Four-Dimensional Representation in Human Cognition and Difficulties with Demonstrations: A Commentary on Wang

The experiment Ranxiao Frances Wang (this issue) carried out with a small number of human subjects suggests that humans can achieve “intuitive comprehension of 4-D space.” Subjects were shown a 3-D projection of a randomly constructed, rotating 4-D object and were asked to estimate the volume of the object. The results showed a significant correlation between subjects’ responses and the calculated volume of the shown 4-D object. Wang concludes that this is empirical evidence that subjects can “directly” apprehend 4-D space, and can build 4-D spatial representations and use them for spatial judgment tasks. This remarkable experiment meets a highly skeptical audience. First, four-dimensional intuition is not likely to have developed in the evolution of human beings—the environment does not present situations where such a capability would be of any benefit. Second, introspection does lead most of us to doubt that we have 4-D imagination or the ability to reason with 4-D objects; all we have is reasoning by analogy, using lower-dimensional (specifically 3-D) objects. Therefore, the article invites a very careful analysis of its claims and the justifications given. Wang herself includes criticism of previous publications for similar claims, and shows how they fail; unfortunately, her own article falls prey to a similar attack.