Symmetries of 2-D Images: Cases without Periodic Translations
Journal of Mathematical Imaging and Vision
Affordances in HCI: toward a mediated action perspective
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
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Affordance is a widely used term in human–computer interaction (HCI) that, while familiar and attractive, does not have a clear operational definition. Using the mathematical concept of symmetry, this paper shows that it is possible to begin developing an operational definition for significant aspects of affordance by forming the theoretical concept of symmetry-affordance. The proposed definition restricts symmetry-affordance to particular contexts but in doing so makes it more useful, as it is clear how to exploit symmetry to aid design. The definition is in standard mathematics (in fact, group theory and model theory) and requires little additional structure. In examining symmetry-affordance, it becomes clear that some other HCI notions can be similarly interpreted by symmetry. The paper provides examples and design insights. Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection. Hermann Weyl [(1952) Symmetry, Princeton University Press, Princeton, NJ]