Tuesday, January 3, 2012

Mental Rotation 1 - Introduction and Discovery

What is "Mental Rotation"?

Fig.1 - trial pairs from
Shepard & Metzler (1971)
The Wikipedia entry on Mental Rotation tells us that the term designates the ability of (certain) animals, including humans, "to rotate mental representations of two-dimensional and three-dimensional objects".

As we will see in this series of posts, this straightforward, even trivial seeming, definition is not necessarily uncontroversial - so, for the moment, it is best to think of "Mental Rotation" as being whatever it is that allows one to look at the pairs of images in Fig. 1 and tell, without manipulating anything in physical space, whether the "object" in the left circle is the same as that in the right.

In this post we will be taking a quick look at the paper that kick-started the study of Mental Rotation and related phenomena.

Shepard and Metzler's 1971 paper  - uncovering the phenomenon

Roger Shepard and Jacqueline Metzler's seminal paper "Mental Rotation of Three-dimensional Objects" is rightly considered to be one of the classics of cognitive psychology because of its beautifully simple design and the implications of its results.

Fig. 2 - Shepard and Metzler's results
Shepard and Metzler (1971) presented their participants (n=8) with pairs of two-dimensional projections of three-dimensional objects such as those in fig.1 above.There were 1600 trials in total, presented in a randomised order. Half of the trials showed the same object in the left and right positions. These projections of the object were rotated, at multiples of 20 degrees, either in the image plane (around the Z axis) or in depth (around the Y axis). The other half of the trials showed different, enantiomorphic, pairs in the left and right positions, similarly rotated in the image plane or in depth.

A tone signalled the start of each trial to the participants, after which the pair of images were revealed and a timer started. The participants were then required to determine whether the objects in the pair of images were the same or different by pulling one of two levers which recorded their response and stopped the timer.

Fig. 2 shows the results of plotting time as a function of angle of rotation between identical images. The top graph shows the results for rotation in the picture plane, while the bottom shows the results for rotation in depth. What is striking about these graphs is their linearity - they show that as the angle of rotation between the two images increased, so did the time taken to recognise if they were the same image. Further, not only did reaction time increase but it increased at a fixed ratio (this is what gives it it's linear shape).

This is the same kind of result one would get if one took two physical (identical) pictures, laid them down next to each other at different angles, and then rotated one of them at a fixed speed until the two images faced the same direction. As you increased the difference in angle between the two images it would take you longer to rotate them until they were both at the same orientation. Incidentally, Shepard and Metzler fixed the average speed of this (mental) rotation to be around 60 degrees per second for their participants.

Importance of work

The biggest impact that Shepard and Metzler's study has most likely had is in the debate around the nature of mental representation, in particular in the debate about whether the nature of our mental representations (assuming there are such structures) are propositional (that is, sentence-like) or image-like (or that are functionally equivalent (Sternberg, 2011) to images).

It has been supposed that, because the relationship between the angle of rotation and reaction time is so strongly linear, there is a continuous, analogue process underlying mental rotation - something reminiscent of the example I gave above of physically rotating a picture at a fixed speed. There are two important things to note here though. First, this does not mean that there are literally pictures in the head being rotated, it only suggests that there is some process that is, like I said above, functionally equivalent to rotating actual images (i.e. they work the same way, they don't have to look the same - this will be explored in more detail in future posts). Second, it doesn't necessarily mean that the subjects are aware that this process is going on - it could be that this rotation of image-like representations is entirely sub-personal or sub-awareness. However, when interviewed, all Shepard and Metzler's subjects reported experiencing some kind of visual imagery which they "rotated" in mind. Of course, as the researchers point out, introspective data is best "interpreted with caution" (Shepard & Metzler, 1971: 701).

References :

Pitt, David, "Mental Representation", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL =

Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701-703.

Sternberg, R., & Sternberg, K. (2011). Cognitive Psychology (6th ed.). London: Wadsworth Publishing.

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