Abstract
It is a long-lasting question whether human beings, who evolved in a physical world of three dimensions, are capable of overcoming this fundamental limitation to develop an intuitive understanding of four-dimensional space. Techniques of analogy and graphical illustration have been developed with some subjective reports of success. However, there has been no objective evaluation of such achievements. Here, we show evidence that people with basic geometric knowledge can learn to make spatial judgments on the length of, and angle between, line segments embedded in four-dimensional space viewed in virtual reality with minimal exposure to the task and no feedback to their responses. Their judgments incorporated information from both the three-dimensional (3-D) projection and the fourth dimension, and the underlying representations were not algebraic in nature but based on visual imagery, although primitive and short lived. These results suggest that human spatial representations are not completely constrained by our evolution and development in a 3-D world. Illustration of the stimuli and experimental procedure (as video clips) and the instruction to participants (as a pdf file) may be downloaded from http://pbr.psychonomic-journals.org/content/supplemental.
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References
Abbott, E. A. (1991). Flatland: A romance of many dimensions. Princeton: Princeton University Press.
Berger, D. (1965). Sphereland: A fantasy about curved spaces and an expanding universe. New York: Crowell.
Bork, A. M. (1964). The fourth dimension in nineteenth-century physics. Isis, 55, 326–338.
Davis, P. J., Hersh, R., & Marchisotto, E. A. (1995). Four dimensional intuition. In The mathematical experience (pp. 442–447). Boston: Birkhäuser.
Durrell, F. (1938). Mathematical adventures. Boston: Humphries.
D’Zmura, M., Colantoni, P., & Seyranian, G. (2000). Virtual environments with four or more spatial dimensions. Presence: Teleoperators & Virtual Environments, 9, 616–631.
Finke, R. A. (1993). Mental imagery and creative discovery. In B. Roskos-Ewoldsen, M. J. Intons-Peterson, & R. E. Anderson (Eds.), Imagery, creativity, and discovery: A cognitive perspective (pp. 255–285). Amsterdam: Elsevier Science.
Francis, G. K. (2005). Metarealistic rendering of real-time interactive computer animations. In M. Emmer (Ed.), Mathematics and culture II (pp. 125–144). Berlin: Springer.
Gardner, M. (1969). The unexpected hanging and other mathematical diversions. New York: Simon & Schuster.
Gardner, M. (1975). Mathematical carnival. New York: Knopf.
Kant, I. (1896). Immanuel Kant’s Critique of pure reason (F. M. Muller, Trans). London: Macmillans. (Original work published 1881)
Kosslyn, S. M. (1994). Image and brain: The resolution of the imagery debate. Cambridge, MA: MIT Press.
Reichenbach, H. (1958). The philosophy of space and time. New York: Dover.
Rucker, R. (1984). The fourth dimension: Toward a geometry of higher reality. Boston: Houghton Mifflin.
Seyranian, G. D. (2001). Human spatial perception in environments with four spatial dimensions. Dissertation Abstracts International, 62B, 1611.
Shepard, R. N., & Cooper, L. (1982). Mental images and their transformations. Cambridge, MA: MIT Press.
Weeks, J. R. (1985). The shape of space. New York: Dekker.
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This work was supported by NSF Grant BCS 03-17681 to R.F.W.
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Ambinder, M.S., Wang, R.F., Crowell, J.A. et al. Human four-dimensional spatial intuition in virtual reality. Psychonomic Bulletin & Review 16, 818–823 (2009). https://doi.org/10.3758/PBR.16.5.818
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DOI: https://doi.org/10.3758/PBR.16.5.818