Last updated: September 13, 2019
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 AbstractMental rotation refers to the ability of one’s mind to identify an image when it is in a normal presentation, mirror-reversed, and rotated about an axis to several different positions.

  In this experiment, the researchers determine whether identifying P or G is easier, and at what rotations (in degrees) the letters are easiest to identify.  It is determined that P is slightly easier to identify than G in all rotations, but that the closer the letter is to its typical presentation (either forward facing or mirror-reversed), the easier it is to identify, and the less response is needed.             Background Development‘Mental Rotation’ is an experiment regarding how the brain processes images; in this case, letters.  If a letter is mirror-reversed (that is, viewed backwards as if held up to a mirror), how easily will be it recognized as it is rotated around an axis?  That is, if a letter is turned so it is upside down, sideways, or at various other points along a circle, will a subject be able to answer “is the image correct or is it mirror-reversed?”Cooper and Shepard did an experiment in mental rotation in 1990, and found basically that as an image is rotated further away from its usual vertical presentation (that is, the way it normally is written, like any of the letters in this sentence), it becomes harder to tell if it is written normally or mirror-reversed.  However, once it is upside down and is moving back towards the normal position again, it becomes easier to tell.The experiment explains the way the brain processes images.

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  That is, if an image is upside down or backwards, the brain automatically changes the image back to its usual presentation so that a person can understand it.  That is, just because a letter is backwards doesn’t mean a person can’t understand that it is the same letter.  The brain can identify images correctly even if their presentations are different.  In this particular experiment, though, changing two ways that the image is presented – both backwards and rotated – makes identifying the image more difficult.     ExperimentIn this particular experiment, a person’s ability to identify the presentations (i.e. is it normally-facing or mirror-reversed) of the letters P and G are being tested.  Both letters will be presented in their normal presentations (that is, like any of the letters of this sentence) and mirror-reversed at a variety of different angles.

  They will be shown at 0, 45, 90, 135, 180, 225, 270, and 315 degrees (rotating around an axis).  The experimenters are also looking at the time needed to respond to the question.  Subjects should answer as quickly as possible when they feel they have found the correct answer.The experiment differs from Cooper and Shepard’s experiment because it is using only the letters P and G in order to test if either letter is easier to identify as it rotates in different positions, or if they are equally difficult to identify.  Cooper and Shepard used all of the different letters in their experiment.The goal of each experiment, though, was to identify how the subjects’ brains processed visual stimuli by testing to see how well they identified letters in various presentations.        HypothesisFirst, the rate of incorrect answers should increase, as should the time needed to answer, as the letters are rotated from 0 to 180, and should decrease as they are rotated from 180 to 315.  Images should be harder to identify in ‘skewed’ positions than in either fully upside down or upright positions, since those are more typical ways of seeing them.

  As the images get closer to these ‘typical’ ways of presentation, they should be easier to identify than when they are further away.  Second, the rate of correct answers should be the same for both P and G, since neither image should be more or less difficult to identify.  Finally, the time needed to identify images should increase as the image is rotated towards 180 and then decrease, since images further from typical presentation will be harder to identify and will therefore require more time to study.            ResultsThe data was summarized by looking at first the accuracy, and then at the response times, for both letters, in both positions (flipped and not flipped).  The data is represented in the graphs below.

        Fig. A       Fig. B  Discussion of Hypotheses / Interpretation of ResultsLooking at the first graph, the hypotheses are supported and proven correct for G, but not entirely for P.  Accuracy for G did decrease as it approached 180, and increase again towards 315.  However, this did not hold true for P.  One of the hypotheses, therefore, was incorrect, as G and P did not receive the same pattern of correct and incorrect responses.

  P was an easier image to identify all the time, and incorrect responses for P actually peaked between 225 and 270.  They were also correct a greater percentage of the time, with incorrect answers never getting nearly as high as the incorrect answers for G.Looking at the second graph, all presentations and letters other than P, not flipped, met the hypotheses.  Response time increased and peaked around 180 for all other presentations.  For P, not flipped, the lowest response time was at 135, although it was fairly similar across the board.  Since P, flipped, does follow the pattern that G does, it is possible that P, not flipped, is simply an easy letter to identify and that this part of the data was an anomaly.

  This data set does fit the hypotheses.In summary, P is an easier letter to identify than G according to the data, suggesting that some images are clearer to the brain and easier to rotate than others.  P is likely easier to identify because, as suggested in some of the literature, it has a vertical line in it and the rest faces a particular direction.  It is easier to identify, therefore, along an axis, as being flipped or not.  So, this hypothesis is not true – all images are not equally easy or difficult to identify.

The experiment does prove that mental rotation is possible, but more difficult at unusual angles.  Further testing would likely reveal the same.BibliographyCooper, L.A. (1975). “Mental rotation of random two-dimensional shapes.”  Cognitive Psychology, 7, 20-43.

 Cooper, L.A., & Shepard, R.N. (1990). “Turning something over in the mind.

”  In R.R. Llinas (Ed.) The workings of the brain:  Development, memory, and perception.  New York:  W.H. Freeman.

 Pylyshyn, Z. (1981). “The imagery debate: analogue media versus tacit knowledge.” Psychological Review, 88, 16-45.