Abstract
We have developed an information theoretic analysis of color naming [12,3]. We compute mutual information (MI, in bits) in a simulated “game” involving a “sender” (S) who names out loud, based on his color idiolect, the colors of samples selected randomly (with replacement) from an array of N samples. A “receiver” (R) attempts to identify S's selections from her duplicate array of color samples, based only on S's color term message and her own color idiolect. MI measures how much S's messages improve R's chances of guessing S's selections correctly. In the past, we have used R's color naming data to predict her performance. However, this strategy does not consider what informants may know but do not volunteer. To address this issue, we have created an iPad application in which groups of informants actually play a networked version of our color game. Each player serves as sender, naming each of 30 color samples displayed randomly one at a time, then as receiver, selecting from the entire array of colors, the one that corresponds to each color name provided by himself and others in the first phase of the experiment. The MI for players identifying the samples corresponding to their own color terms was only slightly better than MI for the color terms deployed other players. Playing the game twice, once naïve to the identification phase and once in full knowledge of the game, produced slightly higher MI in the second round. However, in general, MI never reached its optimum value.
Supported by NSF BCS-1152841.