Copyright 2002 Psychonomic Society Inc 956

Perception amp Psychophysics2002 64 (6) 956-968

When we see a soccer player kick a goal we can see im-mediately what set the ball in motion When a cue ballstrikes another billiard ball and that second ball heads forthe corner pocket we can see that the motion of the cueball has caused the once stationary ball to move In simplecases such as this we perceive causation to take place Butwhat is it to perceive causation What is causality as a per-ceptible property of events and what is the informationthat specifies causality

In the study of event perception the first step is to deter-mine what properties of objects and events can be perceivedand how they are perceived David Hume (1739ndash1740197317481955) is well known for his discussions of the con-ditions under which causation is perceived His method wasintrospection rather than experimentation and he chose bil-liards as his fundamental example His answer was that oursense of causation is evoked by events that are constantlyconjoined in our experience where one is prior to the otherand the two are contiguous in time and space

Michotte (1963) provided the first experimental study ofthe perception of causation using animated two-body col-lisions By manipulating the timing of the collision Mi-chotte found that he could elicit or fail to elicit a judgmentof causation in his observers Contrary to Humersquos analysisrepetition of some events did not suffice to make themlook like causation and others were judged as causal onthe first try even though they were unusual This was a

first step toward discovering the underpinnings of the per-ception of causation However Michottersquos work was lim-ited by subjective measures and experimental manipula-tions that were not founded in a theory of the perceptionof the dynamic variables he was manipulating (Runeson19771983)

Others have extended Michottersquos (1963) study of theperception of causation (see eg Kruschke amp Fragassi1996 Schlottman amp Anderson 1993 Schlottman amp Shanks1992 Weir 1978) but likewise have refrained from a dy-namical analysis of the collision events and so have notshown what physical properties are actually perceivedwhen observers see causality On the other hand the liter-ature of event perception (see eg Gilden amp Proffitt1989 1994 Hecht amp Proff itt 2000 Kaiser amp Proffitt1987 Merfeld Zupan amp Peterka 1999 Proffitt amp Gilden1989 Proffitt Kaiser amp Whelan 1990 Runeson 19771983 1995 Runeson amp Frykholm 1983 Runeson ampVedeler 1993) has addressed the perception of dynamicquantities (eg relative mass elasticity) but has not di-rectly addressed the perception of causality To do so wemust determine what property (or properties) in eventscorrespond to perceived causality Once this is establishedwe can then investigate sources of information about thatproperty and whether observers are indeed sensitive to thatinformation

Dowersquos (2000) conserved-quantity (CQ) theory is con-cerned with demonstrating what aspects of the physicalworld satisfy the causal relations According to the CQtheory causal interactions are marked by the exchange ofCQs between or among causal processes A causal processis a (spacendashtime) trajectory of an object be it a photon ora baseball CQs are whatever quantities are actually con-served in nature and these are taken to be those indicatedby current physics such as charge energy momentumand angular momentum

This research was supported in part by an NSF graduate fellowshipand an Indiana University dissertation-year fellowship to CRT The au-thors thank the reviewers for very valuable revision recommendationsCorrespondence concerning this article should be addressed toC R Twardy School of Computer Science and Software EngineeringMonash University PO Box 26 Clayton VIC 3800 Australia (e-mailctwardy alumniindiana edu)

Causation causal perceptionand conservation laws

CHARLES R TWARDYMonash University Clayton Victoria Australia

and

GEOFFREY P BINGHAMIndiana University Bloomington Indiana

We investigated the perception of causation via the ability to detect conservation violations in simpleevents We showed that observers were sensitive to energy conservation violations in free-fall eventsFurthermore observers were sensitive to gradually perturbed energy dynamics in such events How-ever they were more sensitive to the effect of decreasing gravity than to that of increasing gravity Dis-plays with decreasing gravity were the only displays in which the energy profile was dominated by (ap-parent) potential energy leading to an asymmetric trajectory

CAUSAL PERCEPTION 957

For example a moving billiard ball has energy and mo-mentum in proportion to its speed It will also have otherCQs such as angular momentum A stationary billiard ballalso has energy and momentum and is still a process eventhough (in our reference frame) the values may be zeroDuring a collision the trajectories of two billiard ballsbriefly intersect and the objects (processes) exchange en-ergy and momentum That constitutes a causal interactionTwo ocean waves possessing energy may also ldquocolliderdquobut they do not exchange energy so their interaction is notcausal in that way

The CQ theory provides a principled tie between eventperception and the perception of causality It is not a re-placement for Runesonrsquos kinetics specify the dynamics(KSD) theory of event perception1 It is a philosophicalaccount of causation that happens to tie in very nicely withsomething like KSD which is not in itself a theory of cau-sation Event dynamics consist of exchanges of energymomentum and other CQs the study of event perceptionhas provided evidence that observers are in many casessensitive to event dynamics (eg Bingham Schmidt ampRosenblum 1995 Gilden amp Proffitt 1994 Hecht amp Prof-fitt 2000 Kaiser amp Proffitt 1984 Pittenger 1990 Prof-fitt amp Gilden 1989 Runeson amp Vedeler 1993) There-fore if physical causal interactions are just exchanges ofCQs then in perceiving events observers also perceivesome important aspects of causation itself contrary toHume

This is not to suggest that observers have privileged ac-cess (Bingham et al 1995) to Newtonian ideas of spacetime mass energy or momentum Neither does it suggestthat observers can always identify causes correctly Ob-servers cannot see most exchanges of charge Even whenthey feel a shock they cannot tell positive from negativeObservers have difficulty judging angular momentum(Proffitt amp Gilden 1989 Proffitt et al 1990) althoughthey can become reasonably skilled in certain domainssuch as billiards (Hecht amp Proffitt 2000)

CQ theory does suggest that there are specific physicaldeterminants to causal interactions and that these deter-minants are scientifically known quantities that have spe-cific effects on the resulting kinematics Event perceptionclaims that the data in real observational situations are richenough for observers to perceive at least the qualitativedynamics involved If observers are sensitive to the kindsof dynamic variables (such as energy and momentum) in-volved in conservation laws then on the CQ theory ob-servers are sensitive to causal interactions

That ability alone implies nothing about the phenome-nological manifestations of such a sensitivity Observersneed not be aware of CQs as such or be able to report vi-olations of CQs explicitly even if they are sensitive tosuch violations So it will clearly not do to ask ldquodid yousee energy conservedrdquo Furthermore a falling object dis-sipates some of its energy to air friction and thus obeysthe principle of conservation of energy only approxi-mately Similarly a normal bounce is imperfectly elastic

Some energy is lost We do not expect observers to attuneto perfect conservation but only to that which they expe-rience Hume was right on that count Experience is rele-vant to the perception of causation What we are looking foris sensitivity to deviations from the normal exchanges ofCQs

Of course observers can discriminate only betweenevents for which they can discriminate the forms of mo-tion the trajectories The form of the trajectories by whichobjects exchange energy and momentum over time con-stitutes the structure of an event A particular kind of de-viation from an ldquoexpectedrdquo trajectory should specify anappropriate hidden cause (eg itrsquos not a bouncing ball itrsquosanimate (Bingham et al 1995) In cases in which thespecified cause is not recognizable the event should justlook unnatural

Indeed when Pittenger (1990) used a naturalness ratingtask he found that observers detected deviations as smallas 01ndash02 sec from the natural period of a pendulum Pit-tenger made the pendulum swing faster or slower thannormal by driving it with a second hidden pendulum Infree response participants did not spontaneously reportforces in the anomalous displays but they did sponta-neously describe the natural motion as ldquofree of forcerdquo Ap-parently people do not see gravity as a force at all but asa natural part of (vertical) object behavior They are at-tuned to this invariant in their environment On the otherhand occasional experimenter errors resulting in out-of-place accelerations were detected immediately and wererecognized as external forces or hidden causes exactly aswe would expect from the CQ theory

OVERVIEW

In our experiments we chose a lawful kind of violationthat in the context of the experimental displays did notspecify any kind of naturally occurring energy source orsink We chose unmistakably inanimate events since ob-servers are known to be able to recognize animate motion(the most famous demonstration is the point-light walkersin Johansson 1973) We chose a relatively simple eventmdashnamely a single-body free-fall and bounce under gravityWe chose it in part because the perception of this eventhad been studied extensively before McConnell Muchiskyand Bingham (1998) found that observers shown displaysof balls falling at various distances could tell how far awaythe balls were even though the balls had the same opticalsize indicating that the observers were using dynamicalinformation or at least the average velocity (HechtKaiser amp Banks 1996 see also Saxberg 1987) WarrenKim and Husney (1987) found that observers could judgethe elasticity of a ball by viewing bounces BinghamSchmidt and Rosenblum (1995) found that observerscould distinguish real bounces from hand-driven bounceswith the same period suggesting again that the trajectoryform is the source of information Finally Muchisky andBingham (2002) found that observers are indeed sensitive

958 TWARDY AND BINGHAM

to such variations in trajectory forms (see also Wickelgrenamp Bingham 2001)

We showed observers both possible and impossible mo-tions and asked them to rate the naturalness Assuming theCQ thesis if observers are sensitive to violations of con-servation laws and if we have truly avoided the conflationof our events with other common natural events observerresponses on naturalness rating tasks should indicate theextent to which observers are sensitive to causal relation-ships

EXPERIMENT 1

We used displays similar to those in Muchisky andBingham (1992) and McConnell Muchisky and Bingham(1998) Observers viewed simulations of balls fallingfreely and then bouncing on a hard surface The ball wasalways simulated at the same distance and was always thesame size and mass The bounce event occurred against aground texture with proper occlusion of background ele-ments by foreground elements so that the relative dis-tance was specified by ground contact

The main goal was to test observer sensitivity to a grad-ually introduced conservation violation achieved by al-lowing gravity to vary over time We compared the per-ception of this kind of conservation violation with that ofsimple sudden-onset violations achieved by setting theelasticity of the ball greater than one We also examinedwhether observers were equally sensitive to both additionsand deletions of energy There were therefore two kinds ofdisplays elasticity and varying gravity

In the elasticity displays the ballrsquos elasticity was var-ied from e 5 06 to e 5 12 with gravity remaining earth-normal

In the varying-gravity displays the gravitational field gwas made to increase or decrease during the course of thedisplay following the equation g reg g 1 g t where g is justthe constant by which gravity changed over time so thatg 5 0 for normal displays Five values of g were chosen202 201 0 102 and 104 The maximum rate of de-crease (g 5 202) was chosen so that gravity approachedbut did not quite reach zero by the end of 45 sec Themaximum rate of increase (g 5 104) twice the magni-tude of the maximum rate of decrease was chosen so thatsuccessive bounces were never higher (unlike for e $ 11)eliminating one obvious sign of unnaturalness In thevarying-gravity displays elasticity was always 09 thebounce that looked most natural in an informal pilot studyAn elasticity of 09 corresponds to steel-on-steel or super-ball bounces

