VISUAL COGNITION, 2002, 9 (1/2), 28–40

Larger forward memory displacement in the direction of gravity Masayoshi Nagai, Koji Kazai, and Akihiro Yagi Department of Psychology, Kwansei Gakuin University, Hyogo, 662-8501, Japan An observer’s memory for the final position of a moving stimulus is shifted forward in the direction of its motion. Observers in an upright posture typically show a larger forward memory displacement for a physically downward motion than for a physically upward motion of a stimulus (representational gravity; Hubbard & Bharucha, 1988). We examined whether representational gravity occurred along the environmentally vertical axis or the egocentrically vertical axis. In Experiment 1 observers in either upright or prone postures viewed egocentrically upward and downward motions of a stimulus. Egocentrically downward effects were observed only in the upright posture. In Experiment 2 observers in either upright or prone postures viewed approaching and receding motions of a stimulus along the line of sight. Only in the prone posture did the receding motion produce a larger forward memory displacement than the approaching motion. These results indicate that representational gravity depends not on the egocentric axis but on the environmental axis.

When a stimulus moves and vanishes abruptly, an observer’s memory for the final position of the stimulus is shifted forward in the direction of motion. Freyd and Finke (1984) termed this forward memory displacement representational momentum, because it appears similar to physical momentum. A physical object in motion cannot stop immediately, but coasts some distance because of its momentum. Similarly, an observer’s mental representation of an object in motion seems to exhibit a momentum-like characteristic and cannot stop immediately. This analogy suggests that a forward memory displacement occurs because the law of physical momentum has become incorporated into Please address all correspondenc e to M. Nagai, Department of Intelligence Science and Technology, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan. Email: [email protected] p We thank Robert C. Sutherland , Hiroko Fukuda, and Cindy Mendoca for improving the English expressio n of this paper and Rie Tsubouchi for helping to run Experiment 1. Parts of this study were presente d at European Conference on Visual Perception, Oxford, UK, August 1998. Ó 2002 Psychology Press Ltd http://www.tandf.co.uk/journals/pp/13506285.html DOI:10.1080/13506280143000304

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the representational system during the course of human evolution (Finke & Freyd, 1985; Kelly & Freyd, 1987). This supposition is consistent with Shepard’s (1984, 1994) view that human cognitive activities (e.g., perceiving and imaging) are guided by the internalization of long-enduring constraints in the physical world. Memory displacements may be related to physical principles in the real world. For example, the magnitude of a forward memory displacement increases with increases in velocity (Freyd & Finke, 1985; Hubbard & Bharucha, 1988) and acceleration (Finke, Freyd, & Shyi, 1986) of a stimulus, and this is consistent with the principles of momentum. Implied friction between a moving stimulus and an adjoining surface reduces a forward memory displacement (Hubbard, 1995b). A pointed stimulus moving in the direction of its point elicits a larger forward memory displacement than does a pointed stimulus moving in the other direction, which can be explained by the former’s receiving less friction than the latter (Nagai & Yagi, 2001). Besides these factors, a gravity-like characteristic was found in memory displacements. A stimulus moving downward produced a larger forward memory displacement than did a stimulus moving upward. In addition, a stimulus moving horizontally produced both a forward memory displacement and a downward memory displacement (Hubbard, 1990, 1997a,b; Hubbard & Bharucha, 1988; Hubbard & Ruppel, 1999; Reed & Vinson, 1996; Vinson & Reed, this issue). Additionally, memory for the location of a stationary object is shifted downward (Bertamini, 1993; Freyd, Pantzer, & Cheng, 1988; Hubbard & Ruppel, 2000; Senior, Ward, & David, this issue). Hubbard (1995c, 1997) has referred to this downward displacement as representational gravity. In previous studies observers always sat in an upright posture. Given that in the upright posture both the physical vertical and the head/body axes are parallel to each other, it is not clear if representational gravity reflected a downward bias along the environmental vertical axis or the egocentric vertical axis. The purpose of the present study, then, was to examine whether representational gravity occurs along the environmental axis or the egocentric axis. In other words, we examine whether memory displacement increases in the environmental or the egocentric downward direction. Hereafter in this paper, we use the term downward effect instead of representational gravity, because it is possible that the previously reported downward effect was not along the environmentally vertical axis (the gravitational axis) but along the egocentrically vertical axis (the head/body axis).

