Chapter 4: What Makes a Cube a Cube?: Contingency in Abstract, Concrete, Cultural and Bodily Mathematical Knowings

When presented with the image in Figure 4.1, a person will more often than not immediately see a cube. This happens despite the fact that the drawing is not a cube at all: As the French painter Magritte coined many years ago, the representation of the object is not the object itself. So how is this experience of a cube in a drawing possible?

From the viewpoint of phenomenology of perception, to recognize the figure as a cube, one must experience it bodily (looking at it, eying the image from every angle), and connect the perception to the culturally defined (mathematical) idea of the cube (Merleau-Ponty, 1945). Contemporary phenomenological cognitive science, too, asserts the physical body as the center from which all knowing emerges, while it defines culture as an open network of ways of dealing with the material world and with others, preserved from generation to generation (e.g., Gallese, 2003). In this view, bodily and cultural knowings are mutually constitutive. It is our cultural knowledge that tells us the drawing is a cube, as we recognize in the image a representation typical in Western culture. However, by looking at the image, we not only can recognize a cube, but we also experience three-dimensionality by bodily knowing the relationship between the ink traces on the flat paper and a block on our desk. Indeed, when presented with a similar figure, young children express their puzzlement: “That’s not a cube, there’s no triangle on a cube!” For the cube to be seen, the physical body needs the work of culture, and vice versa.