20) ,. 5.22,p < .01.

To locate the minimum of each function,the transformed fitting equations were differ­entiated, set equal to zero, and solved for R.

'To eliminate I potential source of error, dall fromthe Short group in the Il)..in, condition~ excludedfrom the analysis. In this extreme position the limit ofthe tread mechanism was swpasscd, resulting in springlike,slightly rocking treads that could aid tbe ascenl oflight~isht climbers. ~ment ICSIlI indicatedthat the heavy Tall dimbers hit bottom on the roeki..treads but that the li&bte:r Short dimbcn did not andthus could take adYlIltaae of a 3P"'iftlboard dfect.

~ R:r eumple, in tbc lHn. ccnditioo, tDeIIY expenditurewas 13.4 c:alJk&-m for the Short group and 12-6 c:al/ka:­m for the Tall group. Rkhardlorl (1966) obtaiDed 13.3cal/ka-m (with R ... 7.76 in.; D" 13.3 in. (33.78 em];/ ... 62), and 8eDedict and Parmenter (1928) found 11.9cal/kl-m (with R ... 8.3 in. {21.08 em), D ... 13.8 in.•/ - 45) both with femaJe sub;eds.

'The missing data poiots in the Short lO-in. condition~ n:pIaccd with values from individual fimna equationsfor the analysis of varianoe. .

694 WILLIAM H. WARREN, JR.

This yielded optimal riser heights of 7.72 in.(19.61 em, 13.295 cal/kg·m) for the Shortgroup and 9.52 in. (24.18 em, 12.501 cal/kg-m) for the Tall group.

To examine the similarity hypothesis, thegroup curves are replotted on intrinsic axesin Figure 9, where the ordinate is the ratioof total energy expended in one step cycledivided by vertical work performed in thatstep cycle, a measure of the inverse of ec0­logical efficiency (Warren, 1983). This rendersthe curves nearly parallel and verticallyaligned, although not congruent, indicating

that, under the experimental conditions, Tallclimbers are more efficient overall than Shortclimbers. Expressing the optimal riser heightsintrinsically yields

·l4/L ~ 19.61 cm/74.50 em ~ .26 (16)

for the Short group and

RoiL.., 24.18 crn/93.91 em:: .26 (17)

for the Tall group. The optimal ratio for eachparticipant, based on individual fitting curves.is given in Table 2.

,,

eAlIKe IS

"I"

10

,,,,

x ,.,.P

" 0,,2',,,

5 • 7 8 • I • 11 12

RISER HEIGHT UN. )

SHORT TAllx x x A. ••• 08

••• lS 000 EF••• •• DDD Te

Figwrr 7. Rate of energy expenditure (in caklries per kilor;ram of body v.cig,ht per minute) as a functionof ri$ef hcilhl for each subject. (Solid symbols represent Sbon subjccu: hollow symbols reprt:5m1 Tallsubjects. The tuna are fit 10 each group's data.)

PERCEIVING AFFQROANCES 695

•

,,,",•"

,,,,,,,,,•,,,, ,,,

".......... - ... - .... j---,

•

are based on biomechanica1ly Questionablestandards and other architectural considera­tions. The data help explain the oft-notedcomplaints about monument steps, with their5-in. to 6-in. risers and deep treads, reiteratedby many participants in the present study.Architects have long employed monumentsteps in the belief that a gentler slope is easierto climb and that it is aesthetically pleasing,providing an imposing visual pedestal formajor buildings. But as is apparent in Figure8, far from making long flights of steps easierto climb, low risers increase total energyexpenditure by 15%, and deep treads oftenmake an efficient stride length impossible aswell. This suggests that part of the aggrandiz­ing effect of monument steps may derivefrom increasing the actual "energetic" dis­tance to the summit.

,.

• ,RISER HEICHT lIll.}

Figur~ 8. Melin ellef1Y upendilure (in calories perkikl&ram of body weiaht per vertical meter) as a functionof riser height for each group. (The data and fitlingcurves arc transformed from Figure 7. Minima areindicated by solid circJes.)

Discussion

The results indicate that the riser heightrequiring minimum energy expenditure isjust over one quarter of leg length for bothshort and tall climbers. This finding is takenas evidence of an optimal point in thec1im~r-stair system:

••• SHORT 6 •• TALL

••

,• ••,,,

••

,,,,,,,,,'\ t,,,

"'r----This value is close to the optimal ratio of R.JL ....25 determined from Benedict and Par­menter's (1928) data for women climbers.The result also supports the similarity hy­pothesis that the optimal point is a constantover scale changes in the system.