EXPERIMENT 1 In Experiment 1, observers in either upright or prone postures viewed egocentrically upward and downward motions of a stimulus along the head/ body axis (Figure 1). If the downward effect on memory displacement acts in

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Figure 1. Direction of circle motion and observer posture in Experiment 1. The egocentrically upward and downward motion of the circle along the head/body axis was used in the (a) upright and (b) prone postures.

the environmentally downward direction, then a difference in forward displacement between egocentrically upwards and downwards motion should only be observed in the upright posture. If the downward effect acts in the egocentrically downward direction, the difference in forward memory displacements between the egocentrically upward and downward motions would be observed in both postures.

Method Observers. Twelve undergraduate students at Kwansei Gakuin University volunteered to participate in the present experiment. All observers had normal or corrected-to-normal vision. They were naïve as to the hypothesis. Apparatus. Stimuli were presented on a 14-inch CRT monitor (Sanyo, CMT-D14UD3) controlled with a computer (Apple, Power Macintosh 9500). The monitor, with a resolution of 640 × 480 pixels, was placed at a distance of 50 cm from the eyes of an observer. The signals of the observer’s responses were supplied to the computer via a Key Pad (Advanced Gravis, Mac Gamepad). Stimuli. The stimulus was a filled black circle 0.78 degrees (18 pixels) in diameter, and was presented on a white background. Each trial began with an indicating circle, which showed the starting position of the circle. The indicating circle was presented for 1000 ms at 9.12 degrees (210 pixels) above or below the centre of the screen. The motion of the circle started 500 ms after the offset of the indicating circle. The circle moved upward or downward on the screen. The motion consisted of presenting the circle five, seven, or nine times in various locations on the screen. The duration of each presentation was 100 ms, and the interstimulus interval (ISI) between the presentations was 0 ms. The circle was shifted 1.52 degrees (35 pixels) between the successive presen-

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tations, and this resulted in a velocity of approximately 13.73 degrees/s. The motion terminated at one of three locations: The centre of the screen, 3.05 degrees (70 pixels) above the centre of the screen, or 3.05 degrees (70 pixels) below the centre of the screen. After a 250 ms blank screen (retention interval), a probe, in the form of a circle, was presented. The location of the probe varied about the final position of the moving circle by –0.635, –0.435, –0.217, 0, +0.217, +0.435, or +0.635 degrees (–15, –10, –5, 0, +5, +10, or +15 pixels); all probes were located along the axis of the motion; negatively signed probes were located behind the final position of the moving circle, and positively signed probes were located beyond the final position of the moving circle (the zero, non-signed probe was located at the final position of the moving circle). The probe remained on the screen until the observer responded. The inter-trial interval was approximately 2 s. Procedure. The observers were tested in a dark room. The task of the observers was to press one of two buttons if the probe was presented at the same position as the final position of the moving circle and the other button if it was presented at a different position. The observers were instructed to respond as quickly and accurately as possible. The observers performed the task both in the upright and prone postures. In the upright posture, observers were seated in a chair, and in the prone posture, observers were laid stomach-down on a bed containing a hole through which they could look down on the monitor. In both postures, the monitor was placed at a distance of 50 cm from the observers, and the vertical axis of the monitor was parallel to the head–body axis of the observer. Each observer received 252 trials: 2 postures (upright or prone) × 2 directions of motion (egocentrically upward or downward) × 3 lengths of motion (five, seven, or nine presentations of the circle) × 7 probes (– 0.653, – 0.435, – 0.217, 0, + 0.217, +0.435, or +0.653 deg) × 3 replications. Trials were divided into four blocks of 63 trials each, and within each block observers were only in one of the postures. All trials were preceded by 40 practice trials in either the upright or the prone posture. No error feedback was given throughout the entire session. The entire session lasted about 60 min.

Results Figure 2(a) shows the proportion of same responses for each probe. The data for each plot arose from collapsing the data over three final positions of the moving circle, because in the present study there was no prior prediction about the influence of the final positions. In order to estimate the magnitude of the memory displacement, we calculated a weighted mean of the same responses

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Figure 2. Results of Experiment 1. (a) Proportions of the same responses for each probe. (b) Weighted means of the same responses.

