Mental rotation

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Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is related to the visual representation of such rotation within the human mind.[1]


Mental rotation, as a function of visual representation in the human brain, has been associated with the right cerebral hemisphere. It is thought to be related to the similar areas of the brain associated with perception. It is also thought to be associated with the cognitive rate of spatial processing and general intelligence (Johnson, 1990; Jones, 1982; Hertzog, 1991). Mental rotation can be described as the brain moving objects in order to help understand what they are and where they belong. Mental rotation has been studied to try to figure out how the mind recognizes objects in their environment. Researchers generally call such objects stimuli. A stimulus then would be any object or image seen in the person’s environment that has been altered or changed in some way. Mental rotation is one cognitive function for the person to figure out what the altered object is.

Mental rotation can be separated into the following cognitive stages (Johnson 1990):

  1. Create a mental image of an object
  2. Rotate the object mentally until a comparison can be made
  3. Make the comparison
  4. Decide if the objects are the same or not
  5. Report the decision


In a mental rotation test, the subject is asked to compare two 3D objects (or letters), often rotated in some axis, and state if they are the same image or if they are mirror images (enantiomorphs). Commonly, the test will have pairs of images each rotated a specific amount of degrees (e.g. 0°, 60°, 120° or 180°). Some pairs will be the same image rotated, and others will be mirrored. The subject will be shown a set number of the pairs. The subject will be judged on how accurately and rapidly they can distinguish between the mirrored and non-mirrored pairs.

Notable research[edit]

Roger Shepard and Jacqueline Metzler (1971) did original research concerning this phenomenon. Their research showed that the reaction time for participants to decide if the pair of items matched or not was linearly proportional to the angle of rotation from the original position. That is, the more an object has been rotated from the original, the longer it takes an individual to determine if the 2 images are of the same object or enantiomorphs (Sternberg 247). Shortly afterwards, Robert Sekuler and David Nash (1972) demonstrated that a pair of mental transformations, size scaling and rotation, produced additive effects on reaction time, consistent with serial processing of these transformations.

In further research, Shepard and Cooper (1982) have proposed the concept of a "Mental Imagery" facility, which is responsible for the ability to mentally rotate visual forms. Additionally, it has been found it does not matter on which axis an object is rotated, but rather the degree to which it is rotated that has the most significant effect on response time. So rotations within the depth plane (i.e., 2D rotations) and rotations in depth (3D rotations) behave similarly. Thus, the matching requires more time as the amount of depth rotation increases, just as for within the depth plane.

In subsequent research, it has been found that response times increase for degraded stimuli and can decrease when participants are allowed to practice mentally rotating imagery (Sternberg, 2006). This research has been instrumental in showing how people use mental representations to navigate their environments.

Also, males tend to be slightly faster in mental rotation tasks than females. Indeed, some areas in the brain are more activated in the male brain than in the female brain during a mental rotation exercise. That could explain why the time-response and the accuracy in mental rotation tests tend to be better for males.[2]

The ability to rotate mentally (measured in terms of decline in response time) peaks in young adult-hood, and declines thereafter.[3]

Recent breakthroughs in nuclear magnetic resonance have allowed psychologists to discover what parts of the brain correspond to the use of this mental imagery function. Using functional magnetic resonance imaging, psychologists have shown that when participants are performing mental rotation tasks, there is activation in Brodmann's areas 7A and 7B, the middle frontal gyrus, extra-striate cortex, the hand somastosensory cortex, and frontal cortex (Cohen et al., 1996).

Other recent research has centered on whether there might be multiple neural systems for the rotation of mental imagery. Parsons (1987) found that when participants were presented with line drawings of hands rather than Shepard and Metzler-like 3D blocks showed embodiment effects in which participants were slower to rotate hand stimuli in directions that were incompatible with the way human wrist and arm joints move. This finding suggested that the rotation of mental imagery was underlain by multiple neural systems: that is, (at least) a motoric/tactile one as well as a visual one. In a similar vein Amorim, Isableu and Jarraya (2006) have found that adding a cylindric "head" to Shepard and Metzler line drawings of 3D objects can create facilitation and inhibition effects as compared to standard Metzler-like stimuli, further suggesting that these neural systems rely on embodied cognition.

Studies of the development of mental rotation have revealed the emergence of this ability in male infants by 3 to 5 months of age (Moore & Johnson, 2011; Quinn & Liben, 2008) and in both genders by 9 to 10 months of age (Lauer, Udelson, Jeon, & Lourenco, 2015; Schwarzer, Freitag, & Schum, 2013).

