Cognition and games - an approach to information

Basic structural elements on the way to information involve truth, belief and knowledge as well as ideas about how truth is perceived by an observer, be it a physicist or a statistician. Also, one should ask questions such as ``what {\em can\/} we know?'' When formalizing these philosophical considerations, simple two-person zero-sum games provide important theoretical support. Well known results going back to Chentsov and Csisz\'ar on information projections and Pythagorean inequalities may be illuminated this way. Whether a tie to a truly geometric theory as initiated by the Japanese school led by Amari can also be established is another matter.