(based on Faust, 1990; see also Nagai & Yagi, 2001). The weighted mean for each observer for each direction of the circle’s motion in each posture was calculated by adding up the products of the proportion of the same responses for each probe and that probe position (–0.653 degrees to +0.653 degrees) and dividing the sum of the products by the sum of the proportions of the same responses. A positive value for the weighted mean indicates a memory displacement in the direction of the circle’s motion (a forward memory displacement), and a negative value for the weighted mean reflects a memory displacement in the direction opposite to the circle’s motion (a backward memory displacement). A value of zero indicates no memory displacement. The weighted means were analysed in a 2 Posture × 2 Direction of Motion (egocentrically upward or downward) ANOVA, and are shown in Figure 2(b). A significant main effect for direction, F(1, 11) = 5.48, MSe = 0.0066, p < .05, and a significant interaction were found, F(1, 11) = 11.12, MSe = 0.0019, p < .01. However, a main effect for posture was not significant. Post hoc Tukey’s HSD tests (p < .05) revealed that in the upright posture the egocentrically downward motion (M = 0.22) produced a larger forward memory displacement than the egocentrically upward motion (M = 0.12), but in the prone posture there was no such difference between the motions (upward, M = 0.15; downward, M = 0.17). We performed t-tests to compare the weighted means with zero (a Bonferoni correction for p < .05 was used). The t-tests revealed that all the weighted means were significantly larger than zero: upward motion in upright, t(11) = 3.81, p < .01; downward motion in upright, t(11) = 6.58, p < .0001; upward motion in prone, t (11) = 3.94, p < .01; downward motion in prone, t(11) = 4.52, p < .001. Thus, forward memory displacements for both the egocentrically upward and downward motions occurred in both postures.

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Discussion As shown in Figure 2(b), weighted means for egocentrically downward motions were greater than weighted means for egocentrically upward motions. However, there was a strong interaction of direction and posture such that the difference in displacements between egocentrically upward and downward motions was only obtained when observers were upright. Furthermore, the asymmetry in displacements between egocentrically upward and egocentric downward motions within the upright condition was strong enough to produce a main effect of direction. Overall, the downward effect was obtained when observers in an upright posture viewed egocentrically upward or downward motions, but not when observers in a prone posture viewed egocentrically upward or downward motion.

EXPERIMENT 2 The results of Experiment 1 did not demonstrate conclusively that the downward effect was related solely to the orientation of the environmental axes, because in the upright posture in Experiment 1, the egocentric and environmental vertical axes were aligned. In order to more conclusively establish that the downward effect depends upon the environmental vertical, it is necessary to demonstrate a downward effect for observers in prone postures when the direction of motion corresponds to the environmental vertical and the lack of a downward effect for upright postures when the direction of motion does not correspond to the environmental vertical. In Experiment 2, approaching and receding motion of a stimulus along the line of sight was used in both postures (Figure 3); thus, in the prone posture the stimulus moved only along the environmentally vertical axis, whereas in the upright posture the stimulus did not move along either the environmentally vertical or egocentric vertical axis. If gravity influences memory displacement, then the anisotropy in forward displacements (the downward effect) would be observed only in the prone posture.

Figure 3. Direction of circle motion and observer posture in Experiment 2. The approachin g and receding motion of the circle along the line of sight was used in the (a) upright and (b) prone postures.

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Method Observers. Twelve undergraduate students at Kwansei Gakuin University volunteered to participate in the present experiment; none had participated in Experiment 1. All observers had normal or corrected-to-normal vision. They were naïve as to the hypothesis. Apparatus. The same monitor and computer as in Experiment 1 were used. The monitor was placed at a distance of 30 cm from the eyes of the observer. In addition, the observers wore goggles, and the left and right sides of the goggles each contained a polarizing filter. The left and right side of the monitor were covered with a similar polarizing filter. The polarization plane on the right side of the goggles and the right side of the monitor was aligned with the horizontal axis of the monitor, and the polarization plane on the left side of the goggles and the left side of the monitor was aligned with the vertical axis of the monitor (Figure 4a). The observers could see only the right half of the monitor with their right eyes and the left half of the monitor with their left eyes. This enabled dichoptic stimulation to occur, allowing the observers to perceive stereoscopic motions of the stimulus. Stimuli and procedure. Two black squares (4 × 4 pixels) on a white background were presented on each side of the screen1 and remained visible throughout each trial. In a three-dimensional virtual space the observers viewed a black reference square (4 × 4 mm) at the distance of 38.0 cm from their eyes. The presentation of the reference square allowed the observers to easily perceive motions in depth (Regan, Erkelens, & Collewijn, 1986). Each trial began with a black indicating square (8 × 8 mm) in the virtual space, which was

