7.3 REPRESENTATION TRANSFORMATIONS

Based on the semiotic characterization of the sign to concept relationships as iconic, symbolic, and indexed, it is asserted that a transformed representation can be related in a similar manner. The transformation of one representation to another can be viewed as the manipulation, substitution, and/or creation of signs. This section identifies and defines three types of transformations as derivation, abstraction, and mapping. In positing a representation and its transform as an object and its sign, the semiotic categories of icon, index, and symbolic signs permit a constructive analysis of how meaning is transferred through or across a transform. Figure 82 illustrates the relationships between a representation A and a representation B.

Figure 82 The Semiotics of Transformation Relationships

The subject of examples were centered about non-manifold geometric models and transformations into alternate representations more amenable to numeric simulation operations or knowledge-based analysis. Many of the representations were graph-based with transformation accomplished by an application of rules of grammar.

The study of grammar is an important topic in semiotics in that it goes to the heart of linguistic structure. Chomsky's work of transformational-generative linguistics combines elements of mathematics with linguistic theory. Surface structures could be transformed without changing the deeper meaning these structures represent. Chomsky's work avoids structuralism's self-imposed limitations of descriptive behaviorism for a more flexible and prescriptive formalism.

Semiotics is not weakened against Chomsky's generative linguistics by its association with structuralism. Semiotics' concern is primarily of the communicative nature of symbols within a culture. Following is a taxonomy of the literal transference of information across representations.