Abstract: The invention relates to a method for human-computer interaction (HCI). The method includes: establishing an event set; establishing and referencing one or more events in the event set; establishing and referencing an event to represent the observer in the event set; establishing a representation manifold as an indefinite metric Riemann manifold; representing the events on the representation manifold in such a way that the logical relations between events are coordinate independent and geometrically encoded as causal relations; establishing an input manifold to represent user input; and establishing an output manifold that maps between the representation manifold and a physical output device. Further, based on user input, select any one or more steps from: manipulating the observer event, adjusting manifold metrics, changing mappings, adjusting mapping parameters, and applying mappings. The above steps are repeated when the user input changes.

Abstract: The invention relates to a method for human-computer interaction (HCI). The method includes: establishing an event set; establishing and referencing one or more events in the event set; establishing and referencing an event to represent the observer in the event set; establishing a representation manifold as an indefinite metric Riemann manifold; representing the events on the representation manifold in such a way that the logical relations between events are coordinate independent and geometrically encoded as causal relations; establishing an input manifold to represent user input; and establishing an output manifold that maps between the representation manifold and a physical output device. Further, based on user input, select any one or more steps from: manipulating the observer event, adjusting manifold metrics, changing mappings, adjusting mapping parameters, and applying mappings. The above steps are repeated when the user input changes.