Representational information: a new general notion and measure of information

In what follows, we introduce the notion of representational information (information conveyed by sets of dimensionally defined objects about their superset of origin) as well as an original deterministic mathematical framework for its analysis and measurement. The framework, based in part on categorical invariance theory [30], unifies three key constructs of universal science – invariance, complexity, and information. From this unification we define the amount of information that a well-defined set of objects R carries about its finite superset of origin S, as the rate of change in the structural complexity of S (as determined by its degree of categorical invariance), whenever the objects in R are removed from the set S. The measure captures deterministically the significant role that context and category structure play in determining the relative quantity and quality of subjective information conveyed by particular objects in multi-object stimuli.