Optimal riser heights of 7.7 in. to 9.5 in.(19.5 cm-24.1 cm) are considerably higherthan those found in common stairways, which

.........--~--~--~

F~ 9. Inlrinsic plot; inYene d'I1ciency (energy expendedper step cydc/WOrt. done per S1tp cyck) as a function ofRIL (The filting CUO'eS are lransformed from Fllure 8.Minima are indielted by solid circles: the arrows indicatevisuaJ riser preference as detemlined in Experimenl 3.)

R,/L : .26. (18)

G.' G·'

'"--.-G·' G·'

"'"

6% WlLUAM H. ""RREN. JR.

These findings argue for the replacementof standard monument steps with an CTlo­nomically sound design, incorporating higherrisers and shallower treads. Revised architec­tural guidelines should be based on furtherresearch with both women and men duringdescent as well as ascent; they must also takeinto account the problems faced by children.the elderly, and the handicapped in climbinghigh risers (Corlett et al.. 1972). Consideringthe present results for ascent, a tentativedesign recommendation for the general pop..ulation would be a riser height of approxi­mately 7 in. (17.8 em), with a stair diagonalof 14 in. (35.6 em).

The statistically significant difference inoverall efficiency between the Short and Tallgroups could be accounted for by slight vio­lations of similarity in the experimental con­ditions. First, for true geometric Similarity,stair diagonal D should not have been heldconstant at 14 in. but varied as a proportionof leg length (as in Equation 5). It is known,for example. that preferred stride length inlevel walking varies directly with leg length(Dean, 1965; DuChatinier, Molen, &. Roz·endol, 1970; Murray, Drought, & Kory, J964).and the same should hold true for stairclimbing. This would haVe yielded a. D 3 in.smaller for the Short group. Thus, enforcedoverstriding by Short participants could havereduced their efficiency in all conditions.Second, holding step frequency constant at50 steps/min for both groups introduced aviolation of kinematic similarity (Gunther,1975). Treating the swinging leg as a simplependulum, its natural frequency (requiringminimum energy expenditure) would havebeen higher for the Short participants thanfor Tall participants; such a tendency forpreferred step frequency to vary invenelywith leg length has been observed in levelwalking (Booyens &. Keatinge, 1957; Dean.1965; DuChatinier et aI., 1970; Workman &.Armstrong, 1963). Thus, the experiment'srelatively slow step frequency could havereduced the efficiency of the Short groupmore than that of the Tall group. If thesetwo factors were equated. the overall groupdifference in efficiency should be eliminated.

Now that an optimal point in the climber­stair system has been identified. it can beused to predict perceptual preferences.

Table 3Anlhr()J)OlMtric DaJa 1m Participantsin Ex~ri1Mnl 3

G~p H<;a>l EyehetJht .... LIq

ShonM 164.52 153.SO 76.98 .0.85SD 4.00 J.54 2.97 2.05

T~I

M 190:65 ISO.13 92.99 51.38SD 4.29 3.86 3.53 1.99

Nou. L. leg - lower leg 1cflilh. Meuuremcnts are in em.N. 12 per group.

Experiment 3: Visual Perception ofOptimal Riser Height

Experiment 2 determined that the energet·ically optimal ratio of riser height to leglength is .26 for both short and tall climheB.The present experiment examined the hy.pothesis that the perceptual preference forriser height, symbolized Roo-'L, oorrespondsto this optimal point. Slides of stairways withrisers varying from 5 in. to 10 in..(12.7 cm­25.4 em) were presented to short and tallobservers, and preference judgments 'oYCTeobtained in both forced choice and rating""ks.

Method

Subjtds. Two groups of 12 male: c::oIIqe students'NCI'e p&id 10 participate in the experimcnt, the Short&!"Oup having a mean hciaht or 5 ft. 4.8 in. (1645 em)and the Tall group having a mean Ilc:ight of 6 ft. 3.1 in.(190.7 em). Anthropometric data are prcsmted inTablc 3.' .

