ISOMORPHISM
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1794 ▶ |
| Object type | General information, Epistemology, ontology or semantics, Methodology or model |
- “A mapping which not only involves a one-one correspondence of elements, but which also preserves operational characteristics” (1968, p.108).
As St. BEER explains, this means that the results of an operation on elements of one set correspond to the results of the analogue operation on their homologues in the other set. Thus, there are also relational isomorphisms, which are much more interesting than structural ones.
While an isomorphism may be considered as the perfect analogy, no model is ever totally isomorphic to the modelled object or system. The really significant use of isomorphism is to allow for the creation of classes'' of models characterized by the same properties. This enables us, up to a point, to compare structures or functions of different concrete systems and operate meaningful generalizations. This in turn permits us a certain degree of algorithmization of the knowledge of numerous complex entities or situations, which may be more or less similar. (thus leading to algorithmic compressibility).
L. TRONCALE uses the term “isomorphies' apparently as a synonym of ”isomorphisms“ and defines it as follows: ”A formula, pattern, structure, process or interaction demonstrated to be precisely the same, but in general terms, across many disciplines, and many scales of magnitude of real systems despite the obvious difference of the parts of the diverse systems“ (1985, p.47).
He comments: “Isomorphies are completely context-independent and content-rich (have meaning in themselves and alone). They are manifest only in context, and observable only by comparison of many contexts”.
He goes still farther, adopting a quasi-platonic stand: “The existence of the same interaction across many separate levels implies that the isomorphy is actually as fundamental and real, perhaps more fundamental and real than the parts at different scales of magnitude that exhibit the relationship. In this formulation the abstract isomorphy-across-systems and the physical manifestions-of-systems are equally ”real“ (Ibid).
In a quite different perspective, and according to J.van GIGCH the search for isomorphisms could be computerized through some adequate software, as for instance APPLE's HYPERTEXT and HYPERCARD. (1988, p.269). Quoting J. SCULLEY, he writes: “… the computer will confer the (power and) perspective to compare and contrast (read: 'find isomorphisms') and so free ourselves from the limits imposed by specialization” (Ibid.).