How do you represent an entity with a graphic that tells people everything they need to know about that entity within a fraction of a second?

A logo or mark of an organization must do exactly that. When creating an identity I believe that one must look at an entity as a whole and garner a deep understanding of the personality of this entity. All organizations have traits and principles that get to the core of who they are. Derived from their ethos, their culture, their founders, and intended demographic a designer must distill these traits and principles down to a graphically communicated instantly recognizable mark with all of those feelings and values intact.