Displays. For the cboioc task, bIack.and-wbite slideswere taken or two adjustable wooden stairways staDdingside by side. The six sWrway COPditioas were the sameas in Experimmt 2, with riser bei&bt varyina from 5 in.10 10 in. (12.7 em 10 25.4 em) aDd stride fixed at I" in.(35.6 em). To equate the: vertica1 wcrl: specified rordimbina. the number or IlCp5 in each stairway was setso that tota1 hc:i&ht was as cIoIe as possible 10 40 in.(101.6 em). A box was centered abolooe the: top steps al aheighl of 80 in. (203.2 em). Thc'sWr'dyS WCfC placedwith thc:ir bottom IlCp5 aliped. aDd risers and treadsWCfC. painted white. No mc:renoc objects appeared in the:slides., but a si. stair from the shortest (5 in.• 12.7em) and tallest (10 in.. 25.4 em) conditions was presenlon the Boor of the testifll room be\oll' the: projectedi~. &cause or the duration or the expcrimmt, par­ticipanu remained seated 10 avoid ratitue that mightinfluenoc their judgments.. Othawise. pho!osraphic andprojection conditions were the same as in Experimmt 1.All possiblc nonidentical pairs or stai~ 'NCI'e pholO-

PERCEIVING AFFORDANCES 697'

IIISER HEtCHr 1IIf.)

_ SHOflr ...... TALL

folKllT1' 10. Mean pcrcentqe chosen as I function of riserheight for each I'OUp.

icant interaction. F(5, 110) "" 341.59, p <.001. Due to the c::oaneness of the riser series.a more precise estimate of preferred riserheight for each group was obtained by cal­culating the average of each participant'smost frequently chosen riser. yielding meansof 7.42 in. (18.85 cm. SD = 1.31 cm) for theShort group and 9.00 in. (22.86 cm, SD =1.95 cm) for the Tall group.

The choice data are plotted on an intrinsicRIL axis in Figure II. The resulting curvesare nearly congruent. eliminating the groupdHference. When preferred riser height isexpressed intrinsically. the results are

R../L· 18.85 em/76.98 em.~ .25 (I9)

for the Short grouP. and

R../L - 22.86/92.99 em •.25 (20)

for the Tall group. These values are close tothe optimal ratio of .26 obtained in Experi-

"••7•

,.,,,,,,,,•,,,,,,,,,,

I,,,,,,,,

,

,,•c,•rcHo •,,,

Choice task.. The percentage of trials inwhich each riser was chosen is presented inFigure 10. which shows the Tall group curveshifted to the right of the Short group curve.A two-way repeated measures analysis ofvariance (Riser Height X Group) was per­formed on individual scores. with a significantmain effect or riser height. F(5. 110) - 447.00,P < .001. no main group effect. because thetwo U·shaped curves cover the same range ofscores. F( 1. 22) = 0.63, p> .05, but a signif-

ResullS

~ in each Id\-ri&ht positioa. for a total, of 30

For the rauna task. slides v.cre ldenticaI except thatonly one stairway Ippeared in each. Total stairway hei&htwas IS close IS possible to 40 in. (101.6 em) and the bollwas centered above the top step.

Proadufe. All panicipants received the choice taskfirst and the ratina WIt second, each preceded by a setof instructions. For the choice Wk, siidcs~ arn.naedin a random order and presented once in each direction,for I total of 60 trials. The test sequence was prec:cdcdby two practice triaIs. Iirst a .s-iD.-ID-in. (12.7 cm-25.4em) pW, and thea a 7·in.-I-iD. (17.8 em-20.3 em) paiLParticipants were told to think about "'sIairs thai are·eitheF toO hi3h for you, 10 that each 5leP requires a lotof cfl'ort. or toO $hort for you, 10 that you spend a lot ofcfl'on takina many steps but tettirc nowhcrt" They v.crethen instfUCtCd to indkate on an answer sheet which ofthe two sWl'WI)'5 would be ~more comfortable for youto climb to the top~ in ordef to put I tennis ball in theboll, climbing one steP at I time It a comfortable speed.It was Clplicitly stated that the stairways always wenl upto the same total height, and the two steps in the testingroom were identified IS the endpoints of the te51 series.corrcspondins to the stairways in the first practice slide.

For the ratins task, slides of the six stairways werepresented in a random order for a [otal of 60 trials.pI"eCCded by two practice slides (5 in. and 10 in.. 12.7em and 25.4 em) which were identified as the endpointsof the test series. Participants were tokt that they 'WOUldbe sccina the same set of stairways apin. one at a time.They were instructed to rate each sWMO'ay on a ak ofI to 7, with 1 col'iespondina to 1/100'. UJ'K:Onf!onoblestairway and 7 a good, eotrifonoble staiMil2y to climb tothe top. In both tub. test s1idcs were presented forapprolimatdy 8 s. and the experiment Iastcd about30 min.

