Academic journal article Psychonomic Bulletin & Review

Human Four-Dimensional Spatial Intuition in Virtual Reality

Academic journal article Psychonomic Bulletin & Review

Human Four-Dimensional Spatial Intuition in Virtual Reality

Article excerpt

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.

Representations of space and time are deeply rooted in human thinking, reasoning, and perception of the world (Abbott, 1991; Bork, 1964; Durrell, 1938; Gardner, 1975; Kant, 1881/1896; Reichenbach, 1958; Rucker, 1984). However, living in a physical world of three dimensions, humans have their perceptual and cognitive systems tailored for sensing, storing, transforming, and reasoning about three-dimensional (3-D) objects. Some thinkers (e.g., Kant, 1881/1896) believe that space is an innate concept, whereas perceptual experience simply fills it with objects. Thus, humans may develop symbolic systems to conceptualize multidimensional entities that they call highdimensional space, but they can never overcome the innate constraint and add another dimension to the 3-D mental space that corresponds to the physical world, because they can never figure out where that dimension could be put.

Much effort has been made to challenge this cognitive limitation and to develop human four-dimensional (4-D) intuitions (Davis, Hersh, & Marchisotto, 1995; Gardner, 1969; Rucker, 1984; Seyranian, 2001; Weeks, 1985). Two basic techniques were proposed to help people obtain an intuition of 4-D space. The first is by analogy to 3-D space. This technique has been widely used. For example, Berger (1965; Abbott, 1991) explained how a 4-D creature can enter a 3-D locked closet from the fourth dimension by describing how a 3-D creature enters a two-dimensional (2-D) enclosure from above without touching its walls.

The second technique is to lift an observer into the higher dimensional space, so that he or she can directly experience it perceptually (Abbott, 1991; Berger, 1965; Rucker, 1984; Seyranian, 2001). For example, Abbott suggested that a 2-D creature can obtain 3-D intuition when it is taken into the 3-D space and views its world from above. Although this approach is hypothesized to be the most powerful means of acquiring 4-D intuition, it was not possible to implement the technique until virtual reality was available (D'Zmura, Colantoni, & Seyranian, 2000; Francis, 2005).

There have been informal subjective reports that mathematicians who actively interacted with computer- graphical simulations of 4-D geometric objects obtained sudden, novel insights of higher dimensional space (e.g., Davis et al., 1995). However, there has been no objective evaluation of such achievements. In the present study, we examined the dimensionality limitation in human spatial representations by constructing 4-D geometric objects in virtual reality and measuring judgments of distance (a property of one-dimensional [1-D] space) and angle (a property of 2-D space), which are spatial properties of the lowest dimensions and serve as the building blocks of higher dimensional spatial properties. …

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