Quantitative study of color category boundaries

We use World Color Survey (WCS) data to design quantitative methods to study color categorization, with the focus on the "geometric" properties of categories, in particular, on studying their shape, and creating a consistent methodology to identify category boundaries. We introduce the notion of "No Man's Land" and "Some Man's Land" to distinguish color chips that belong to no color category and those that belong to some color category. We introduce a "color-stimulus-strength" function that characterizes color boundaries. While categories may come in a variety of shapes, and their boundaries are nonuniform and can vary in thickness, there are universal patterns that emerge. For example, the boundary-to-category-mass ratio is a decreasing function of category strength (i.e., stronger categories have relatively thinner boundaries), and boundary mass obeys a "square root"-like law as a function of category mass (i.e., roughly speaking, color categories behave like 2D circles). We further identify a relationship between color boundaries and Shannon's entropy, which can be calculated by using the field data of the WCS. We find that depending on the informational content of a given chip, it can belong to three distinct types: (I) strongly belonging to a color category; (II) belonging to a boundary between two or more categories; (III) not belonging to a category or a boundary. The last two cases can be interpreted in terms of evolution and temporal dynamics of color categories.