The one factor that cou)d not be controlled in theptfC'CJl(ua1 tasks was the observefs potential step fre­quent')', which could affca judgmcnlS of preferred riSCfheight. However, pilot data oa cneray expenditure by one5ubjca indicated that optimal riser height was the samewhen determined at frequencies of 30, SO, and 70 step$/min (Warren, 1983). Thus. optimal riser height appearsto be independent ofstep fnlquCflcy, and lcavioa fnlquencyunspecified in the perceptual asks should not haveaffcaed judamenlS of preferred riser hci&hL

698 WILLIAM H. WARREN. JR.

•,, ,,,,T,Ho •s,,

,,,,,,,,

, ",

When the rating data are ploUed on anintrinsic R/L axis in Figure 13, the groupcurves again appear nearly congruent. EX­pressing preferred riser height intrinsically,

Ro./L'" 18.42 cmj76.98 cm = .24 (21)

for the Short group, and

Ro./L"" 21.49 cm/92.99 cm "" .23 (22)

for the Tall group. These ratios are slightlylower than those obtained in the choice task(Equations 19 and 20).

Discussion

The results of the choice task indicate thatboth short and tall observers visually prefera riser height that is one quarter of their leglength, in order to climb through a given

,

0.' 0.2 0.' 0.'

Figu" II. Intrinsic plot: mean pem:nta&e chosen as afunction of RIL for each group.

ment 2 (Equations 16 and 17; see arrows inFigure 9).

Rating task.. Mean ratings are plotted inFigure 12 for each group. As with the choicedata, the TaU curve is shifted to the right ofthe Short curve. A t~way repeated measuresanalysis of variance on individual ratingsyielded a significant main effect of riser height,F(S, 110) :: 33.76, p < .001, a significantgroup effect, apparently due to the asymmetryof the Tall group curve, £(1,22):: 6.42, p <.01, and a significant interaction. F(5. 110) =27.19, P < .001. A precise estimate of pre­ferred riser height was obtained by averagingeach participant's highest-rated riser, yieldingmeans of 7.25 in. (18.42 em, SD "" 1.91 em)for the Short group and 8.46 in. (21.49 em,SD :: 2.39) for the Tall group. Althoughmore variable and slightly lower, these valuesare reasonably close to those obtained in thechoice task.

"...... TAlL_SHORT

, 7 • t

RISER ttE1CKT (ilL)

s

,,,,,2 ,,,,

Figure IZ. Mean ratings of "dimbat)jlity~as a runctionor riser height ror each group.

,•r •,,,

...... TAlL'"_ SItORT

PERCEIVING AFFORD.4.NCES 699

Figure 13, Intrinsic plot: mean ratings of "climbabilily"as a function of RIL for each group.

vertical distance. This value closely matchesthe energetically optimal ratio of R.JL "" .26established in Experiment 2, lending supportto the hypothesis that optimal points predictperceptual preferences and to the similarityhypothesis that these values are constant overscale changes in the system.

Converging evidence is provided by the'rating task, although ratings of preferred riserheight were somewhat more conservative andmore variable across participants. This dif·ference may be due to the relative insensitivityor more cognitiw: nature of the rating taskwhen compared with forced choice. Nev­ertheless, the rating results are reasonablyclose to the choice results, and a generaloptimal pi value for perception and action instair climbing appears to be justified, approx­imately

The experiments provide evidence thatfunctional perceptual categories and prefer­ences correspond to critical and optimalpoints in an animal-environment system.First, the visual category boundary betweenclimbable and unclimbable stairs was pre­dicted by a biomechanical model of criticalriser height, yielding a critical ratio of -"t' "".88. Second, visually preferred riser heightwas predicted by the energetically optimalriser, yielding an optimal ratio of approxi­mately -"0 = .25. Finally, these values wereconstants across short and tall participants,as predicted by the similarity hypothesis.,suggesting that intrinsically determined crit-

General Discussion

It is important to note that the visuallypreferred risers, although closely matchingthe energetic minima for both groups, areconsiderably higher than those found in or­dinary stairways. This indicates that subjectsdo not simply prefer what is familiar, as aresult of years of experience with normalstairways, and argues in favor of the hypoth­esis that perceptual preferences are related tothe energetics of action. The difference inpreferred riser height between the two groupsalso supports this assessment, because bothshort and tall subjects have had experiencewith the same range of common stairways.

