This chapter describes a geometric approach to human cognition centering on the concept of mental configuration space. As a case study of the approach, this work details a study that derives performance models for an important class of motor behavior—pointing in the two dimensional space. The five derived models and three existing models in the literature are compared using an experimental study. It is found that the models developed on the basis of mental configuration space fit the empirical data better than other models. It is argued that the mental configuration space concept points to a potentially fruitful direction of research. Finally, the chapter discusses the implications of such an approach for user interface research and development.
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Gärdenfors (2004) proposes a geometric mode of mental representation complementary to the more prominent approaches of the symbolic (Newell, 1990) and the connectionist (Rumelhart & McClelland, 1986) mode of representations in cognitive science. He suggests that the representation of vector spaces is more satisfactory than symbolic and connectionist representations for modeling concept formation, semantics and reasoning. For representing sensory stimuli such as spectral composition of light, intensity of sound, velocity of self-rotation and so on, Gallistel (1990) indicates that vector space representation is organism’s natural means of internalizing the environment. Though promising, this geometric line of investigation has not grown outside the realm of cognitive science to influence user interface research and design. This chapter attempts to bring readers’ attention to this line of inquiry, and uses a case study to illustrate the potential viability of the geometric approach.
The case study centers on extending Fitts’ law (Fitts, 1954) to give a more detailed account of user performance in a variety of situations. As one of the best well known contributions of psychology to the field of user interface research (Card, et al., 1983), Fitts’ law is generally used as a tool for evaluating user interfaces or devices (Soukoreff & MacKenzie, 2004), and has helped launching some important input devices, including the ubiquitous mouse (Card, et al., 1978). Despite its usefulness, a lack of consensus in its fundamental nature limits its applicability and hinders the development of similarly predictive laws. This work attempts to alleviate this kind of conceptual deficiency by extending the law from the perspective of mental configuration space.
In the following sections, several lines of research on mental configuration space are first briefly reviewed. The possible optimization principles in mental configuration are then proposed. Turning to the case study, 1D and 2D pointing tasks are described. The chapter proceeds to derive five models of 2D pointing performance based on progressively richer assumptions on the shape and distribution of 2D pointing mental configuration space. The derived models are tested with an experiment. Three previous models in the literature are also tested with the experimental data. Results suggest that models based the optimization principles in mental configuration space fit well with the empirical data. The chapter concludes with discussions on the implications of the work.