Mental Rotation Notes PDF

Mental Rotation What is mental rotation? Mental rotation means that we can manipulate object representations in our minds. Let’s say you’re in the process of moving, or you decide to rearrange furniture in your room. Before putting in the effort required to move the furniture, you probably would ima...

Mental Rotation What is mental rotation? Mental rotation means that we can manipulate object representations in our minds. Let’s say you’re in the process of moving, or you decide to rearrange furniture in your room. Before putting in the effort required to move the furniture, you probably would imagine where the furniture would fit in the space. For example, you could mentally rotate your furniture to compare potential furniture configurations. Shepard & Metzler (1971) The most famous mental rotation experiment was performed by Shepard & Metzler in 1971. In the task, participants compared two images that depicted the same shape or mirror images and responded “same” or “different.” The difference is that mirror images are not the same. For example, your left hand is a mirror image of your right hand. If you put your hands on one another, with both palms facing up, the shapes do not match. The authors created new shapes that participants would not have everyday experience with. The shapes were 3-dimensional block segments and were rotated in depth (towards and away from the screen) or in the same plane (for example, from side to side). To compare the objects, subjects had to rotate them first mentally. Before their experiment, mental rotation was a known phenomenon. However, the time course consists of how long it takes to rotate an object's mental representation and whether the rotation's magnitude affects the time course. Participants reported that they indicated their decisions for each stimulus after mentally rotating the images to match their orientation. Using the reaction time data for these decisions, the authors found that their sample's rotation rate was 60 degrees per second (º/s). Further, the authors found a direct relationship between the angle of rotation between the stimuli and reaction time (the time required to make the decision). However, in their study, the rotation between the stimuli only ranged from 0 - 180 degrees. Would a rotation greater than 180° require more time, or is the absolute rotation angle what matters? Cooper & Shepard (1973) In a later study, Cooper and Shepard rotated familiar stimuli (letters) using a broader range of rotation values. They found that the absolute rotation angle determines the time course of mental rotation. In other words, participants will rotate the stimuli as little as is required to decide.  Mental Rotation of Three-Dimensional Objects Abstr.act. The time required to recognize that two perspective drawings portray objects of the same three-dimensional shape is found to be (i) a linearly increasing f1111ctio11 of the angular difference in the portrayed orientations of the two objects and (ii) no shorter for differences corresponding simply to a rigid rotation of one of the two-dimensional drawings in its own picture plane than for differences correspo11di11gto a rotation of the three-dimensional object in depth. Human subjects are often able to increase linearly with the angular dif- determine -that two two-dimensional ference in portrayed orientation and pictures portray objects of the same (ii) to be no longer for a rotation in three-dimensional shape even though depth than for a rotation merely in the the objects.are depicted in very different picture plane. These findings appear to orientations. The experiment reported place rather severe constraints on pos- here was designed to measure the time sible explanations of how subjects go that subjects require to determine such about determining identity of shape of identity of shape as a function of the differently oriented objects. They are, angular difference in the portrayed ori- however, consistent with an explanation entations of the two three-dimensional suggested by the subjects themselves. objects. Although introspective reports must be This angular difference was produced interpreted with caution, all subjects either by a rigid rotation of one of two claimed (i) that to make the required identical pictures in its own picture comparison they first had to imagine plane or by a much more complex, one object as rotated into the same nonrigid transformation, of one of the orientation as the other and that they pictures, that corresponds to a (rigid) could carry out this "mental rotation" rotation of the three-dimensional ob- at no greater than a certain limiting ject in depth. rate; and (ii) that, since they perceived This reaction time is· found (i) to the two-dimensional pictures as objects 19 FEBRUARY 1971 701  in three-dimensional space, they could some distinctive feature possessed by presented twice. The remaining 800 imagine the rotation around whichever only one of the two objects and thereby pairs, randomly intermixed with these, axis was required with equal ease. reachir:g a decision of noncongruencc consisted of 400 unique "different" In the experiment each of eight adult without actually having to carry out pairs, each of which (again) was