The results indicate that an interpretationof optimal, or best 6t, affordances in termsof energetics is relevant to visual perceptionand predicts visual preferences. In selectinga path of locomotion, an actor must in somesense be perceiving "the work to be done"on various routes to achieve a particular goal.For example, there is evidence in the literatureon optimal foraging that many species per­form visually guided behavior sequences thatare energetically efficient (Pyke, Pulliam, &Chamov, 1977; zach & Smith, 1981). Thisis not to suggest that an animal computes itsown metabolic efficiency for each potentialroute, but rathtT that there must be intrinsicoptical information specific to paths of leastwork. The actor could thereby perceive thebest energetic 6t between itself and the envi·ronment to guide a particular activity.

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700 WILLIAM H. WARREN. JR.

ical and optimal points are scale independent.The effects of adopting natural or intrinsicunits of measurement are underscored by thenear congruence ofgroup curves when plottedon intrinsic axes, thereby "annihilating"group differences and rendering them func­tionally equivalent (cr. Rosen, 197880 1978b).

These results support the proposition thatobservers are capable of perceiving alford.ances, including their critical and optimalpoints. If this is so, it represents a step towardanswering the Question of how animals visu­ally guide their activities in a cluttered envi­ronment. By perceiving environmental objectsin relation to their action capabilities. animalscan dete<:t the possible and most economicalcourses of action in a given situation and caneven act to alter the situation adaptively.

One possible account of this ability is thatenvironmental dimensions and body dimen­sions are perceived and represented indepen­dently, in units of some extrinsic or absolutemetric. These two separate sets of measureswould then have to be calibrated and criticaland optimal values computed on the basis ofprior experience. Alternatively, a body-scaledor action-scaled metric could be adopted forthe analysis of visual information and per­ceptual-motor performance. The perceptionof affordances would be based on intrinsicoptical information for the relationship be­twet:n environmental properties and proper­ties of the observer's own action system, suchas the ratio RIL. The advantages of this latterapproach are twofold: First, intrinsic opticalinformation is available to observers undernatural viewing conditions, whereas the ex­istence ofabsolute information is problematic:second, intrinsic information is directly rele­vant to the control of action. without com­putation or the calibration of extrinsic met­rics. This approach yields a simpler modelthat has the potential to account for the highdegree of accuracy in perceptual performance.

In the present case, the successful guidanceof stair climbing could be accomplished withoptical information about the relationship ofriser height to leg length or to some otherrelated body dimension such as standing eyeheight (RIL ., .51 Rle in the present sample).It can be demonstrated that, under naturalviewing conditions, both static and optical

flow information exist to specify the heightof any object as a ratio of eye height (Lee,1980; Sedgwick, 1973, 1980; Warren, 1983).Particular margin values of such an opticalvariable specify the critical and optimal pointsof RIL, and could be exploited for the controlof climbing. In the case of behavior requiringthe perception of time to contact with asurface, for ell3mple, margin values of theinverse of the rate ofoptical expansion (whichspecifies time to contact for motion of con­stant velocity) have been found for the initi·ation of wing-folding in diving water birds(Lee & Reddish, 1981), landing decelerationin houseflies (Wagner, 1982), muscle activityduring falls in humans (Dietz & Noth, 1978),and arm extension when hitting an approach­ing ball (Lee, Young, Reddish, Lough, &Cayton, 1983).

Although the origin of such margin valuesis uncertain, one possibility is that they areindexed for a perceiver by the Qualitativefeatures of system dynamics during explor­atory activity. Thus, the energy minima iIIus-­trated in Figure 9 could act to "point out"the optical margjn value that corresponds tooptimal riser height. Action-scaled informa·tion for affordances is most likely based onsuch a complex of ecological relations (seeKugler & Turvey, in press). It remains forfurther research to determine whether theavailable eyeheight information is actuallyutilized by human climbers.

The principles of intrinsic measurementand the dynamics of critical and optimalpoints are general and can be applied toother alfordances and related problems suchas the design of architectural environments(e.g., Panero & Zelnik, 1979). The materialand informational bases for such activities asreaching, grasping, lifting, sitting, passingthrough apertures, stepping down ledges.jumping gaps, locomotion over surfaces withvarying properties, foraging and food selec­tion, predation, and so on are amenable tosuch an analysis. By anchoring perception inthe biomechanics and energetics of action,this approach seeks a natural basis for themany categorical distinctions and preferencesmade in the course of ordinary activity, 3Jld,conversely. seeks a lawful explanation for thesuccessful visual control of action.

PERCEIVING AffOR~NCES 701

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Received January 25, 1984Revision received April 23, 1984 •