Twisting space: are rigid and non-rigid mental transformations separate spatial skills?

Cognitive science has primarily studied the mental simulation of spatial transformations with tests that focus on rigid transformations (e.g., mental rotation). However, the events of our world are not limited to rigid body movements. Objects can undergo complex non-rigid discontinuous and continuous changes, such as bending and breaking. We developed a new task to assess mental visualization of non-rigid transformations. The Non-rigid Bending test required participants to visualize a continuous non-rigid transformation applied to an array of objects by asking simple spatial questions about the position of two forms on a bent transparent sheet of plastic. Participants were to judge the relative position of the forms when the sheet was unbent. To study the cognitive skills needed to visualize rigid and non-rigid events, we employed four tests of mental transformations—the Non-rigid Bending test (a test of continuous non-rigid mental transformation), the Paper Folding test and the Mental Brittle Transformation test (two tests of non-rigid mental transformation with local rigid transformations), and the Vandenberg and Kuse (Percept Motor Skills 47:599–604, 1978) Mental Rotation test (a test of rigid mental transformation). Performance on the Mental Brittle Transformation test and the Paper Folding test independently predicted performance on the Non-rigid Bending test and performance on the Mental Rotation test; however, mental rotation performance was not a unique predictor of mental bending performance. Results are consistent with separable skills for rigid and non-rigid mental simulation and illustrate the value of an ecological approach to the analysis of the structure of spatial thinking.