pre- subjects was presented with 1600 pairs any mental rotation. As a further pre- sented twice. Each of these "different" of perspective line drawings. For each caution, the ten different three-dimen- pairs corresponded to one "same" pair pair the subject was asked to pull a sional objects depicted in the various (of either the "depth" or "picture-plane" right-hand lever as soon as he deter- perspective drawings were chosen to variety) in which, however, one of the mined that the two drawings portrayed be relatively unfamiliar and meaning- three-dimensional objects had been re- objects that were congruent with respect less in overall three-dimensional shape. flected about some plane in three-di- to three-dimensional shape and to pull Each object consisted of ten solid mensional space. Thus the two objects a left-hand lever as soon as he deter- cubes attached face-to-face to form a in each "different" pair differed, in gen- mined that the two drawings depicted rigid armlike structure with exactly eral, by both.a reflection and a rota- objects of different three-dimensional three right-angled "elbows" (see Fig. 1). tion. shapes. According to a random se- The set of all ten shapes included two The 1600 pairs were grouped into quence, in half of the pairs (the "same" subsets of five: within either subset, no blocks of not more than 200 and pre- pairs) the two objects could be rotated shape could be transformed into itself sented over eight to ten 1-hour ses- into congruence with each other (as in or any other by any reflection or rota- sions (depending upon the subject). Fig. I, A and B), and in the other half tion (short of 360°). However, each Also, although it is only of incidental (the "different" pairs) the two objects shape in either subset was the mirror interest here, each such block of pres- differed by a reflection as well as a image of one shape in the other sub- entations was either "pure," in that all rotation and could not be rotated into set, as required for the construction of pairs involved rotations of the same congruence (as in Fig. lC). the "different" pairs. type ("depth" or "picture-plane"), or The choice of objects that were mir- For each of the ten objects, 18 dif- "mixed," in that the two types of rota, ror images or "isomers" of each other ferent perspective projections-corre- for the "different" pairs was intended sponding to one complete turn around to prevent subjects from discovering the vertical axis by 20° steps-were 5 generated by digital computer and asso- A (Pict~re-plane pairs) ciated graphical output (I). Seven of the 18 perspective views of each object 4 were then selected so as (i) to avoid any V, tl views in which some p.art of the object C was wholly occluded by another part 8 Q) 3..!!!., and yet (ii) to permit the construction l.': of two pairs that differed in orientation ·g_2 by each possible angle, in 20° steps, Q) from 0° to 180°. These 70 line draw- E ings· were then reproduced by photo- offset process and were attached to... £ 5 cards in pairs for presentation to the Q) E B (Depth pairs) subjects. :.,::; Half of the "same" pairs (the "depth" pairs) represented two objects that dif- :e C 4 "' e fered by some multiple of a 20° rota- lii 3 tion about a vertical axis (Fig. lB). For Q) 2 each of these pairs, copies of two appro- priately different perspective views were 2 simply attached to the cards in the orientation in which they were origi- 0 nally generated. The other half of the O 20 40 60 80 100 120 140 160 180 "same" pairs (the "picture-plane" pairs) Angleof rotation(degrees) represented two objects that differed by some multiple of a 20° rotation in the Fig. 2. Mean reaction times to two perspec- tive line drawings portraying objects of the plane of the drawings themselves (Fig. same three-dimensional shape. Times are lA). For each of these, one of the plotted as a function of angular difference seven perspective views was selected in portrayed orientation: (A) for pairs for each object and two copies of this differing by a rotation in the pictu~e picture were attached to the card in plane only; and (B) for pairs differing by a rotation in depth. (The centers of Fig. 1. Examples of pairs of perspective appropriately different orientations. Al- the circles indicate the means and, when line drawings presented to the subjects. together, the 1600 pairs presented to they extend far enough to show outside (A) A "same" pair, which differs by an each subject included 800 "same" pairs, these circles, the vertical bars around 80° rotation in the picture plane; (B) a which consisted of 400 unique pairs (20 each circle indicate a conservative esti- "same" pair, which differs by an 80° ro- mate of the standard error of that mean "depth" and 20 "picture-plane" pairs based on the distribution of the eight tation in depth; and (C) a "different" pair, which cannot be brought into con- at each of the ten angular differences component means contributed by the in- gruence hy any rotation. from 0° to 180°), each of which was dividual subjects.) 