Although the displays were intermixed these manipu-lations were carried out separately Each manipulation hadfive levels In addition in order to control for duration ef-fects all the displays were constrained to last 25 35 or45 sec In the elasticity experiment the ball was alwaysdropped from the same maximal height2 of 35 m

In the varying-gravity displays once we fixed the du-ration we had a choice We could maximize the number

of bounce cycles or the distinctness of each bounce Morecycles would give the observer greater variation in bounceperiod However once duration was fixed to show morecycles we would have to lower the drop heights and reducethe trajectory information Alternatively we could maxi-mize the drop height and make larger more distinct cy-cles but sacrifice the information from variations in bounceperiod We did not know whether it would be more im-portant for observers to witness a greater number of cyclesor fewer but larger and more distinct cycles Thereforethere were two conditions First we kept the drop heightconstant and maximal at 45 m and cut off the displaywhenever the time was up second we varied the dropheight so as to guarantee that each display had exactly fiveground strikes in the allotted time3 (fixed number ofbounces condition) As we will see the fixed-height con-dition was much easier for observers and was the onlycondition used in follow-up studies

Method Observers Twelve graduate and undergraduate students at Indi-

ana University participated in the experiment All had normal orcorrected-to-normal vision The observers were paid $5h

Display generation A large (054 m) heavy (68 kg) ball wassimulated at a viewing distance of 50 m The ball appeared as a two-dimensional black outline with gray shading and a black radial lineto indicate orientation and rotation The background was a sagebrushtexture gradient (see Figure 1) QuickTime movies of simple planarevents were created using event-dynamic models generated by theInteractive Physics II application (1992) All models included com-ponents for gravity and air resistance A Runge-Kutta algorithm wasused to calculate positions at successive time intervals of Dtcalc 500015 sec Every 10th such position was used to generate an ani-mation frame so that Dtdisplay 5 0015 sec or 667 Hz The Macro-Mind Accelerator (1989) application was used to lock the frame rateof the simulations to the refresh rate of the monitor (667 Hz) re-sulting in smooth animation without aliasing Interactive Physics IIdoes not simulate compression during bounce so this was approxi-mated by cutting off the bottom 2 pixels of the QuickTime movie re-sulting in a flattening of the ball upon impact

Animations were generated in advance for each of the 45 condi-tions investigated In each display the ball appeared stationary at itsstarting location and began moving when observers clicked themouse At the end of the movement the ball disappeared A trialconsisted of a bounce sequence repeated three times in response toobserver mouse clicks followed by a judgment (written on paper)The whole set of 45 trials was presented in a predetermined randomorder broken up into two blocks of 22 and 23 trials separated by asmall break Each observer saw three repetitions of the 45 trials Foreach repetition a different ordering for the trials was used

The displays used the full 248 3 185 cm (640 3 480 pixel) dis-play of the Macintosh II and the observers sat approximately 05 mfrom the display

Instructions Instructions were presented one sentence at a timeon screen in response to observer mouse clicks in a slide-show for-mat The observers saw the following (where semicolons separateslides and each sentence was given a bullet ldquordquo)

You will view simulations of a simple inanimate event a ball bounc-ing The simulated ball is almost 2 feet in diameter and about 15 poundsThe ball appears as if it were about 165 feet away Some bounces will benatural throughout some will not You are to judge how natural theevents appear Base your judgment on the way the ball moves

Things you do not have to worry about The balls start at differentheights from almost 0 to offscreen They all start moving to the right at

CAUSAL PERCEPTION 959

the same speed They will all disappear suddenly sometimes soonsometimes late The spinning is always natural and is there to help youWhen the ball hits it may get a little flat on the bottom Thatrsquos OK Thesagebrush is for perspective only The ground is actually quite hard

OK herersquos the setting Imagine you are sitting in a chair at groundlevel Imagine this monitor is a window to the ground outside The sage-brush is about 6 inches high Look at the form of motion Look at thetiming of the motion Ask yourself if that could be a real eventrsquos motion

Final instructions Each event will repeat (exactly) 3 times when youclick Try to use all 3 times to make your judgment Rate the event from1 (unnatural) to 5 (natural) on your scoresheet If it looks unnaturalwrite down why if you can You will have 6 blocks of 22 or 23 eventseach You may take breaks between the blocks of trials

Ask now if you have any questions

In short the observers were told to watch all three repetitions and torate the naturalness paying special attention to the form and timingof the motion The first 5 observers were asked to follow their rat-ing with a short free-response description of what if anythingseemed unnatural

Because it took so long to describe what seemed unnatural Ob-servers 5ndash12 were told to perform the free-response task for onlyone of the sets of 45 trials

Procedure The observers were seated in front of the computerwith a mouse an answer sheet and a pencil in front of them An ar-chitectrsquos lamp illuminated the answer sheet and the overhead lightswere shut off to reduce glare on the screen and help with the illusionthat the observer was looking out through the monitor The observersread the instructions looked over the response sheets and had theopportunity to ask the experimenter any further questions They thenworked through a practice block of six trials in order to become fa-miliar with the mechanics of the program and the range of natural-ness of the displays No feedback was given during the practiceblock After answering any further questions the experimenter thenleft the room Experimental sessions lasted about 1 h

Results Elasticity data We performed an analysis of variance

(ANOVA) on the data from the 12 observers There was a

main effect of duration [F(220) 5 354 p 05] indi-cating that at shorter durations the observers had moredifficulty discriminating natural and unnatural displaysMore important there was a statistically significant effectof elasticity [F(440) 5 1876 p 001]

Figure 2 illustrates that the observers detected e 5 11and e 5 12 as being very unnatural Although perceivednaturalness appears to show a peak at e 5 09 a TukeyHSD post hoc analysis on the data combined for all dura-tions shows that the two points (e 5 06 e 5 10) were notsignificantly different from e 5 09 Likewise the pointse 5 11 and e 5 12 were not significantly different fromeach other although both were significantly differentfrom all of the other points (using p 5 05 as the signifi-cance level)

There was a statistically significant two-way interactionbetween duration and elasticity [F(880) 5 319 p 005] Figure 2 shows that this interaction was due chieflyto the unnatural (high-elasticity) eventsrsquo looking evenmore unnatural at longer durations as one would expect

Because the data were response frequencies we com-piled two frequency tables for the responses (Table 1) toverify the results of the ANOVA The left side of Table 1shows the total response frequencies by elasticity for alldurations The right side shows the response frequenciesfor the longest duration (45 sec)

From both sides of Table 1 we can see that the observerswere most confident that e 5 09 was natural They werebeginning to find e 5 10 unnatural but they definitelyrated e $ 11 as unnatural The bimodal distribution at e 506 indicates some confusion On the one hand it gener-ated more 5 ratings than any other category but on the otherhand there were about as many 1 as 5 ratings4

Figure 1 Display for Experiment 1 an elapsed-time view of the bounce trajectory for normal gravity (g 5 0) normalelasticity (e 5 09) and air friction proportional to velocity Initial height 45 m 300 frames sampled every 8 frames

960 TWARDY AND BINGHAM

Gravity study An ANOVA with order as a between-subjects variable yielded main effects of gravity [F(440) 52971 p 001] duration [F(220) 5 1467 p 001]and fixed-condition [whether number of bounces or initialheight was held fixed F(110) 5 871 p 05] Therewere statistically significant interactions between gravityand fixed-condition [F(440) 5 2274 p 001] and be-tween gravity and duration [F(880) 5 365 p 005] Athree-way interaction between gravity duration and orderof presentation was also statistically significant [F(880) 5228 p 05]

The main effect of gravity reflected the fact that dis-plays simulating decreasing gravity appeared unnaturalalthough the participants did not discriminate betweennormal gravity and increasing gravity (using a Tukey testp 5 for all conditions) The main effect of duration in-dicates that once again shorter durations made discrimi-nation more difficult The main effect of fixed conditionindicates that the observers were better able to discrimi-nate when the initial screen height was large resulting insizable and well-defined bounces

The two-way interaction between gravity and f ixedcondition (see Figure 3) confirms that when the number ofbounces was held f ixed (making some bounces quite

small) discriminability dropped almost to zero [a TukeyHSD test revealed that in the upper curve only the ex-treme left point (g 5 202) could be discriminated andonly in the 45-sec condition] In contrast on the curve de-picting a fixed initial height the observers discriminatedall three leftmost points

The two-way interaction between gravity and durationfalls naturally out of those two main effects At short du-rations the participants were less sensitive to the gravitymanipulations At longer durations they became more sen-sitive to decreasing gravity but not to increasing gravity

One potential worry was that the number of bounces(which varied according to initial height and duration inaddition to gravity) might be a better predictor than grav-ity However a multiple regression of gravity durationand number of bounces on naturalness rating was statisti-cally significant [F(3176) 5 299 p 001 R2 5 30]and yielded statistically significant effects for gravity(partial F 5 155 p 001) and duration (partial F 5 59p 02) but no statistically significant effect for numberof bounces ( p 2)

The two frequency tables for the responses to the grav-ity manipulations are given in Table 2 The left side showsthe total response frequencies by gravity for all durations

Figure 2 Ratings of naturalness according to level of elasticity

Table 1Elasticity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

e 1 2 3 4 5 1 2 3 4 5

06 28 15 10 23 30 7 7 2 7 1109 1 10 25 46 24 1 4 8 16 710 6 29 34 27 12 4 11 12 6 311 50 42 9 6 1 21 12 2 1 012 86 14 2 2 2 34 1 0 1 0Total 171 110 80 104 69 67 35 24 31 21

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 957

For example a moving billiard ball has energy and mo-mentum in proportion to its speed It will also have otherCQs such as angular momentum A stationary billiard ballalso has energy and momentum and is still a process eventhough (in our reference frame) the values may be zeroDuring a collision the trajectories of two billiard ballsbriefly intersect and the objects (processes) exchange en-ergy and momentum That constitutes a causal interactionTwo ocean waves possessing energy may also ldquocolliderdquobut they do not exchange energy so their interaction is notcausal in that way

The CQ theory provides a principled tie between eventperception and the perception of causality It is not a re-placement for Runesonrsquos kinetics specify the dynamics(KSD) theory of event perception1 It is a philosophicalaccount of causation that happens to tie in very nicely withsomething like KSD which is not in itself a theory of cau-sation Event dynamics consist of exchanges of energymomentum and other CQs the study of event perceptionhas provided evidence that observers are in many casessensitive to event dynamics (eg Bingham Schmidt ampRosenblum 1995 Gilden amp Proffitt 1994 Hecht amp Prof-fitt 2000 Kaiser amp Proffitt 1984 Pittenger 1990 Prof-fitt amp Gilden 1989 Runeson amp Vedeler 1993) There-fore if physical causal interactions are just exchanges ofCQs then in perceiving events observers also perceivesome important aspects of causation itself contrary toHume