Shepard and Metzler in depth[edit]

In 1971, Roger N. Shepard and Jacqueline Metzler conducted some of the early studies done on mental rotation. They were the first to introduce this idea to cognitive science. Their experiment specifically tested mental rotation on three-dimensional objects. Each subject was presented with multiple pairs of three-dimensional, asymmetrical lined or cubed objects. The experiment was designed to measure how long it would take each subject to determine whether the pair of objects were indeed the same object or two different objects. For each pair, the subject was asked to pull a right-handed lever if the two objects were congruent with respect to a three-dimensional shape and to pull a left-handed lever if the objects were not. Shepard’s hypothesis was that this task would be done by creating a mental three-dimensional image of the first depict object and mentally rotating that object to see if it matches its pair. The results of the experiment confirmed the original hypothesis. The time it took for each subject to identify if two objects were identical was directly proportional to the angular rotational difference between them. The greater the angular rotational difference, the greater the time it took to identify the similarity (Shepard & Metzler, 1971).

Vandenburg and Kuse[edit]

In 1978, Steven G. Vandenberg and Allan R. Kuse developed a test to assess mental rotation abilities that was based on Shepard and Metzler’s (1971) original study. This test was constructed using India ink drawings. Each stimulus was a two-dimensional image of a three-dimensional object drawn by a computer. The image was then displayed on an oscilloscope. Each image was then shown at different orientations rotated around the vertical axis. Following the basic ideas of Shepard and Metzler's experiment, this study found a significant difference in the mental rotation scores between both the two genders. Correlations with other measures showed strong association with tests of spatial visualization and no association with verbal ability (Vandenberg & Kuse, 1978).

The brain[edit]

In 1999, a study done by seven scientists was conducted to find out which part of the brain is activated during mental rotation. Seven volunteers between the ages of twenty-nine to sixty-six participated in this experiment. None of the volunteers had a history of neurological illness. A PET scan was used to record the brain activity. Each subject was presented with eight characters during each scan, twice in its normal position and twice reversed. Scanning was conducted with the lights dimmed and the noise level low. After being placed in the scanner, each subject received both oral and written instructions and was given thirty-two practice trials. Each trial started with showing the subjects a black screen for two seconds, followed by thirty-two stimuli presented at a rate of two seconds each. The subject had those two seconds to respond to each stimuli or else the image would immediately switch to the next. If they did respond, the screen went black until the end of the two-second interval. With each stimulus presented, the subject had one of two buttons to push: one if the image shown was normal and one if the image was mirror-reversed. rCBF was measured in the brain by recording the distribution of the cerebral radioactivity following an injection of H215O into a small vein in each of the subject's left forearm. The only area of the brain in which the rCBF levels changed and that was found directly correlated with the mental rotation tasks was in the right posterior parietal lobe, specifically surrounded around the intraparietal sulcus. A small area of activation was also recorded in the left parahippocampal gyrus. The results this study collected are evidence that the task of mental rotation recruits visual-spatial changes that are implemented in this brain region (Harris, Egan, 1999).

Functional magnetic resonance imaging (fMRI) is a technique that measures brain activity by detecting changes in cerebral blood flow. It relies on the fact that, when neuronal activity increases, cerebral blood flow to the active area also increases. Thus, by monitoring which regions of the brain get increased blood flow, one can identify which regions are becoming more active during the execution of a task.

fMRI studies of brain activation during mental rotation reveal consistent increased activation of the parietal lobe, specifically the inter-parietal sulcus, that is dependent on the difficulty of the task. In general, the larger the angle of rotation, the more brain activity associated with the task. This increased brain activation is accompanied by longer times to complete the rotation task and higher error rates. Researchers have argued that the increased brain activation, increased time, and increased error rates indicate that task difficulty is proportional to the angle of rotation (Carpenter, Just, Keller, Eddy & Thulborn, 1999a; Desrocher, Smith, & Taylor, 1995; Peronnet & Farah, 1989; Wijers, Otten, Feenstra, Mulder, & Mulder, 1989; Just & Carpenter, 1985).

Since Shepard and Metzler's experiment, additional studies have been done to uncover the exact nature of the mental representation that is being rotated. Shepard & Metzler's original work demonstrated monotonically increasing response times with increasing angles of rotation, consistent with the hypothesis that people have a three-dimensional mental representation of the object. However, more recent work reveals that the representation is most likely not fully three-dimensional, but instead "two-and a half dimensional". More formally, the cognitive process of mental rotation has been proposed to proceed as follows:

  1. The object is initially represented three-dimensionally.
  2. The object is then reduced to a two-dimensional representation in the relevant plane in preparation for rotation.
  3. The object is then rotated and expanded back into its full three-dimensional form (Just et al., 2001).

