Source: Questia, Oct 2009

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.

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).