This is not to suggest that observers have privileged ac-cess (Bingham et al 1995) to Newtonian ideas of spacetime mass energy or momentum Neither does it suggestthat observers can always identify causes correctly Ob-servers cannot see most exchanges of charge Even whenthey feel a shock they cannot tell positive from negativeObservers have difficulty judging angular momentum(Proffitt amp Gilden 1989 Proffitt et al 1990) althoughthey can become reasonably skilled in certain domainssuch as billiards (Hecht amp Proffitt 2000)

CQ theory does suggest that there are specific physicaldeterminants to causal interactions and that these deter-minants are scientifically known quantities that have spe-cific effects on the resulting kinematics Event perceptionclaims that the data in real observational situations are richenough for observers to perceive at least the qualitativedynamics involved If observers are sensitive to the kindsof dynamic variables (such as energy and momentum) in-volved in conservation laws then on the CQ theory ob-servers are sensitive to causal interactions

That ability alone implies nothing about the phenome-nological manifestations of such a sensitivity Observersneed not be aware of CQs as such or be able to report vi-olations of CQs explicitly even if they are sensitive tosuch violations So it will clearly not do to ask ldquodid yousee energy conservedrdquo Furthermore a falling object dis-sipates some of its energy to air friction and thus obeysthe principle of conservation of energy only approxi-mately Similarly a normal bounce is imperfectly elastic

Some energy is lost We do not expect observers to attuneto perfect conservation but only to that which they expe-rience Hume was right on that count Experience is rele-vant to the perception of causation What we are looking foris sensitivity to deviations from the normal exchanges ofCQs

Of course observers can discriminate only betweenevents for which they can discriminate the forms of mo-tion the trajectories The form of the trajectories by whichobjects exchange energy and momentum over time con-stitutes the structure of an event A particular kind of de-viation from an ldquoexpectedrdquo trajectory should specify anappropriate hidden cause (eg itrsquos not a bouncing ball itrsquosanimate (Bingham et al 1995) In cases in which thespecified cause is not recognizable the event should justlook unnatural

Indeed when Pittenger (1990) used a naturalness ratingtask he found that observers detected deviations as smallas 01ndash02 sec from the natural period of a pendulum Pit-tenger made the pendulum swing faster or slower thannormal by driving it with a second hidden pendulum Infree response participants did not spontaneously reportforces in the anomalous displays but they did sponta-neously describe the natural motion as ldquofree of forcerdquo Ap-parently people do not see gravity as a force at all but asa natural part of (vertical) object behavior They are at-tuned to this invariant in their environment On the otherhand occasional experimenter errors resulting in out-of-place accelerations were detected immediately and wererecognized as external forces or hidden causes exactly aswe would expect from the CQ theory

OVERVIEW

In our experiments we chose a lawful kind of violationthat in the context of the experimental displays did notspecify any kind of naturally occurring energy source orsink We chose unmistakably inanimate events since ob-servers are known to be able to recognize animate motion(the most famous demonstration is the point-light walkersin Johansson 1973) We chose a relatively simple eventmdashnamely a single-body free-fall and bounce under gravityWe chose it in part because the perception of this eventhad been studied extensively before McConnell Muchiskyand Bingham (1998) found that observers shown displaysof balls falling at various distances could tell how far awaythe balls were even though the balls had the same opticalsize indicating that the observers were using dynamicalinformation or at least the average velocity (HechtKaiser amp Banks 1996 see also Saxberg 1987) WarrenKim and Husney (1987) found that observers could judgethe elasticity of a ball by viewing bounces BinghamSchmidt and Rosenblum (1995) found that observerscould distinguish real bounces from hand-driven bounceswith the same period suggesting again that the trajectoryform is the source of information Finally Muchisky andBingham (2002) found that observers are indeed sensitive

958 TWARDY AND BINGHAM

to such variations in trajectory forms (see also Wickelgrenamp Bingham 2001)

We showed observers both possible and impossible mo-tions and asked them to rate the naturalness Assuming theCQ thesis if observers are sensitive to violations of con-servation laws and if we have truly avoided the conflationof our events with other common natural events observerresponses on naturalness rating tasks should indicate theextent to which observers are sensitive to causal relation-ships

EXPERIMENT 1

We used displays similar to those in Muchisky andBingham (1992) and McConnell Muchisky and Bingham(1998) Observers viewed simulations of balls fallingfreely and then bouncing on a hard surface The ball wasalways simulated at the same distance and was always thesame size and mass The bounce event occurred against aground texture with proper occlusion of background ele-ments by foreground elements so that the relative dis-tance was specified by ground contact

The main goal was to test observer sensitivity to a grad-ually introduced conservation violation achieved by al-lowing gravity to vary over time We compared the per-ception of this kind of conservation violation with that ofsimple sudden-onset violations achieved by setting theelasticity of the ball greater than one We also examinedwhether observers were equally sensitive to both additionsand deletions of energy There were therefore two kinds ofdisplays elasticity and varying gravity

In the elasticity displays the ballrsquos elasticity was var-ied from e 5 06 to e 5 12 with gravity remaining earth-normal

In the varying-gravity displays the gravitational field gwas made to increase or decrease during the course of thedisplay following the equation g reg g 1 g t where g is justthe constant by which gravity changed over time so thatg 5 0 for normal displays Five values of g were chosen202 201 0 102 and 104 The maximum rate of de-crease (g 5 202) was chosen so that gravity approachedbut did not quite reach zero by the end of 45 sec Themaximum rate of increase (g 5 104) twice the magni-tude of the maximum rate of decrease was chosen so thatsuccessive bounces were never higher (unlike for e $ 11)eliminating one obvious sign of unnaturalness In thevarying-gravity displays elasticity was always 09 thebounce that looked most natural in an informal pilot studyAn elasticity of 09 corresponds to steel-on-steel or super-ball bounces

Although the displays were intermixed these manipu-lations were carried out separately Each manipulation hadfive levels In addition in order to control for duration ef-fects all the displays were constrained to last 25 35 or45 sec In the elasticity experiment the ball was alwaysdropped from the same maximal height2 of 35 m

In the varying-gravity displays once we fixed the du-ration we had a choice We could maximize the number

of bounce cycles or the distinctness of each bounce Morecycles would give the observer greater variation in bounceperiod However once duration was fixed to show morecycles we would have to lower the drop heights and reducethe trajectory information Alternatively we could maxi-mize the drop height and make larger more distinct cy-cles but sacrifice the information from variations in bounceperiod We did not know whether it would be more im-portant for observers to witness a greater number of cyclesor fewer but larger and more distinct cycles Thereforethere were two conditions First we kept the drop heightconstant and maximal at 45 m and cut off the displaywhenever the time was up second we varied the dropheight so as to guarantee that each display had exactly fiveground strikes in the allotted time3 (fixed number ofbounces condition) As we will see the fixed-height con-dition was much easier for observers and was the onlycondition used in follow-up studies

Method Observers Twelve graduate and undergraduate students at Indi-

ana University participated in the experiment All had normal orcorrected-to-normal vision The observers were paid $5h

Display generation A large (054 m) heavy (68 kg) ball wassimulated at a viewing distance of 50 m The ball appeared as a two-dimensional black outline with gray shading and a black radial lineto indicate orientation and rotation The background was a sagebrushtexture gradient (see Figure 1) QuickTime movies of simple planarevents were created using event-dynamic models generated by theInteractive Physics II application (1992) All models included com-ponents for gravity and air resistance A Runge-Kutta algorithm wasused to calculate positions at successive time intervals of Dtcalc 500015 sec Every 10th such position was used to generate an ani-mation frame so that Dtdisplay 5 0015 sec or 667 Hz The Macro-Mind Accelerator (1989) application was used to lock the frame rateof the simulations to the refresh rate of the monitor (667 Hz) re-sulting in smooth animation without aliasing Interactive Physics IIdoes not simulate compression during bounce so this was approxi-mated by cutting off the bottom 2 pixels of the QuickTime movie re-sulting in a flattening of the ball upon impact

Animations were generated in advance for each of the 45 condi-tions investigated In each display the ball appeared stationary at itsstarting location and began moving when observers clicked themouse At the end of the movement the ball disappeared A trialconsisted of a bounce sequence repeated three times in response toobserver mouse clicks followed by a judgment (written on paper)The whole set of 45 trials was presented in a predetermined randomorder broken up into two blocks of 22 and 23 trials separated by asmall break Each observer saw three repetitions of the 45 trials Foreach repetition a different ordering for the trials was used

The displays used the full 248 3 185 cm (640 3 480 pixel) dis-play of the Macintosh II and the observers sat approximately 05 mfrom the display

Instructions Instructions were presented one sentence at a timeon screen in response to observer mouse clicks in a slide-show for-mat The observers saw the following (where semicolons separateslides and each sentence was given a bullet ldquordquo)

You will view simulations of a simple inanimate event a ball bounc-ing The simulated ball is almost 2 feet in diameter and about 15 poundsThe ball appears as if it were about 165 feet away Some bounces will benatural throughout some will not You are to judge how natural theevents appear Base your judgment on the way the ball moves

Things you do not have to worry about The balls start at differentheights from almost 0 to offscreen They all start moving to the right at

CAUSAL PERCEPTION 959

the same speed They will all disappear suddenly sometimes soonsometimes late The spinning is always natural and is there to help youWhen the ball hits it may get a little flat on the bottom Thatrsquos OK Thesagebrush is for perspective only The ground is actually quite hard

OK herersquos the setting Imagine you are sitting in a chair at groundlevel Imagine this monitor is a window to the ground outside The sage-brush is about 6 inches high Look at the form of motion Look at thetiming of the motion Ask yourself if that could be a real eventrsquos motion

Final instructions Each event will repeat (exactly) 3 times when youclick Try to use all 3 times to make your judgment Rate the event from1 (unnatural) to 5 (natural) on your scoresheet If it looks unnaturalwrite down why if you can You will have 6 blocks of 22 or 23 eventseach You may take breaks between the blocks of trials

Ask now if you have any questions

In short the observers were told to watch all three repetitions and torate the naturalness paying special attention to the form and timingof the motion The first 5 observers were asked to follow their rat-ing with a short free-response description of what if anythingseemed unnatural

Because it took so long to describe what seemed unnatural Ob-servers 5ndash12 were told to perform the free-response task for onlyone of the sets of 45 trials

Procedure The observers were seated in front of the computerwith a mouse an answer sheet and a pencil in front of them An ar-chitectrsquos lamp illuminated the answer sheet and the overhead lightswere shut off to reduce glare on the screen and help with the illusionthat the observer was looking out through the monitor The observersread the instructions looked over the response sheets and had theopportunity to ask the experimenter any further questions They thenworked through a practice block of six trials in order to become fa-miliar with the mechanics of the program and the range of natural-ness of the displays No feedback was given during the practiceblock After answering any further questions the experimenter thenleft the room Experimental sessions lasted about 1 h