Figure 4. (a) The arrangemen t of the polarized displays used in Experiment 2. Two polarizing filters were attached to the screen of the monitor. The goggles through which observers viewed the stimuli were also covered with two polarizing filters. (b) An example of the presentation of the square’s motion (the receding motion). 1

According to the width of an observer ’s eyes, we selected the positions at each side of the reference square, the indicating square, and the moving square. This manipulation enabled the retinae of all the observers to be stimulated by a similar arrangement of the squares.

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formed by presenting two black squares (8 × 8 mm) on each side of the screen. The indicating square showed the starting position of the motion in depth. The observers viewed the indicating square at a distance of 40.0 cm or 36.0 cm from their eyes. The indicating square at 40.0 cm signified that an approaching motion would follow and the indicating square at 36.0 cm signified that a receding motion would follow. The duration of the indicating squares was 1500 ms. In order to simulate approaching and receding motion of a black square (8 × 8 mm) in the virtual space, 500 ms after the offset of the indicating square, two black squares (8 × 8 pixels) on each side of the screen moved horizontally toward or away from the centre of the screen (Figure 4b). The observers viewed an approaching motion of the perceived square when the two squares moved toward the centre of the screen, or viewed a receding motion of the perceived square when the two squares moved away from the centre. On the screen the path of the moving squares was 10 pixels above the position of the black squares that formed the reference square in the virtual space. Consequently, the path of the motion in the virtual space was 10 mm above the reference square. The squares were presented five times, and perceived motion were always along the line of sight. The duration of each presentation was 100 ms, and the ISI between the presentations was 0 ms. On the screen the two squares were displaced 1 pixel between successive presentations. The perceived velocity of the square’s motion was 4.0 cm/s. The final position of the square’s motion was always viewed at the distance of 38.0 cm from the observers’ eyes (only one final position of the moving square was used, because several final positions of the stereoscopic motion made the task very difficult in preliminary experiments). After a 250 ms blank screen (retention interval), the observers viewed a black probe in the form of the square (8 × 8 mm) in the virtual space, which was formed by presenting two black squares (8 × 8 pixels) on each side of the screen. The position of the probe in the virtual space varied about the final position of the moving square by –1.0, –0.5, 0, +0.5, or +1.0 cm (displacements of each square on the screen: –2, –1, 0, +1, or +2 pixels); all probes were located along the axis of motion. The inter-trial interval was approximately 2 s. Observers’ eye movements were not restricted. Each observer received 200 trials: 2 postures (upright or prone) × 2 directions of motion (approaching or receding) × 5 probes (–1.0, –0.5, 0, +0.5, or +1.0 cm) × 10 replications. The other details of the procedure were the same as in Experiment 1. Each block contained 50 trials.

Results Figure 5(a) shows proportion of same responses for each probe. Figure 5(b) shows the weighted means for both approaching and receding motion in both postures. The weighted means were analysed in a 2 Posture × 2 Direction of Motion (approaching or receding) ANOVA. A significant interaction was

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Figure 5. Results of Experiment 2. (a) Proportion of same responses for each probe. (b) Weighted means of the same responses.

found, F(1, 11) = 7.30, MSe = 0.0024, p < .05. However, main effects for posture and direction were not significant. Post hoc Tukey’s HSD tests (p < .05) revealed that in the prone posture the receding motion (M = 0.22) produced a larger forward displacement than the approaching motion (M = 0.11), but in the upright posture there was no such difference between these motions (approaching, M = 0.14; receding, M = 0.18). The results mean that the anisotropy in forward memory displacements appeared only in the prone posture. Bonferoni corrected t-tests revealed that the weighted means for receding motion in both postures were greater than zero: in upright, t(11) = 3.52, p < .01; in prone, t(11) = 4.89, p < .001. Although the weighted means for the approaching motions in both postures were positive, they were not significantly different from zero: in upright, t(11) = 1.88, p = .087; in prone, t(11) = 1.55, p = .15.

