The cumulative cultural evolution of category structure in an infinite meaning space

Current iterated learning experiments use meaning spaces that are discrete, finite, pre- specified, and low-dimensional. Such meaning spaces are poor representations of the world. For this reason, we have conducted two experiments to look at the cumulative cultural evolution of category structure in an infinite meaning space. In the first experiment, the number of words used to describe the stimuli collapses dramatically after only a few generations. Within a few more generations, a system emerges that arbitrarily divides the space into a small number of categories pertaining primarily to the size and shape of the stimuli. In the second experiment, we apply an artificial constraint which prevents the size of the languages from collapsing. This constraint was implemented to model the pressure for expressivity that exists in languages when they are used functionally for communication. We predicted that this would allow compositional structure to emerge so that the space could be carved up in more finely grained and/or higher dimensional ways using a compressible linguistic system. However, there was little sign of compositionality emerging under the parameters of this experiment. Although the meaning space presented here is a simple one, we hope that this project represents a first step towards thinking about how iterated learning experiments deal with the problem of discrete infinity. We briefly discuss the background literature, then present the methods and results for this project, and end with some discussion about how the results relate to our research questions