Results Elasticity data We performed an analysis of variance

(ANOVA) on the data from the 12 observers There was a

main effect of duration [F(220) 5 354 p 05] indi-cating that at shorter durations the observers had moredifficulty discriminating natural and unnatural displaysMore important there was a statistically significant effectof elasticity [F(440) 5 1876 p 001]

Figure 2 illustrates that the observers detected e 5 11and e 5 12 as being very unnatural Although perceivednaturalness appears to show a peak at e 5 09 a TukeyHSD post hoc analysis on the data combined for all dura-tions shows that the two points (e 5 06 e 5 10) were notsignificantly different from e 5 09 Likewise the pointse 5 11 and e 5 12 were not significantly different fromeach other although both were significantly differentfrom all of the other points (using p 5 05 as the signifi-cance level)

There was a statistically significant two-way interactionbetween duration and elasticity [F(880) 5 319 p 005] Figure 2 shows that this interaction was due chieflyto the unnatural (high-elasticity) eventsrsquo looking evenmore unnatural at longer durations as one would expect

Because the data were response frequencies we com-piled two frequency tables for the responses (Table 1) toverify the results of the ANOVA The left side of Table 1shows the total response frequencies by elasticity for alldurations The right side shows the response frequenciesfor the longest duration (45 sec)

From both sides of Table 1 we can see that the observerswere most confident that e 5 09 was natural They werebeginning to find e 5 10 unnatural but they definitelyrated e $ 11 as unnatural The bimodal distribution at e 506 indicates some confusion On the one hand it gener-ated more 5 ratings than any other category but on the otherhand there were about as many 1 as 5 ratings4

Figure 1 Display for Experiment 1 an elapsed-time view of the bounce trajectory for normal gravity (g 5 0) normalelasticity (e 5 09) and air friction proportional to velocity Initial height 45 m 300 frames sampled every 8 frames

960 TWARDY AND BINGHAM

Gravity study An ANOVA with order as a between-subjects variable yielded main effects of gravity [F(440) 52971 p 001] duration [F(220) 5 1467 p 001]and fixed-condition [whether number of bounces or initialheight was held fixed F(110) 5 871 p 05] Therewere statistically significant interactions between gravityand fixed-condition [F(440) 5 2274 p 001] and be-tween gravity and duration [F(880) 5 365 p 005] Athree-way interaction between gravity duration and orderof presentation was also statistically significant [F(880) 5228 p 05]

The main effect of gravity reflected the fact that dis-plays simulating decreasing gravity appeared unnaturalalthough the participants did not discriminate betweennormal gravity and increasing gravity (using a Tukey testp 5 for all conditions) The main effect of duration in-dicates that once again shorter durations made discrimi-nation more difficult The main effect of fixed conditionindicates that the observers were better able to discrimi-nate when the initial screen height was large resulting insizable and well-defined bounces

The two-way interaction between gravity and f ixedcondition (see Figure 3) confirms that when the number ofbounces was held f ixed (making some bounces quite

small) discriminability dropped almost to zero [a TukeyHSD test revealed that in the upper curve only the ex-treme left point (g 5 202) could be discriminated andonly in the 45-sec condition] In contrast on the curve de-picting a fixed initial height the observers discriminatedall three leftmost points

The two-way interaction between gravity and durationfalls naturally out of those two main effects At short du-rations the participants were less sensitive to the gravitymanipulations At longer durations they became more sen-sitive to decreasing gravity but not to increasing gravity

One potential worry was that the number of bounces(which varied according to initial height and duration inaddition to gravity) might be a better predictor than grav-ity However a multiple regression of gravity durationand number of bounces on naturalness rating was statisti-cally significant [F(3176) 5 299 p 001 R2 5 30]and yielded statistically significant effects for gravity(partial F 5 155 p 001) and duration (partial F 5 59p 02) but no statistically significant effect for numberof bounces ( p 2)

The two frequency tables for the responses to the grav-ity manipulations are given in Table 2 The left side showsthe total response frequencies by gravity for all durations

Figure 2 Ratings of naturalness according to level of elasticity

Table 1Elasticity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

e 1 2 3 4 5 1 2 3 4 5

06 28 15 10 23 30 7 7 2 7 1109 1 10 25 46 24 1 4 8 16 710 6 29 34 27 12 4 11 12 6 311 50 42 9 6 1 21 12 2 1 012 86 14 2 2 2 34 1 0 1 0Total 171 110 80 104 69 67 35 24 31 21

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

958 TWARDY AND BINGHAM

to such variations in trajectory forms (see also Wickelgrenamp Bingham 2001)

We showed observers both possible and impossible mo-tions and asked them to rate the naturalness Assuming theCQ thesis if observers are sensitive to violations of con-servation laws and if we have truly avoided the conflationof our events with other common natural events observerresponses on naturalness rating tasks should indicate theextent to which observers are sensitive to causal relation-ships

EXPERIMENT 1

We used displays similar to those in Muchisky andBingham (1992) and McConnell Muchisky and Bingham(1998) Observers viewed simulations of balls fallingfreely and then bouncing on a hard surface The ball wasalways simulated at the same distance and was always thesame size and mass The bounce event occurred against aground texture with proper occlusion of background ele-ments by foreground elements so that the relative dis-tance was specified by ground contact

The main goal was to test observer sensitivity to a grad-ually introduced conservation violation achieved by al-lowing gravity to vary over time We compared the per-ception of this kind of conservation violation with that ofsimple sudden-onset violations achieved by setting theelasticity of the ball greater than one We also examinedwhether observers were equally sensitive to both additionsand deletions of energy There were therefore two kinds ofdisplays elasticity and varying gravity

In the elasticity displays the ballrsquos elasticity was var-ied from e 5 06 to e 5 12 with gravity remaining earth-normal

In the varying-gravity displays the gravitational field gwas made to increase or decrease during the course of thedisplay following the equation g reg g 1 g t where g is justthe constant by which gravity changed over time so thatg 5 0 for normal displays Five values of g were chosen202 201 0 102 and 104 The maximum rate of de-crease (g 5 202) was chosen so that gravity approachedbut did not quite reach zero by the end of 45 sec Themaximum rate of increase (g 5 104) twice the magni-tude of the maximum rate of decrease was chosen so thatsuccessive bounces were never higher (unlike for e $ 11)eliminating one obvious sign of unnaturalness In thevarying-gravity displays elasticity was always 09 thebounce that looked most natural in an informal pilot studyAn elasticity of 09 corresponds to steel-on-steel or super-ball bounces

Although the displays were intermixed these manipu-lations were carried out separately Each manipulation hadfive levels In addition in order to control for duration ef-fects all the displays were constrained to last 25 35 or45 sec In the elasticity experiment the ball was alwaysdropped from the same maximal height2 of 35 m

In the varying-gravity displays once we fixed the du-ration we had a choice We could maximize the number

of bounce cycles or the distinctness of each bounce Morecycles would give the observer greater variation in bounceperiod However once duration was fixed to show morecycles we would have to lower the drop heights and reducethe trajectory information Alternatively we could maxi-mize the drop height and make larger more distinct cy-cles but sacrifice the information from variations in bounceperiod We did not know whether it would be more im-portant for observers to witness a greater number of cyclesor fewer but larger and more distinct cycles Thereforethere were two conditions First we kept the drop heightconstant and maximal at 45 m and cut off the displaywhenever the time was up second we varied the dropheight so as to guarantee that each display had exactly fiveground strikes in the allotted time3 (fixed number ofbounces condition) As we will see the fixed-height con-dition was much easier for observers and was the onlycondition used in follow-up studies

Method Observers Twelve graduate and undergraduate students at Indi-

ana University participated in the experiment All had normal orcorrected-to-normal vision The observers were paid $5h

Display generation A large (054 m) heavy (68 kg) ball wassimulated at a viewing distance of 50 m The ball appeared as a two-dimensional black outline with gray shading and a black radial lineto indicate orientation and rotation The background was a sagebrushtexture gradient (see Figure 1) QuickTime movies of simple planarevents were created using event-dynamic models generated by theInteractive Physics II application (1992) All models included com-ponents for gravity and air resistance A Runge-Kutta algorithm wasused to calculate positions at successive time intervals of Dtcalc 500015 sec Every 10th such position was used to generate an ani-mation frame so that Dtdisplay 5 0015 sec or 667 Hz The Macro-Mind Accelerator (1989) application was used to lock the frame rateof the simulations to the refresh rate of the monitor (667 Hz) re-sulting in smooth animation without aliasing Interactive Physics IIdoes not simulate compression during bounce so this was approxi-mated by cutting off the bottom 2 pixels of the QuickTime movie re-sulting in a flattening of the ball upon impact

Animations were generated in advance for each of the 45 condi-tions investigated In each display the ball appeared stationary at itsstarting location and began moving when observers clicked themouse At the end of the movement the ball disappeared A trialconsisted of a bounce sequence repeated three times in response toobserver mouse clicks followed by a judgment (written on paper)The whole set of 45 trials was presented in a predetermined randomorder broken up into two blocks of 22 and 23 trials separated by asmall break Each observer saw three repetitions of the 45 trials Foreach repetition a different ordering for the trials was used

The displays used the full 248 3 185 cm (640 3 480 pixel) dis-play of the Macintosh II and the observers sat approximately 05 mfrom the display

Instructions Instructions were presented one sentence at a timeon screen in response to observer mouse clicks in a slide-show for-mat The observers saw the following (where semicolons separateslides and each sentence was given a bullet ldquordquo)

You will view simulations of a simple inanimate event a ball bounc-ing The simulated ball is almost 2 feet in diameter and about 15 poundsThe ball appears as if it were about 165 feet away Some bounces will benatural throughout some will not You are to judge how natural theevents appear Base your judgment on the way the ball moves

Things you do not have to worry about The balls start at differentheights from almost 0 to offscreen They all start moving to the right at

CAUSAL PERCEPTION 959

the same speed They will all disappear suddenly sometimes soonsometimes late The spinning is always natural and is there to help youWhen the ball hits it may get a little flat on the bottom Thatrsquos OK Thesagebrush is for perspective only The ground is actually quite hard

OK herersquos the setting Imagine you are sitting in a chair at groundlevel Imagine this monitor is a window to the ground outside The sage-brush is about 6 inches high Look at the form of motion Look at thetiming of the motion Ask yourself if that could be a real eventrsquos motion

Final instructions Each event will repeat (exactly) 3 times when youclick Try to use all 3 times to make your judgment Rate the event from1 (unnatural) to 5 (natural) on your scoresheet If it looks unnaturalwrite down why if you can You will have 6 blocks of 22 or 23 eventseach You may take breaks between the blocks of trials

Ask now if you have any questions

In short the observers were told to watch all three repetitions and torate the naturalness paying special attention to the form and timingof the motion The first 5 observers were asked to follow their rat-ing with a short free-response description of what if anythingseemed unnatural

Because it took so long to describe what seemed unnatural Ob-servers 5ndash12 were told to perform the free-response task for onlyone of the sets of 45 trials