Discussion As shown in Figure 5(b), there was a strong interaction of direction and posture such that the difference in displacements between approaching and receding motion was only obtained when observers were upright. The main effects of direction and of posture did not influence displacements. Given that the line of sight was aligned with the environmental vertical in the prone posture and was not aligned with the environmental vertical in the upright posture, these results suggest that the downward effect is obtained only when stimulus motion is along the environmental vertical. This pattern excludes the possibility that the downward effect requires an alignment of environmental vertical and egocentric vertical axes. In addition to demonstrating the dependence of the downward effect on the environmental vertical axis, the present experiment also demonstrated that forward memory displacement for approaching motion was smaller in general than forward displacement for receding motion. This directional bias in

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forward memory displacement might be due to different characteristics between convergence and divergence eye movements (Hung, Zhu, & Ciuffreda, 1997). Forward memory displacements for motion in depth was also found by Hayes, Sacher, Thornton, Sereno, and Freyd (1996) and Hubbard (1996). Consistent with the present findings, Hubbard also found that approaching motion yielded smaller forward displacements than did receding motion, but the stimuli he presented were contracting and expanding rectangles in the picture plane, which implied motion in depth. In addition, Munger, Solberg, and Horrocks (1999) found that objects rotated in depth produced a forward memory displacement (see also Munger & Minchew, this issue).

GENERAL DISCUSSION Both Experiments 1 and 2 suggested that the downward effect occurred along the environmentally vertical axis. In Experiment 1, the downward effect occurred not along the egocentrically vertical axis but along the environmentally vertical axis. However, it was possible that the downward effect was observed only when the stimulus moved along both the environmentally and egocentrically vertical axes. Experiment 2 excluded this possibility and demonstrated that the downward effect was observed even when a stimulus moved only along the environmentally vertical axis. As a useful addition, Experiment 2 also revealed that stereoscopic motions produced forward memory displacements. This is the first study to investigate cross-modal interactions between vision and graviception in forward memory displacements, although previous studies (Freyd, Kelly, & Dekay, 1990; Hubbard, 1993, 1995a) found that forward memory displacements could be observed in a non-visual modality (auditory forward memory displacements or representational momentum). The gravitationally downward effect we found suggests that the visual representational system where forward memory displacements occur receives information about gravity from non-visual modalities (otoliths, somatosensory organs, etc.). Why would memory and visual displacements be influenced by information regarding the direction of gravitational attraction? Hubbard (1998, 1999) proposed that the ability to automatically extrapolate the subsequent position of a moving object could offer a selective evolutionary advantage, and thus memory displacements in the direction dictated by implied physical principles (e.g., gravity, momentum) would occur. Consistent with Hubbard’s idea, we hypothesize that actions directed towards a moving object (catching, hitting, etc.) are implemented by an extrapolation mechanism, which in turn produces forward memory displacements. According to this hypothesis, in order to catch a ball whatever posture one takes, the extrapolation system should accurately