Supporting this description, people asked to rotate an object around 2 different axes (e.g. rotation within the picture plane, rotation in depth) made more mistakes and had higher activation of relevant brain regions than those asked to rotate the same object around a single axis by the equivalent distance. When subjects rotate the object around a single axis, they only need to compress the image a single time and rotate it through the same plane. When rotating around 2 axes however, they must first compress and rotate the image around 1 axis, then expand and re-compress the image to rotate it around the second axis (Just & Carpenter, 1985; Just et al., 2001).

Rotation in depth 90 degrees
Rotation in the picture plane 90 degrees


Physical objects that people imagine rotating in everyday life have many properties, such as textures, shapes, and colors. A study at the University of California Santa Barbara was conducted to specifically test the extent to which visual information, such as color, is represented during mental rotation. This study used several methods such as reaction time studies, verbal protocol analysis, and eye tracking. In the initial reaction time experiments, those with poor rotational ability were affected by the colors of the image, whereas those with good rotational ability were not. Overall, those with poor ability were faster and more accurate identifying images that were consistently colored. The verbal protocol analysis showed that the subjects with low spatial ability mentioned color in their mental rotation tasks more often than participants with high spatial ability. One thing that can be shown through this experiment is that those with higher rotational ability will be less likely to represent color in their mental rotation. Poor rotators will be more likely to represent color in their mental rotation using piecemeal strategies (Khooshabeh & Hegarty, 2008).

Effect on athleticism and artistic ability[edit]

Research on how athleticism and artistic ability affect mental rotation has also been done. Pietsch, S., & Jansen, P. (2012) showed that people who were athletes or musicians had faster reaction times than people who were not. They tested this by splitting people from the age of 18 and higher into three groups. Group 1 was students who were studying math, sports students and education students. It was found that through the mental rotation test students who were focused on sports did much better than those who were math or education majors. Also it was found that the male athletes in the experiment were faster than females, but male and female musicians showed no significant difference in reaction time.

Moreau, D., Clerc, et al. (2012) also investigated if athletes were more spatially aware than non-athletes. This experiment took undergraduate college students and tested them with the mental rotation test before any sport training, and then again afterward. The participants were trained in two different sports to see if this would help their spatial awareness. It was found that the participants did better on the mental rotation test after they had trained in the sports, than they did before the training. There are ways to train your spatial awareness. This experiment brought to the research that if people could find ways to train their mental rotation skills they could perform better in high context activities with greater ease.

Tsubasa Kawasaki (2016) investigated of mental rotation on postural stability. Participants performed a MR task involving either foot stimuli, hand stimuli, or a non-body stimuli (a car). After 10 minutes of the MR task, the body sway of participants standing on one foot was measured immediately after the MR task, and again after 10, 30, and 60 minutes. The results suggest that MR tasks involving foot stimuli were more effective at improving balance than hand or car stimuli, even after 60 minutes.[4]

Real life application[edit]

Further information: Abstraction

If the previously cited research on the mental rotation times of athletes are replicated and confirmed, then there may be relationships between competent bodily movement and the speed with which individuals can perform mental rotation. This may apply to dancers, but further research is required to confirm or deny this speculation. Furthermore, if the previously cited research is confirmed, then musical training and proficiency with an instrument may be related to the speed with which the musician can perform mental rotation. Again, further research is required to confirm or deny this speculation.[citation needed]

See also[edit]


  1. ^ Shepard, Roger N.; Metzler, Jacqueline (1971-02-19). "Mental Rotation of Three-Dimensional Objects". Science. 171 (3972): 701–703. doi:10.1126/science.171.3972.701. ISSN 0036-8075. PMID 5540314. 
  2. ^ Semrud-Clikeman, Margaret; Goldenring Fine, Jodene; Bledsoe, Jesse; C. Zhu, David (2012). "Gender Differences in Brain Activation on a Mental Rotation Task". International Journal of Neuroscience. doi:10.3109/00207454.2012.693999. ISSN 1543-5245. 
  3. ^ "Mental Rotation Experiment". Archived from the original on July 22, 2012. Retrieved Feb 20, 2006. 
  4. ^ Kawasaki, Tsubasa (July 2016). "Improvement of postural stability during quiet standing obtained after mental rotation of foot stimuli.". Journal of Motor Behavior. 48 (4). doi:10.1080/00222895.2015.1100978 – via PsychINFO. 

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