Procedure The observers were seated in front of the computerwith a mouse an answer sheet and a pencil in front of them An ar-chitectrsquos lamp illuminated the answer sheet and the overhead lightswere shut off to reduce glare on the screen and help with the illusionthat the observer was looking out through the monitor The observersread the instructions looked over the response sheets and had theopportunity to ask the experimenter any further questions They thenworked through a practice block of six trials in order to become fa-miliar with the mechanics of the program and the range of natural-ness of the displays No feedback was given during the practiceblock After answering any further questions the experimenter thenleft the room Experimental sessions lasted about 1 h

Results Elasticity data We performed an analysis of variance

(ANOVA) on the data from the 12 observers There was a

main effect of duration [F(220) 5 354 p 05] indi-cating that at shorter durations the observers had moredifficulty discriminating natural and unnatural displaysMore important there was a statistically significant effectof elasticity [F(440) 5 1876 p 001]

Figure 2 illustrates that the observers detected e 5 11and e 5 12 as being very unnatural Although perceivednaturalness appears to show a peak at e 5 09 a TukeyHSD post hoc analysis on the data combined for all dura-tions shows that the two points (e 5 06 e 5 10) were notsignificantly different from e 5 09 Likewise the pointse 5 11 and e 5 12 were not significantly different fromeach other although both were significantly differentfrom all of the other points (using p 5 05 as the signifi-cance level)

There was a statistically significant two-way interactionbetween duration and elasticity [F(880) 5 319 p 005] Figure 2 shows that this interaction was due chieflyto the unnatural (high-elasticity) eventsrsquo looking evenmore unnatural at longer durations as one would expect

Because the data were response frequencies we com-piled two frequency tables for the responses (Table 1) toverify the results of the ANOVA The left side of Table 1shows the total response frequencies by elasticity for alldurations The right side shows the response frequenciesfor the longest duration (45 sec)

From both sides of Table 1 we can see that the observerswere most confident that e 5 09 was natural They werebeginning to find e 5 10 unnatural but they definitelyrated e $ 11 as unnatural The bimodal distribution at e 506 indicates some confusion On the one hand it gener-ated more 5 ratings than any other category but on the otherhand there were about as many 1 as 5 ratings4

Figure 1 Display for Experiment 1 an elapsed-time view of the bounce trajectory for normal gravity (g 5 0) normalelasticity (e 5 09) and air friction proportional to velocity Initial height 45 m 300 frames sampled every 8 frames

960 TWARDY AND BINGHAM

Gravity study An ANOVA with order as a between-subjects variable yielded main effects of gravity [F(440) 52971 p 001] duration [F(220) 5 1467 p 001]and fixed-condition [whether number of bounces or initialheight was held fixed F(110) 5 871 p 05] Therewere statistically significant interactions between gravityand fixed-condition [F(440) 5 2274 p 001] and be-tween gravity and duration [F(880) 5 365 p 005] Athree-way interaction between gravity duration and orderof presentation was also statistically significant [F(880) 5228 p 05]

The main effect of gravity reflected the fact that dis-plays simulating decreasing gravity appeared unnaturalalthough the participants did not discriminate betweennormal gravity and increasing gravity (using a Tukey testp 5 for all conditions) The main effect of duration in-dicates that once again shorter durations made discrimi-nation more difficult The main effect of fixed conditionindicates that the observers were better able to discrimi-nate when the initial screen height was large resulting insizable and well-defined bounces

The two-way interaction between gravity and f ixedcondition (see Figure 3) confirms that when the number ofbounces was held f ixed (making some bounces quite

small) discriminability dropped almost to zero [a TukeyHSD test revealed that in the upper curve only the ex-treme left point (g 5 202) could be discriminated andonly in the 45-sec condition] In contrast on the curve de-picting a fixed initial height the observers discriminatedall three leftmost points

The two-way interaction between gravity and durationfalls naturally out of those two main effects At short du-rations the participants were less sensitive to the gravitymanipulations At longer durations they became more sen-sitive to decreasing gravity but not to increasing gravity

One potential worry was that the number of bounces(which varied according to initial height and duration inaddition to gravity) might be a better predictor than grav-ity However a multiple regression of gravity durationand number of bounces on naturalness rating was statisti-cally significant [F(3176) 5 299 p 001 R2 5 30]and yielded statistically significant effects for gravity(partial F 5 155 p 001) and duration (partial F 5 59p 02) but no statistically significant effect for numberof bounces ( p 2)

The two frequency tables for the responses to the grav-ity manipulations are given in Table 2 The left side showsthe total response frequencies by gravity for all durations

Figure 2 Ratings of naturalness according to level of elasticity

Table 1Elasticity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

e 1 2 3 4 5 1 2 3 4 5

06 28 15 10 23 30 7 7 2 7 1109 1 10 25 46 24 1 4 8 16 710 6 29 34 27 12 4 11 12 6 311 50 42 9 6 1 21 12 2 1 012 86 14 2 2 2 34 1 0 1 0Total 171 110 80 104 69 67 35 24 31 21

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 959

the same speed They will all disappear suddenly sometimes soonsometimes late The spinning is always natural and is there to help youWhen the ball hits it may get a little flat on the bottom Thatrsquos OK Thesagebrush is for perspective only The ground is actually quite hard

OK herersquos the setting Imagine you are sitting in a chair at groundlevel Imagine this monitor is a window to the ground outside The sage-brush is about 6 inches high Look at the form of motion Look at thetiming of the motion Ask yourself if that could be a real eventrsquos motion

Final instructions Each event will repeat (exactly) 3 times when youclick Try to use all 3 times to make your judgment Rate the event from1 (unnatural) to 5 (natural) on your scoresheet If it looks unnaturalwrite down why if you can You will have 6 blocks of 22 or 23 eventseach You may take breaks between the blocks of trials

Ask now if you have any questions

In short the observers were told to watch all three repetitions and torate the naturalness paying special attention to the form and timingof the motion The first 5 observers were asked to follow their rat-ing with a short free-response description of what if anythingseemed unnatural

Because it took so long to describe what seemed unnatural Ob-servers 5ndash12 were told to perform the free-response task for onlyone of the sets of 45 trials

Procedure The observers were seated in front of the computerwith a mouse an answer sheet and a pencil in front of them An ar-chitectrsquos lamp illuminated the answer sheet and the overhead lightswere shut off to reduce glare on the screen and help with the illusionthat the observer was looking out through the monitor The observersread the instructions looked over the response sheets and had theopportunity to ask the experimenter any further questions They thenworked through a practice block of six trials in order to become fa-miliar with the mechanics of the program and the range of natural-ness of the displays No feedback was given during the practiceblock After answering any further questions the experimenter thenleft the room Experimental sessions lasted about 1 h

Results Elasticity data We performed an analysis of variance

(ANOVA) on the data from the 12 observers There was a

main effect of duration [F(220) 5 354 p 05] indi-cating that at shorter durations the observers had moredifficulty discriminating natural and unnatural displaysMore important there was a statistically significant effectof elasticity [F(440) 5 1876 p 001]

Figure 2 illustrates that the observers detected e 5 11and e 5 12 as being very unnatural Although perceivednaturalness appears to show a peak at e 5 09 a TukeyHSD post hoc analysis on the data combined for all dura-tions shows that the two points (e 5 06 e 5 10) were notsignificantly different from e 5 09 Likewise the pointse 5 11 and e 5 12 were not significantly different fromeach other although both were significantly differentfrom all of the other points (using p 5 05 as the signifi-cance level)

There was a statistically significant two-way interactionbetween duration and elasticity [F(880) 5 319 p 005] Figure 2 shows that this interaction was due chieflyto the unnatural (high-elasticity) eventsrsquo looking evenmore unnatural at longer durations as one would expect

Because the data were response frequencies we com-piled two frequency tables for the responses (Table 1) toverify the results of the ANOVA The left side of Table 1shows the total response frequencies by elasticity for alldurations The right side shows the response frequenciesfor the longest duration (45 sec)

From both sides of Table 1 we can see that the observerswere most confident that e 5 09 was natural They werebeginning to find e 5 10 unnatural but they definitelyrated e $ 11 as unnatural The bimodal distribution at e 506 indicates some confusion On the one hand it gener-ated more 5 ratings than any other category but on the otherhand there were about as many 1 as 5 ratings4

Figure 1 Display for Experiment 1 an elapsed-time view of the bounce trajectory for normal gravity (g 5 0) normalelasticity (e 5 09) and air friction proportional to velocity Initial height 45 m 300 frames sampled every 8 frames

960 TWARDY AND BINGHAM

Gravity study An ANOVA with order as a between-subjects variable yielded main effects of gravity [F(440) 52971 p 001] duration [F(220) 5 1467 p 001]and fixed-condition [whether number of bounces or initialheight was held fixed F(110) 5 871 p 05] Therewere statistically significant interactions between gravityand fixed-condition [F(440) 5 2274 p 001] and be-tween gravity and duration [F(880) 5 365 p 005] Athree-way interaction between gravity duration and orderof presentation was also statistically significant [F(880) 5228 p 05]

The main effect of gravity reflected the fact that dis-plays simulating decreasing gravity appeared unnaturalalthough the participants did not discriminate betweennormal gravity and increasing gravity (using a Tukey testp 5 for all conditions) The main effect of duration in-dicates that once again shorter durations made discrimi-nation more difficult The main effect of fixed conditionindicates that the observers were better able to discrimi-nate when the initial screen height was large resulting insizable and well-defined bounces

The two-way interaction between gravity and f ixedcondition (see Figure 3) confirms that when the number ofbounces was held f ixed (making some bounces quite

small) discriminability dropped almost to zero [a TukeyHSD test revealed that in the upper curve only the ex-treme left point (g 5 202) could be discriminated andonly in the 45-sec condition] In contrast on the curve de-picting a fixed initial height the observers discriminatedall three leftmost points

The two-way interaction between gravity and durationfalls naturally out of those two main effects At short du-rations the participants were less sensitive to the gravitymanipulations At longer durations they became more sen-sitive to decreasing gravity but not to increasing gravity

One potential worry was that the number of bounces(which varied according to initial height and duration inaddition to gravity) might be a better predictor than grav-ity However a multiple regression of gravity durationand number of bounces on naturalness rating was statisti-cally significant [F(3176) 5 299 p 001 R2 5 30]and yielded statistically significant effects for gravity(partial F 5 155 p 001) and duration (partial F 5 59p 02) but no statistically significant effect for numberof bounces ( p 2)

The two frequency tables for the responses to the grav-ity manipulations are given in Table 2 The left side showsthe total response frequencies by gravity for all durations

Figure 2 Ratings of naturalness according to level of elasticity

Table 1Elasticity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

e 1 2 3 4 5 1 2 3 4 5

06 28 15 10 23 30 7 7 2 7 1109 1 10 25 46 24 1 4 8 16 710 6 29 34 27 12 4 11 12 6 311 50 42 9 6 1 21 12 2 1 012 86 14 2 2 2 34 1 0 1 0Total 171 110 80 104 69 67 35 24 31 21