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integrate the information of gravity and of vision. As a result of this integration, memory displacements would be affected by information about gravity. These ideas suggest that observers should be able to use gravity information, but studies on performance on a variety of perceptual tasks have shown that observers do not correctly use gravity information unless those observers are in an upright orientation. For example, tilting a head or a body laterally from the physical vertical results in a judged error of the subjective visual vertical in the direction of the tilt or in the opposite direction. The direction and size of the error depends on the angle of a head or body tilt (e.g., Ebenholtz, 1970; Mittelstaedt, 1983). In addition, a visual shape-processing system is not affected by the information of gravity, and always assumes that the light source is at the top in a retina regardless of observers’ postures (Ramachandran, 1988). It seems that the crucial difference between the present study on forward memory displacements and previous studies (Ebenholtz, 1970; Mittelstaedt, 1983; Ramachandran, 1988) is the dynamics of the object; the former study used moving objects, whereas the latter studies used static objects. In the case of the static objects, the extrapolation mechanism would not work. The idea that moving or static objects might be processed different is consistent with the notion of Bridgeman, Perry, and Anand (1997) that there are two visual maps of space: a motor map, and a cognitive map (see also Kourtzi & Nakayama, this issue). The motor map provides correct information on absolute positions and orientations of objects in the world, in order to enable accurate visually guided motor responses. This map is not available to consciousness of the visual world. In contrast, the cognitive map contains detailed relative positions and orientations of objects to construct the visual world, but does not have the information on absolute position and orientation.2 If our hypothesis is true, the extrapolation mechanism might access the motor map, whereas other visual systems (e.g., modules for processing the orientation, or the subjective visual vertical, and the shape) access the cognitive map. In order to localize objects in their precise future positions, the extrapolation mechanism, unlike many visual systems, may access the motor map and accurately integrate information from other modalities. Consequently, forward memory displacements may increase in the direction of gravity, not in the subjective physical downward direction. In the present experiments, observers knew their own posture: upright or prone. The present results imply that information from the graviceptors dominates knowledge about the egocentric axes (one’s own posture) in memory displacements. As mentioned earlier, there exist some factors that influence memory displacements. It should be noted that, as to the priority between the factors, the present study revealed only that information from the graviceptors dominates the knowledge about the egocentric axis. Therefore, the priorities 2

The similar framework is proposed by Goodale (e.g., Goodale & Humphery, 1998).

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between the factors are still unknown. This problem requires further examination in future studies.

REFERENCES Bertamini, M. (1993). Memory for position and dynamic representations . Memory and Cognition, 21, 449–457. Bridgeman, B., Perry, S., & Anand, S. (1997). Interactio n of cognitive and sensorimoto r maps of visual space. Perception and Psychophysic s, 59, 456–469. Ebenholtz, S.M. (1970). Perception of the vertical with body tilt in the median plane. Journal of Experimental Psychology, 2, 15–30. Faust, M. (1990). Representationa l momentum: A dual process perspective . Unpublished doctoral dissertation, University of Oregon, Eugene, USA. Finke, R.A., & Freyd, J.J. (1985). Transformation s of visual memory induced by implied motions of pattern elements. Journal of Experimental Psychology : Learning, Memory and Cognition, 11, 780–794. Finke, R.A., Freyd, J.J., & Shyi, G. C. W. (1986). Implied velocity and acceleratio n induce transformations of visual memory. Journal of Experimental Psychology : General, 115, 175–188. Freyd, J.J., & Finke, R.A. (1984). Representationa l momentum. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 126–132. Freyd, J.J., & Finke, R.A. (1985). A velocity effect for representationa l momentum. Bulletin of the Psychonomic Society, 23, 443–446. Freyd, J.J., Kelly, M.H., & Dekay, H.K. (1990). Representationa l momentum in memory for pitch. Journal of Experimental Psychology : Learning, Memory, and Cognition, 10, 1107– 1117. Freyd, J.J., Pantzer, T.M., & Cheng, J.L. (1988). Representin g statics as forces in equilibrium . Journal of Experimental Psychology: General, 117, 395–407. Goodale, M.A., & Humphery, G.K. (1998). The objects of action and perception. Cognition, 67, 181–207. Hayes, A., Sacher, G., Thornton, I.M., Sereno, M.E., & Freyd, J.J. (1996). Representationa l momentum in depth using stereopsis . Investigativ e Ophthalmolog y and Visual Science, 37(Suppl. 3), s467. Hubbard, T.L. (1990). Cognitive representatio n of linear motion: Possible direction and gravity effects in judged displacement. Memory and Cognition, 18, 299–309. Hubbard, T.L. (1993). Auditory representationa l momentum: Musical schemata and modularity. Bulletin of the Psychonomic Society, 31, 201–204. Hubbard, T.L. (1995a). Auditory representationa l momentum: Surface form, direction , and velocity effects. American Journal of Psychology, 108, 255–274. Hubbard, T.L. (1995b). Cognitive representatio n of motion: Evidence for representationa l friction and gravity analogues . Journal of Experimental Psychology : Learning, Memory, and Cognition, 21, 1–14. Hubbard, T.L. (1995c). Environmenta l invariant s in the representatio n of motion: Implied dynamics and representationa l momentum, gravity, friction, and centripeta l force. Psychonomic Bulletin and Review, 2, 322–338. Hubbard, T.L. (1996). Displacement in depth: Representationa l momentum and boundary extension. Psychological Research/Psychologische Forschung, 59, 33–47. Hubbard, T.L. (1997a). Target size and displacemen t along the axis of implied gravitationa l attraction: Effects of implied weight and evidence of representationa l gravity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 1484-1493 .

