Shepard, R. N., & Metzler, J. (1971). Mental Rotation of Three-Dimensional Objects. Science, 171(3972), 701–703. doi:10.1126/science.171.3972.701

Summary

Shepard and Metzler showed participants 2D line drawings of 3D objects which differed by either a rotation (the “same” pairs) or a rotation and a reflection (the “different” pairs). They found that as the angle of rotation increased for the “same” pairs, participants’ response times increased linearly. The conclusion (based both on this response time data, as well as experience reports) was that participants were performing a “mental rotation” of the images in order to compare them.

Methods

Shepard & Metzler had 8 participants who each judged 1600 (!) pairs of line drawings. 800 of the pairs were “picture plane” rotations, while the other 800 were “depth” rotations. Each of these sets of stimuli were further broken down into 400 “same” and 400 “different” pairs. These 400 pairs were composed of 10 unique stimuli repeated twice at each one of ten angles from $0^\circ$ to $180^\circ$ in $20^\circ$ increments (side note: there seems to be another factor of 2 missing here; I’m not sure where that comes from?). Participants had as much time to respond as they wanted, and they could look at the images as long as they wanted, though they were instructed to respond as quickly as possible while still being accurate.

Algorithm

n/a

Takeaways

I still think this is such a cool result, though I am still unsatisfied by the rotation explanation. One quote from the paper is potentially illuminating, though:

In the postexperimental interview, the subjects typically reported that they attempted to rotate one end of one object into congruence with the corresponding end of the other object; they discovered that the two objects were different when, after this “rotation,” the two free ends still remained noncongruent.

This point is going to elaborated on further in the next paper I am going to read, by Just & Carpenter.