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

960 TWARDY AND BINGHAM

Gravity study An ANOVA with order as a between-subjects variable yielded main effects of gravity [F(440) 52971 p 001] duration [F(220) 5 1467 p 001]and fixed-condition [whether number of bounces or initialheight was held fixed F(110) 5 871 p 05] Therewere statistically significant interactions between gravityand fixed-condition [F(440) 5 2274 p 001] and be-tween gravity and duration [F(880) 5 365 p 005] Athree-way interaction between gravity duration and orderof presentation was also statistically significant [F(880) 5228 p 05]

The main effect of gravity reflected the fact that dis-plays simulating decreasing gravity appeared unnaturalalthough the participants did not discriminate betweennormal gravity and increasing gravity (using a Tukey testp 5 for all conditions) The main effect of duration in-dicates that once again shorter durations made discrimi-nation more difficult The main effect of fixed conditionindicates that the observers were better able to discrimi-nate when the initial screen height was large resulting insizable and well-defined bounces

The two-way interaction between gravity and f ixedcondition (see Figure 3) confirms that when the number ofbounces was held f ixed (making some bounces quite

small) discriminability dropped almost to zero [a TukeyHSD test revealed that in the upper curve only the ex-treme left point (g 5 202) could be discriminated andonly in the 45-sec condition] In contrast on the curve de-picting a fixed initial height the observers discriminatedall three leftmost points

The two-way interaction between gravity and durationfalls naturally out of those two main effects At short du-rations the participants were less sensitive to the gravitymanipulations At longer durations they became more sen-sitive to decreasing gravity but not to increasing gravity

One potential worry was that the number of bounces(which varied according to initial height and duration inaddition to gravity) might be a better predictor than grav-ity However a multiple regression of gravity durationand number of bounces on naturalness rating was statisti-cally significant [F(3176) 5 299 p 001 R2 5 30]and yielded statistically significant effects for gravity(partial F 5 155 p 001) and duration (partial F 5 59p 02) but no statistically significant effect for numberof bounces ( p 2)

The two frequency tables for the responses to the grav-ity manipulations are given in Table 2 The left side showsthe total response frequencies by gravity for all durations

Figure 2 Ratings of naturalness according to level of elasticity

Table 1Elasticity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

e 1 2 3 4 5 1 2 3 4 5

06 28 15 10 23 30 7 7 2 7 1109 1 10 25 46 24 1 4 8 16 710 6 29 34 27 12 4 11 12 6 311 50 42 9 6 1 21 12 2 1 012 86 14 2 2 2 34 1 0 1 0Total 171 110 80 104 69 67 35 24 31 21

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 961

The right side shows the response frequencies for thelongest duration (45 sec) In both cases they were com-puted by using all the data not just those of fixed initialheight so if anything they should underestimate statisti-cal significance

As in the elasticity analysis multiple x2 analyses sup-port the intuitive observation that the rows in the tables aredifferent from each other and from a uniform distribu-tion5 As a whole both tables show statistically significantrelationships well below the p 5 001 level Row-by-rowanalyses confirm what you see by inspection The ob-servers thought that decreasing-gravity bounces lookedless natural than a normal bounce and that increasing-gravity bounces looked as natural as (or perhaps more nat-ural than) normal bounces

As a f inal sanity check we computed x2 for non-matched samples to see whether there was a statisticallysignificant difference between the elastisity data for thee 5 09 displays and the gravity data for the g 5 00 dis-plays Since these displays were generated with the sameparameters there should have been no significant differ-ence There was no significant difference (p 1)

Discussion Observer responses to the elasticity displays showed

sensitivity to unnatural increases of energy during thebounce It will be helpful to think of this as the negative-entropy condition Other studies (Bingham 1995 Bing-ham et al 1995 Gibson amp Kaushall 1973 Pittenger1990 Wickelgren amp Bingham 2001) on event dynamicstime-reversed motions and animate versus inanimate dy-namics have shown similar sensitivity to negative-entropymotion There was no statistically significant sensitivity tonormal but relatively inelastic bounces6

In the varying-gravity displays gravitational energyleaked into or out of the system smoothly and continu-ously making it harder to perceive a distinct energy sourceor sink than in the elasticity displays Also in contrast tothe elasticity displays there were two ways for an event tobe unnatural It could have an energy source strong enoughto overcome entropic losses making the local motion atleast negatively entropic or it could have an energy sinkin addition to regular entropy

If we thought only in terms of entropic or negative-entropic motion as in the elasticity displays we would pre-

Figure 3 Two-way interaction between gravity and fixed condition

Table 2Gravity Displays Response Frequencies

Response Rating All Durations Response Rating 45 sec

g 1 2 3 4 5 1 2 3 4 5

202 53 59 34 42 26 43 21 2 3 1201 10 41 59 60 44 9 17 22 13 10

00 0 17 49 83 67 0 9 16 24 23102 1 9 38 86 81 1 1 16 25 28104 2 19 34 76 84 1 7 10 26 28Total 66 145 214 347 302 54 55 66 91 90

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

962 TWARDY AND BINGHAM

dict that observers should be sensitive to negative-entropicmotion (increasing gravity) but not to entropic motion(decreasing gravity) However the effect of decreasinggravity is not at all like the effect of increasing entropyWith decreasing gravity the bounces do get slower butthey also remain quite high and the time course of thebounce is therefore much different The bounces havedifferent spacendashtime trajectories

So following the lead of the CQ hypothesis we predictedthat both increasing and decreasing gravity should spec-ify a hidden cause (which of course they did) but be-cause that cause was so far outside the observersrsquo experi-ence instead of seeing a changing gravitational field theywould see both manipulations as cases of unnatural motion

In fact this is not what happened The observers werequite sensitive to the cases of decreasing gravity (g 0)but not at all to cases of increasing gravity (g 0)

It is not really surprising that the observers consideredthe cases of decreasing gravity to be unnatural What is puz-zling is why they did not also consider the cases of in-creasing gravity to be unnatural The first question to askis whether the observers could even detect any differencebetween increasing and normal gravity

We ran a follow-up experiment to find out whether theobservers could discriminate between normal cases andincreasing-gravity cases (even though they might not cor-rectly interpret a detected difference)

EXPERIMENT 2

We reasoned that a fairly straightforward samendashdifferenttask would answer the question Rather than rating natu-ralness the observers had only to say whether two dis-plays were of the same kind (the discrimination task) Theobservers were instructed not to latch onto any peculiari-ties (such as in which weed a ball landed) but to judge onthe basis of the overall motion They were given feedbackafter each trial After a session in that condition the ob-servers returned on a different day and were then given atwo-alternative forced-choice (2AFC) task without feed-back On the 2AFC task they had to decide which of twodisplays was the more natural (the naturalness task) Theidea was to train the observers to discriminate using feed-back and then later to add the task of deciding which wasmore natural If the observers could discriminate but notinterpret correctly their performance should have beengood on the discrimination task and poor on the natural-ness task7

Method Observers Five undergraduate students at Indiana University

participated in the experiment All had normal or corrected-to-normalvision The observers were paid $7h

Display generation The displays were generated like the varying-gravity displays in Experiment 1 with a few exceptions First onlythe fixed-duration 45-sec (300-frame) displays were used Secondwe randomized the initial heightsrsquo coming from either the low range(33ndash38 m) or the high range (43ndash48 m) so that each pair had onehigh and one low in random order Likewise we randomized the

initial horizontal velocity also in two groups low (10ndash20 msec)and high (30ndash 40 msec) In addition we randomized the directionof motion for each pair (from the left edge of the screen movingright or conversely) Again all the displays were generated and se-quenced in advance Finally the ball was given a textured surface8

Instructions Instructions were presented slide-show style as be-fore On the discrimination task the observers were instructed tocheck same or different after watching a pair of bounces and to in-dicate how sure they were On the naturalness task they were told tochoose which one looked more normal As before they were told topay attention to the form and timing of the motion and not to fixateon minor details In addition they were told that the initial positionsand velocities were slightly randomized to prevent them from beingable to cue off of specific conditions In the discrimination task theywere told that they would receive feedback In the naturalness taskthey were told that they would not After the naturalness task the ob-servers completed a short free-response form

Procedure The observers were seated in front of the computer andmade their answers on printed answer forms as before The overheadlights were left on this time Alternate observers were counterbal-anced for order of presentation Twelve blocks were presented inabout an hour 6 blocks of decreasing gravity and 6 of increasinggravity Each block within a gravity condition had 12 trial pairs indifferent orders Letting ldquoNrdquo stand for natural and ldquoUrdquo for unnat-ural each block had 4 NU 4 UN and 4 NN pairsThe UN and NU pairs were divided equally between the twolevels of unnaturalness (eg g 5 201 g 5 202) Therefore eachblock yielded four data points for each level of g

Results The discrimination dcent data are presented in Table 3 Re-

call that in Experiment 1 the observers rated decreasinggravity as unnatural but not increasing gravity The pur-pose of Experiment 2 was to find out whether the ob-servers nevertheless could distinguish hypergravity casesfrom normal cases when the task did not involve explicitnaturalness judgments If we examine the increasing-gravity portion of Table 3 (the bottom half) we see thatthe observers do appear to be able to distinguish these hy-pergravity displays from the ordinary ones

However oddly the top half of Table 3 indicates that theobservers were unable reliably to distinguish decreasing-gravity displays from normal ones which is the opposite

Table 3Percentage Correct () and d cent Data for the

Discrimination Task (SamendashDifferent)

Observer Hits False Alarms 6 d cent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 67 58 59 66 079 0622 71 58 61 64 097 0633 54 50 53 68 051 0614 73 54 64 63 119 0635 77 50 68 59 147 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 81 67 65 62 101 0662 85 42 76 50 199 0663 67 33 67 60 162 0644 60 46 58 66 098 0625 85 33 79 45 223 068

Notemdash n 5 24 NN n 5 48 UN or NU Error values (6) are95 confidence intervals

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 963

of what we found in Experiment 1 In fact none of the ob-servers achieved more than threshold (75 correct) in thehypogravity condition and all the observers were atchance for recognizing NN displays as same on thediscrimination task in the hypogravity condition and wereonly slightly above chance for the hypergravity condition

The naturalness task data show a different pattern (seeTable 4) There was a clear difference in discriminabilityfor hypogravity and hypergravity and the observers coulddo the hypogravity task reasonably well but could not dothe hypergravity properly as we saw in Experiment 1

Discussion The data are encouraging but suggest that the observers

did not understand part of the samendashdifferent task If welook just at the hypergravity data the experiment has doneexactly what we wanted The observers discriminated hy-pergravity from normal gravity when asked whether theywere the same or different but judged the hypergravitydisplays to be at least as natural as the normal ones show-ing that the asymmetry in Experiment 1 was due not to aninability to discriminate but to a genuine impression ofnaturalness