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Hubbard, T.L. (1997b). Target size and representationa l momentum: A re-evaluatio n of the momentum metaphor. In Proceeding s of the 19th annual conferenc e of the Cognitive Science Society (pp. 953). Mahwah, NJ: Lawrence Erlbaum Associates Inc. Hubbard, T.L. (1998). Representationa l momentum and other displacement s in memory as evidence for nonconsciou s knowledge of physical principles . In S.R. Hameroff, A.W. Kaszniak, & A.C. Scott (Eds.), Towards a science of consciousness : II. The second Tuscon discussion s and debates (pp. 505–512). Cambridge, MA: MIT Press. Hubbard, T.L. (1999). How consequence s of physical principle s influence mental representation : The environmenta l invariant s hypothesis . In P.R. Killeen & W.R. Uttal (Eds.), Fechner Day 99: The end of 20th century psychophysics —proceeding s of the 15th annual meeting of the Internationa l Society for Psychophysic s (pp. 274–279). Tempe, AZ: Internationa l Society for Psychophysics. Hubbard, T.L., & Bharucha, J.J. (1988). Judged displacemen t in apparent vertical and horizonta l motion. Perception & Psychophysic s, 44, 211–221. Hubbard, T.L., & Ruppel, S.E. (1999). Representationa l momentum and the landmark and attraction effect. Canadian Journal of Experimental Psychology, 53, 242–255. Hubbard, T.L., & Ruppel, S.E. (2000). Spatial memory averaging, the landmark attraction effect, and representational gravity. Psychological Research/Psychologische Forshung, 64, 41–45. Hung, G.K., Zhu, H., & Ciuffreda, K.J. (1997). Convergenc e and divergenc e exhibit different response characteristics to symmetric stimuli. Vision Research, 37, 1197–1205. Kelly, M.H., & Freyd, J.J. (1987). Extrapolation s of representationa l momentum. Cognitive Psychology, 19, 369–401. Kourtzi, Z., & Nakayama, K. (this issue). Distinct mechanism s for the representatio n of moving and static objects. Visual Cognition, 9, 248–264. Mittelstaedt , H. (1983). A new solution to the problem of the subjective vertical. Naturwissenschaften, 70, 272–281. Munger, M.P., & Minchew, J.H. (this issue). Parallels between remembering and predictin g an object’s location. Visual Cognition, 9, 177–194. Munger, M.P., Solberg, J.L., & Horrocks, K.K. (1999). The relationship between mental rotation and representationa l momentum. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25,1557–1568. Nagai, M., & Yagi, A. (2001). The pointednes s effect on representationa l momentum. Memory and Cognition, 29, 91–99. Ramachandran, V.S. (1988). Perception of shape from shading. Nature, 331, 163–166. Reed, C.L., & Vinson, N.G. (1996). Conceptual effect on representationa l momentum. Journal of Experimental Psychology: Human Perception and Performance, 22, 839–850. Regan, D., Erkelens, C.J., & Collewijn, H. (1986). Necessary condition s for the perceptio n of motion-in-depth. Investigative Ophthalmology of Visual Science, 27, 806–809. Senior, C., Ward, J., & David, A.S. (this issue). Representationa l momentum and the brain: An investigation into the functional necessity of V5/MT. Visual Cognition, 9, 81–92. Shepard, R.N. (1984). Ecological constraint s on internal representation : Resonant kinematics of perceiving, imaging, thinking, and dreaming. Psychological Review, 94, 417–447. Shepard, R.N. (1994). Perceptual-cognitiv e universal s as reflection s of the world. Psychonomic Bulletin and Review, 1, 2–28. Vinson, N.G., & Reed, C.L. (this issue). Sources of object-specifi c effects in representationa l momentum. Visual Cognition, 9, 41–65.