Representational information: a new general notion and measure of information

Abstract

a b s t r a c tIn 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.

Gaze and informativeness during category learning: Evidence for an inverse relation

“…In RIT, a new general way of characterizing information is proposed that is based on five principles: (1) that humans communicate via concepts or, in other words, mental representations of categories of objects (where a category is simply a set of objects that are related in some way); (2) concepts are the mediators of information; (3) concepts are relationships between qualitative objects in the environment that are defined dimensionally; (4) the degree of coherence or Gestalt homogeneity of a category (i.e., to what overall extent its objects are indistinguishable) as well as its cardinality (i.e., size) determine the learnability or complexity of its associated concept; and (5) information is the rate of change of that complexity (and more specifically, for discrete functions, the proportional change of that complexity). The first three principles are frequently adopted by researchers in the field of human concept learning (Bourne, 1966;Estes, 1994;Garner, 1974;Vigo, 2009aVigo, , 2009bVigo, , 2009c, and the fourth and fifth form the basis of the theory proposed by Vigo (2009aVigo ( , 2011bVigo ( , 2013b Combined, these principles support the proposition that the amount of information conveyed by a subset of instances of a dimensionally defined category is the rate of change in the structural complexity of the category whenever the instances are removed from it (Vigo, 2011a). The rate of change is the percent increase or decrease in the structural complexity of the category.…”

“…We propose that certain key constructs underlying prototype models of categorization may be useful in accounting for fixation times at the whole-object level of processing during category learning. In addition to these key constructs, a general measure of information proposed by Vigo (2011a) is included to articulate and interpret the results. Next, we describe these constructs and how they may be used to account for eye movement during category learning.…”

“…Representational Information Theory, or RIT (Vigo, 2011a), provides a possible solution to the problem of how humans judge the degree to which an object is informative depending on the context within which it occurs. In RIT, a new general way of characterizing information is proposed that is based on five principles: (1) that humans communicate via concepts or, in other words, mental representations of categories of objects (where a category is simply a set of objects that are related in some way); (2) concepts are the mediators of information; (3) concepts are relationships between qualitative objects in the environment that are defined dimensionally; (4) the degree of coherence or Gestalt homogeneity of a category (i.e., to what overall extent its objects are indistinguishable) as well as its cardinality (i.e., size) determine the learnability or complexity of its associated concept; and (5) information is the rate of change of that complexity (and more specifically, for discrete functions, the proportional change of that complexity).…”

“…Qualitatively, when learning a category, participants appear to focus on the least informative objects rather than their more informative counterparts. As such, we interpret these results (Vigo, 2011a(Vigo, , 2013a and by adding 1 to the results to make any negative values positive. After, the inverse (1/x) of the values is taken and then standardized on the [0, 1] real number interval by using the min/max standardization procedure described in the main text (where the minimum value is set at 0).…”

“…A well-defined category is a set containing objects that are defined in terms of a preset finite number of dimensions and their values. In Representational Information Theory (RIT; Vigo, 2011a), the amount and quality of subjective information conveyed by a subset R of a well-defined category z}|{ F is defined as the proportional or percent change (i. e., the percent change divided by 100) in the perceived (or subjective) structural complexity c of G and z}|{ F respectively, and f is the degree of categorical invariance of a well-defined category of objects (see Vigo, 2009aVigo, , 2011aVigo, , 2011bVigo, , 2013b for a detailed discussion of structural complexity and categorical invariance).…”