On the discrimination task (samendashdifferent) the ob-servers were able to distinguish hypergravity trials fromnormal trials with dcents ranging from 10 to 22 Howeverthat very solid discriminability performance fell apart onthe naturalness task (2AFC) Four of the observers had dcentsnot significantly different from 0 whereas 1 observer ex-hibited nearly perfect discriminability but with the seman-tics completely reversed Observer 4 clearly identified thehypergravity trials each time they occurred and thoughtthat they looked more natural than the normal trials

However for hypogravity displays the observers didworse on the easier samendashdifferent questions than on theharder which is more natural task In fact the samendashdifferenttask was quite ambiguous because same did not meanidenticalmdashsince no displays were identicalmdashbut samekind As was noted discriminability performance was un-

expectedly low on the samendashdifferent task a task we al-ready knew (from Experiment 1) that observers could doMuch of the poor performance is explained by the fact thatthe observers remained at chance on judging NN tri-als They did not understand what was being asked andhad to guess

Consequently hypogravity performance was better onthe no-feedback naturalness (2AFC) task which meansthat for these displays at least the separate tasks did notperform their intended functions Therefore to make surethat the hypergravity results of Experiment 2 were not ad-versely affected by these issues we ran a short follow-upthat addressed the shortcomings of Experiment 2 by mak-ing the instructions and the task more straightforward

EXPERIMENT 3

Method Observers Two observers were run a graduate student and a

Bloomington resident in his mid-twenties9 The observers were paid$6h with a $20 incentive reward for best performance All the ob-servers had normal or corrected-to-normal vision

Display generation The displays for Experiment 3 were a sub-set of those from Experiment 2 We removed the intermediate val-ues of g from the stimuli so the observers saw only g 5 104 g 50 and g 5 202 An example slide show was added to the instruc-tions The examples showed several cases that were to be called sameand contrasted them with extreme cases of different so that the ob-servers would know the kind of overall differences that interested us

Procedure The experiment proceeded much as Experiment 2The order of presentation for both of the observers was the same onboth days Six blocks of decreasing gravity were followed by six blocksof increasing gravity Each block within a gravity condition presentedthe same 24 trial pairs in different orders Letting ldquoNrdquo stand for nat-ural and ldquoUrdquo for unnatural each block had 6 NU 6 UN and12 NN pairs Therefore each NN cell had 12 3 6 5 72 datapoints as did the combined UN and NU cells

Results The results were very clear On the samendashdifferent task

both observers had very high dcents for both decreasing andincreasing gravity conditions On the 2AFC naturalnesstask the observers had high positive d cents for the hypo-gravity cases and high negative dcents for the hypergravitycases (see Figure 4) Therefore the proper way to interpretthe asymmetry in Experiment 1 is that the observers wereor would have been able to distinguish hypergravity dis-plays from natural displays but that nevertheless thesedisplays did not appear unnatural The observers weresensitive to the difference but unaware of its semantic con-tent This result confirmed Experiment 2 without Exper-iment 2rsquos unfortunate glitch in observer response to thehypogravity condition

Looking at the free responses both Observers 1 and 2found the samendashdifferent task hard and the naturalnesstask easy Both indicated attending to the overall timingand shape of the motion but did not discover any rulesTheir performances resembled those of the observers inthe previous experiments

Table 4Percentage Correct () and d cent Data for the Naturalness Task

(ldquoWhich is more naturalrdquo 2AFC)

Observer Hits False Alarms 6 dcent 6

Hypogravity (Collapsed Over g 5 201 and 202) 1 71 29 71 84 078 0742 94 11 92 21 199 0863 75 01 83 38 146 0744 83 06 89 27 181 0835 81 31 75 51 097 064

Hypergravity (Collapsed Over g 5 102 and 104) 1 38 75 31 89 2070 0752 47 36 56 67 020 0593 42 69 36 63 2051 0604 03 94 04 11 2248 1075 44 61 42 66 2030 058

Notemdashn = 36 Error values (6) are 95 confidence intervals

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

964 TWARDY AND BINGHAM

GENERAL DISCUSSION

In Experiment 1 the observers showed an asymmetricsensitivity to energy violations (see Figure 3) To determinewhy we first had to establish whether the apparent insen-sitivity to increasing gravity was a true indistinguishabil-ity or merely a question of what looked natural or unnat-ural In Experiments 2 and 3 we determined that theobservers could discriminate between the hypergravitybounces and the normal gravity bounces but that the hy-pergravity bounces did not look unnatural In fact the hy-pergravity bounces looked more natural than the referencecase This is puzzling Can the results be reconciled withthe CQ theory or even with the general sensitivity to dy-namics supposed by KSD

Figure 5 shows the graph of energy versus time forthree bounces quickly decreasing gravity (g 5 202)normal gravity (g 5 0) and quickly increasing gravity(g 5 104) The top graph displays true energy taking thechanging gravity into account The bottom graph displaysapparent energy the energy computed from the kinemat-ics while assuming that gravity is constant at earth-normal(g 5 0)

Within each series there are discontinuous losses whenthe ball hits the ground because e 1 In normal gravity(g 5 0) energy loss between bounces is due only to airfriction which is highest near the bounces when velocityis highest For g 5 0 total energy decreases monotoni-cally For the two unnatural cases what happens dependson whether we consider true or apparent energy

If we consider true energy the data suggest that the ob-servers thought rapidly decreasing energy was more un-

natural than rapidly increasing energymdasha puzzling resultindeed considering the elasticity data from Experiment 1However if we look at apparent energy in the bottomgraph the distinction is not so neat The salient differencebetween g 5 202 and g 5 104 then is not the overallincrease or decrease in apparent energy which is about thesame but when it increases and when it decreases

In the case of an increase of the gravitational field (g 5104) when the ball reaches the ground it is going fasterthan it should given its starting height so apparent energyincreases during the descent After the bounce as the ballleaves it is traveling quite quickly but does not get as highas it should given its rebound speed Apparent energy de-creases during the ascent hitting a local minimum at theapex of the ballrsquos trajectory

In the case of a decrease of the gravitational field (g 5202) the ball falls more slowly than it should reachingthe ground with less speed than one would expect Ap-parent energy decreases during the descent After the re-bound the ball rises higher than it should given its re-bound speed Apparent energy increases during the ascent

The asymmetries in observer sensitivity mimic asym-metries in the entropy dynamics of real events In a realbounce the potential energy at apex could at most almostequal the kinetic energy exiting the previous bounce butit could assume almost any value below that dependingon how much the ball is affected by friction So from ex-perience observers should have a tight upper bound onexpected height but a broad lower bound favoring the hy-pergravity bounces

To analyze the descent it will be convenient to split theenergy into kinetic and potential energy Figure 6 breaks

Figure 4 Experiment 3 d cent data The discrimination task on the left shows that both ob-servers could distinguish both hypo- and hypergravity from normal The naturalness task onthe right shows that hypergravity looked very natural whereas hypogravity looked unnat-ural

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 965

down the energy profile into kinetic and potential energyso that we may see how the energy is exchanged over timerather than just looking at the total energy Et The rightcolumn provides the true values but we are interested inthe apparent values which are in the left column

The middle left figure shows the normal energy profileEP and EK exchange dominance of the energy budgetabout halfway through each arc and the curve for Et com-bines both and resembles neither

For increasing gravity (g 5 104 the top left figure)Et is dominated by and resembles in form the curve forEK However it is still true that EP and EK alternate aboutmidway through each arc and the EK arcs are roughlysymmetric about their minima

For decreasing gravity (g 5 202) the curves differmore strongly In the lower left graph we can see that nowEP accounts for most of Et most of the time especiallyafter the first bounce and that the EK curves are highlyskewed (asymmetric) about their minima One symptomof the asymmetric EK curve is the laconic descent of theball a motion described by many observers as ldquofloatyrdquo Inthe lower left graph EK increases too slowly during de-

scent meaning that the ball falls much too slowly whencompared with the height lost given its relatively rapid as-cent

Both increasing and decreasing gravity are conserva-tion violations In particular they upset the normal balancebetween the exchange of EK and EP Both increasing anddecreasing gravity differ in form from the normal caseUnlike normal gravity and increasing gravity howeveronly decreasing gravity results in markedly asymmetrictrajectories reflected in EK profiles asymmetric abouttheir minima at the bottom of Figure 6

Since the observers were sensitive only to decreasinggravity we tentatively conclude that observers detectedthis asymmetry The result was that they preferentially de-tected an excess of potential energy for the amount of ki-netic (or total) energy rather than the other way around

A potentially simpler explanation is that the observerspicked up on the progression of bounce frequencies In anatural bounce the interbounce interval shortens mean-ing that the bounce frequency increases with each succes-sive bounce Bounces under increasing gravity also haveincreasing bounce frequencies However bounces under

Figure 5 Comparative energy profile of total energy (Et 5 EK 1 EP) versust for three principal values of g where g reg g(1 1 gt ) In the top graph energyis measured in the objective or simulation frame of reference In the lowergraph apparent energy is measured as if gravity were constant at earth-normalThe vertical lines show the cutoff times for the 25- 35- and 45-sec durations

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

966 TWARDY AND BINGHAM

Figure 6 Kinetic and potential energy Each row shows the relationship between EK and EP for one level of g The leftcolumn shows apparent E versus t The right column shows actual E versus t (for row 2 the actual is the apparent sothere is a blank)

decreasing gravity (as well as hyperelastic bounces) havedecreasing frequencies marking them as unnatural

Figure 7 shows that bounce frequency does divide neatlyon either side of g 5 100 and indeed 1 participant inExperiment 1mdasha psychology graduate student and a musicianmdashspecifically mentioned that after awhile hebegan to judge timing between bounces using increasingfrequency as a criterion for naturalness

Nevertheless we do not think that bounce frequency isthe whole story Even the participant noted above came tothat criterion by trying to discern why some bounces lookedmore or less natural In addition other participantsrsquo free-response data pointed to properties of the overall trajec-tory The observers frequently described the decreasing-gravity bounces as too ldquofloatyrdquo an apt description of theballrsquos tendency to rise too high for its speed and to berather laconic in its subsequent descent Even the observernoted above also mentioned that the unnatural bouncesseemed to have oddly asymmetric trajectories

Finally despite our instructions and indeed the infor-mation specified in the trajectories the observers may nothave regarded the stimulus as a large heavy ball very far

away After all what they saw was a 1-cm disk about 05 min front of them However although it is true that a smallball seen up close will match the hypergravity bouncemore closely than any others there is still a huge differ-ence By the time the hypergravity ball has had one bouncethe 1-cm ball has had six

CONCLUSION

First we have demonstrated that observers are sensitiveto gradually perturbed energy dynamics Second we havedemonstrated that observers are more sensitive to the ef-fect of decreasing gravity than to that of increasing grav-ity Third we have begun to show how observers combineinformation about kinetic and potential energy in their as-sessments of the naturalness of a free-fall and bounceFourth we have thereby provided some support for theidea that perceptions of causation are tied to exchanges ofenergy and momentum

