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

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Abstract

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.

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Notes

  1. Two separate conditions were designed to pick up potential strategies that involved using a frame of reference within the bent sheet to make the left–right judgments. For example, rather than mentally unfolding the plastic sheet, a participant might try to mentally construct an imaginary line parallel to the sides of the sheet that extended from one form and then judge whether the other form was to the left or right of this line. Such a strategy would have been suggested by finding that the grid stimuli were easier than the texture stimuli. No subjects spontaneously reported using this strategy, while a number mentioned mentally unfolding the plastic sheet, and as reported below, there was no evidence of a difference between the two stimuli types.

  2. To investigate the relationship between the background pattern and the amount of bending on performance on the Non-rigid Bending test, a mixed-design ANOVA with a within-subject factor of level of bending (easy, medium, hard) and a between-subject factor of condition (Gridlines, Texture) was conducted. Mauchly’s test indicated that the assumption of sphericity had been violated (χ 2(2) = 56.37, p < .001), and therefore, degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε = .72). The analysis revealed no effect of condition, n.s. An analysis of RT revealed a similar pattern: There was no effect of condition and no significant interaction, n.s. As there was no effect of background pattern condition on accuracy or RT on the Non-rigid Bending test, data from the two conditions were collapsed for further analysis.

  3. Due to the dichotomous nature of the Non-rigid Bending test, split-half reliability was also calculated for both Gridlines and Texture conditions (Spearman-Brown coefficients were .89 and .60, respectively).

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Acknowledgments

Except the first author, all subsequent authors are listed alphabetically. This research was supported by a grant to the Spatial Intelligence and Learning Center, funded by the National Science Foundation (SBE-0541957 and SBE-1041707), and by a Fostering Interdisciplinary Research on Education grant, funded by the National Science Foundation (grant number DRL-1138619).

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Authors and Affiliations

  1. Department of Psychology, Temple University, 1701 North 13th Street, Philadelphia, PA, 19122, USA

    Kinnari Atit & Thomas F. Shipley

  2. Department of Geology, University of Wisconsin-Madison, Madison, WI, USA

    Basil Tikoff

  3. Department of Geoscience, University of Wisconsin-Madison, 1215 W Dayton Street, Madison, WI, 53706, USA

    Basil Tikoff

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  1. Kinnari Atit
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  2. Thomas F. Shipley
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  3. Basil Tikoff
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Correspondence to Kinnari Atit.

Additional information

This article is part of the special issue on “Spatial Learning and Reasoning Processes”, guest-edited by Thomas F. Shipley, Dedre Gentner and Nora S. Newcombe. Handling editor of this manuscript: Dedre Gentner.

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Atit, K., Shipley, T.F. & Tikoff, B. Twisting space: are rigid and non-rigid mental transformations separate spatial skills?. Cogn Process 14, 163–173 (2013). https://doi.org/10.1007/s10339-013-0550-8

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