702 SCIENCE, VOL. 171 tion were randomly intermi,xed within ner for the "different" pairs. The overall the pictures in each presented pair as the same block. mean reaction time for these pairs was well as the time taken actually to carry Each trial began with a warning tone, found, however, to be 3.8 seconds- out the process, once it was chosen. which was followed half a second later nearly a second longer than the cor- However, even for these highly prac- by the presentation of a stimulus pair responding overall means for the "same" ticed subjects, the reaction times were and the simultaneous onset of a timer. pairs. (In the postexperimental inter- still linear and were no more than 20 The lever-pulling response stopped the view, the subjects typically reported percent lower in the "pure" blocks of timer, recorded the subject's reaction that they attempted to rotate one end of presentations (in which the subjects time and terminated the visual display. one object into congruence with the knew both the axis and the direction The line drawings, which averaged be- corresponding end of the other object; of the required rotation in advance of tween 4 and 5 cm In maximum linear they discovered that the two objects each presentation) than in the "mixed" extent, appeared at a viewing distance were different when. after this "rota- blocks (in which the axis of rotation of about 60 cm. They were positioned, tion," the two free ends still remained was unpredictable). Tentatively, this with a center-to-center spacing that noncongruent.) suggests that 80 percent of a typical subtended a visual angle of 9 °, in two Not only are the two functions shown one of these reaction times may rep- circular apertures in a vertical black in Fig. 2 both linear but they are very resent some such process as "mental surface (see Fig. l. A to C). similar to each other with respect to rotation" itself, rather than a prelimi- The subjects were instructed to re- intercept and slope. Indeed, for the nary process of preparation or search. spond as quickly as possible while keep- larger.angular differences the reaction Nevertheless, in further research now ing errors to a minimum. On the aver- times were, if anything, somewhat underway, we are seeking clarification age only 3.2 percent of the responses shorter for rotation in depth than for of this point and others. were incorrect (ranging from 0.6 to rotation in the picture plane. However, ROGER N. SHEPARD 5.7 percent for individual subjects). The since this small difference is either ab- JACQUELINE METZLER reaction-time data presented below in- sent or reversed in four of the eight Department of Psychology, clude only the 96.8 percent correct re- subjects, it is of doubtful significance. Stanford University, sponses. However, the data for the in- The determination of identity of shape Stanford, California 94305 correct responses exhibit a similar pat- may therefore be based, in both cases, References and Notes tern. upon a process of the same general l. Mrs. Jih-Jie Chang of the Bell Telephone Lab- 1n Fig. 2, the overall means of the kind. If we can describe this process as oratories generated the 180 perspective projec- reaction times as a function of angular some sort of "mental rotation in three- tions for us by means of the Bell Laboratories' Stro1nbcrg--Carlson 4020 microfihn recorder and difference in orientation for all correct dimensional space," then the slope of the computer prog-ra1n for constn1cting- such (right-hand) responses to "same" pairs the obtained functions indicates that projections developed there by A. M. Noll. Sec, for example, A. M. Noll, Computers are plotted separately for the pairs dif- the average rate at which these particu- Automation 14, 20 (1965). fering by a rotation in the picture plane lar objects can be thus "rotated" is 2. We thank Mrs. Chang [sec (])]; and we also thank Dr. J. D. Elashoff for her suggestions (Fig. 2A) and for the pairs differing by roughly 60° per second. concerning- the statistic~:tl analyses. Assistance a rotation in depth (Fig. 2B). In both Of course the plotted reaction times in the c01nputcr graphics was provided by the Dell Telephone Laboratories. Supported by cases, reaction time is a strikingly linear necessarily include any times taken by NSF grant GS-2283 to R.N.S. function of the angular difference be- the subjects to decide how to process 9 l'>farch 1970; revised 8 September 1970 tween the two three-dimensional objects portrayed. The mean reaction times for individual subjects increased from a value of about l second at 0° of rota- tion for all subjects to values ranging from 4 to 6 seconds at 180° of rotation, depending upon the particular individ- ual. J\Ioreover, despite such variations in slope, the linearity of the function is clearly evident when the data are plotted separately for individual three- dimensional objects or for individual subjects. Polynomial regression lines were computed separately for each sub- ject under each type of rotation. In all 16 cases the functions were found to have a highly significant linear com- ponent (P <.001) when tested against deviations from linearity. No significant quadratic or higher-order effects were found (P >.05, in all cases). The angle through which different three-dimensional shapes must be ro- tated to.achieve congruence is not of course. defined. Therefore, a function like those plotted in Fig. 2 cannot be constructed in any straightforward man- 19 FEDRUARY 1971 703