The observers could discriminate only event types thathad different trajectory forms Both increasing and de-creasing gravity generated significant changes in the en-

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

CAUSAL PERCEPTION 967

ergy profile of a bounce However under decreasing grav-ity potential energy dominated the trajectory and the ki-netic energy trajectory was asymmetric The observersthought such trajectories unnatural

The observers did not find the trajectories under in-creasing gravity to be unnatural even though they coulddiscriminate them from normal trajectories in a samendashdifferent task Such trajectories were unnaturally domi-nated by kinetic energy but still had basically symmetricexchanges of kinetic and potential energy

Since actual causation in this world is tied to the ex-change of conserved quantities such as energy and mo-mentum (Dowe 2000) we expect that the perception ofcausation is likewise tied to such exchanges of physicalquantities If so we can extend Runesonrsquos (Runeson19771983) KSD theory to the perception of causation

In a natural motion the proper exchange of energy andmomentum among visible objects reveals that these ob-jects are in fact the causes of the resultant motion Mo-tions that require a cause that can neither be seen norrapidly inferred will be judged to be unnatural An other-wise ldquounnaturalrdquo motion can be explained or made senseof by adding an appropriate and unobserved cause In ourexperiment it was very difficult to hypothesize the actualhidden cause a dynamic change of gravity Thereforesome of the displays did not look natural

That displays with increasing gravity did look naturalsuggests that humans give more weight to excesses of po-tential energy (given the kinetic or the total energy) whendetecting unnatural motion or causal anomalies We wouldnot expect humans to be perfect conservation detectorsbecause humans do not observe perfect conservation inthe world Therefore motion with negative entropy shouldlook unnatural in part because it specifies either reversed-

time motion or backward causation However in our ex-periment the observers detected motion with negative en-tropy only when it resulted in an asymmetric energy profile

Human ideas of causality are more general than thekinds of causes that can be so perceived However accountsof ldquohigher orderrdquo causation such as the more reasoning-and-judgment approach to causation pursued by Chengand Spellman (Cheng 1997 Cheng amp Holyoak 1995Glymour amp Cheng 1998 Spellman 1996) and the causalmodeling framework of Judea Pearl (Pearl 2000) all relyon some prior primitive notion of causal mechanism Inrelated studies Ahn and colleagues (Ahn amp Bailenson1995 Ahn Kalish Medin amp Gelman 1995) have shownthat humans prefer mechanism-style explanations to evenmore predictively powerful covariational accounts Wethink that this prior notion of mechanism stems from theperception of actual physical causation which is governedby the exchange of conserved quantities among objects

REFERENCES

Ahn W-K amp Bailenson J (1995) Causal attribution as a search forunderlying mechanisms An explanation of the conjunction fallacyand the discounting principle Cognitive Psychology 31 82-123

Ahn W-K Kalish C W Medin D L amp Gelman S A (1995)The role of covariation versus mechanism information in causal attri-bution Cognition 54 299-352

Bingham G P (1995) Dynamics and the problem of visual eventrecognition In R Port amp T van Gelder (Eds) Mind as motion Ex-plorations in the dynamics of cognition (pp 403-448) CambridgeMA MIT Press Bradford Books

Bingham G P Schmidt R C amp Rosenblum L D (1995) Dy-namics and the orientation of kinematic forms in visual event recog-nition Journal of Experimental Psychology Human Perception ampPerformance 21 1473-1493

Cheng P W (1997) From covariation to causation A causal power the-ory Psychological Review 104 367-405

Figure 7 Graph of bounce (and apex) frequency between successive extrema (bounce or apex) forvarious values of g

968 TWARDY AND BINGHAM

Cheng P W amp Holyoak K J (1995) Complex adaptive systems asintuitive statisticians Causality contingency and prediction In J-AMeyer amp H Roitblat (Eds) Comparative approaches to cognition(pp 271-302) Cambridge MA MIT Press

Dowe P (2000) Physical causation New York Cambridge UniversityPress

Gibson J J amp Kaushall P (1973) Reversible and irreversible events[Film] (Psychological Cinema Register Pennsylvania State CollegeUniversity Park)

Gilden D L amp Proffitt D R (1989) Understanding collision dy-namics Journal of Experimental Psychology Human Perception ampPerformance 15 372-383

Gilden D L amp Proffitt D R (1994) Heuristic judgment of massratio in two-body collisions Perception amp Psychophysics 56 708-720

Glymour C amp Cheng P (1998) Causal mechanism and probabilityA normative approach In M Oaksford amp N Chater (Eds) Rationalmodels of cognition (pp 296-313) Oxford Oxford University Press

Hecht H Kaiser M K amp Banks M S (1996) Gravitational accel-eration as a cue for absolute size and distance Perception amp Psy-chophysics 58 1066-1075

Hecht H amp Proffitt D (2000) What cues do billiard experts useConceptual and perceptual judgments of spin Unpublished manuscript

Hume D (1955) An inquiry concerning human understanding Indi-anapolis Bobbs-Merrill (Original work published 1748)

Hume D (1973) A treatise of human nature London Oxford Univer-sity Press Clarendon Press (Original work published 1739ndash1740reprinted from Selby-Biggersquos 1888 edition)

Interactive physics II [Computer software] (1992) San FranciscoKnowledge Revolution

Johansson G (1973) Visual perception of biological motion and amodel for its analysis Perception amp Psychophysics 14 201-211

Kaiser M K amp Proffitt D R (1984) The development of sensitiv-ity to causally relevant dynamic information Child Development 551614-1624

Kaiser M K amp Proffitt D R (1987) Observersrsquo sensitivity to dy-namic anomalies in collisions Perception amp Psychophysics 42 275-280

Kruschke J K amp Fragassi M M (1996) The perception of causal-ity Feature binding in interacting objects In Proceedings of the Eigh-teenth Annual Conference of the Cognitive Science Society (pp 441-446) Hillsdale NJ Erlbaum

MacroMind Accelerator [Computer software] (1989) San FranciscoMacroMind

McConnell D S Muchisky M M amp Bingham G P (1998) Theuse of time and trajectory forms as visual information about spatialscale in events Perception amp Psychophysics 60 1175-1187

Merfeld D M Zupan L amp Peterka R J (1999) Humans use in-ternal models to estimate gravity and linear acceleration Nature 398615-617

Michotte A (1963) The perception of causality (T Miles amp E MilesTrans) London Methuen (C A Mace Ed originally published asLa perception de la causaliteacute 1946 and 1954)

Muchisky M M amp Bingham G P (1992) Perceiving size in eventsvia kinematic form In J Kruschke (Ed) Proceedings of the 14th An-nual Conference of the Cognitive Science Society (pp 1002-1007)Hillsdale NJ Erlbaum

Muchisky M M amp Bingham G P (2002) Trajectory forms as a sourceof information about events Perception amp Psychophysics 64 15-31

Pearl J (2000) Causality New York Cambridge University Press Pittenger J B (1990) Detection of violations of the law of pendulum

motion Observersrsquo sensitivity to the relation between period andlength Ecological Psychology 2 55-71

Proffitt D R amp Gilden D L (1989) Understanding natural dy-namics Journal of Experimental Psychology Human Perception ampPerformance 15 384-393

Proffitt D R Kaiser M K amp Whelan S M (1990) Under-standing wheel dynamics Cognitive Psychology 22 342-373

Runeson S (1983) On visual perception of dynamic events (ActaUniversitatis Upsaliensis Studia Psychologica Upsaliensia No 9)Uppsala Academiae Upsaliensis (Original work published 1977)

Runeson S (1995) Support for the cue-heuristic model is based onsuboptimal observer performance Response to Gilden and Proffitt(1994) Perception amp Psychophysics 57 1262-1273

Runeson S amp Frykholm G (1983) Kinematic specification of dy-namics as an informational basis for person-and-action perceptionExpectation gender recognition and deceptive intention Journal ofExperimental Psychology General 112 585-615

Runeson S amp Vedeler D (1993) The indispensability of precolli-sion kinematics in the visual perception of relative mass Perceptionamp Psychophysics 53 617-632

Saxberg B V (1987) Projected free fall trajectories I Theory andsimulation Biological Cybernetics 56 159-175

Schlottman A amp Anderson N H (1993) An information integra-tion approach to phenomenal causality Memory amp Cognition 21785-801

Schlottman A amp Shanks D (1992) Evidence for a distinction be-tween judged and perceived causality Quarterly Journal of Experi-mental Psychology 44A 321-342

Spellman B A (1996) Acting as intuitive scientists Contingencyjudgments are made while controlling for alternative potential causesPsychological Science 7 337-342

Warren W H Jr Kim E E amp Husney R (1987) The way the ballbounces Visual and auditory perception of elasticity and control ofthe bounce pass Perception 16 309-336

Weir S (1978) The perception of motion Michotte revisited Percep-tion 7 247-260

Wickelgren E A amp Bingham G P (2001) Infant sensitivity to tra-jectory form Journal of Experimental Psychology Human Percep-tion amp Performance 27 942-952

NOTES

1 KSD states that the kinematics specify the dynamics That is somedynamical properties are fully specified by the kinematics of the eventand furthermore can be directly perceived

2 Any higher and the bounce with elasticity 5 12 went off screen 3 We could not do this for the elasticity experiment because at low

elasticities only two or three bounces are distinguishable even for max-imal drop heights After that the ball just rolls

4 Several x2 analyses added little to the ANOVA The patterns visi-ble in the table were statistically significant

5 A uniform distribution is the most obvious null hypothesis (reallya nil hypothesis) but by no means the only one that should be investi-gated We also checked against two other nulls (H2) 5 all rows are nodifferent from g 5 00 and (H3) 5 all rows are no different from the av-erage row

6 It is certainly possible to perceive low elasticity as unnatural Onecan buy from teaching supply stores a pair of small apparently identicalrubber balls one of which bounces quite nicely whereas the other al-though it feels the same to the touch hits the floor with a solid thud andbounces almost not at all The effect is quite surprising

7 One reviewer quite sensibly worried about confounding pres-enceabsence of feedback with different tasks Observers could just dobetter with feedback than without Fortunately the data answer thisworry The fact that the observers split not so much on task but on hypo-versus hypergravity shows the difference to be due not to feedback butto semantics Experiment 3 demonstrated this quite clearly

8 While testing the upgrade to the dynamics package we noticed thatthe earlier version had used only one half the cross section in approxi-mating the air resistance The main effect was that the balls in Experi-ment 1 traveled horizontally a bit farther than they should have (a cou-ple of ball widths after 45 sec) The effect on bounce height was smallUsing the correct cross section is unlikely to have changed the generalresult In Experiments 2 and 3 we used the correct value rather thanmatching the previous error

9 A 3rd observer who was not naive about the experiment design isnot included She performed at ceiling on both tasks

(Manuscript received July 5 2000revision accepted for publication January 22 2002)