ISOMORPHISMS and HOMOMORPHISMS
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1795 ▶ |
| Object type | General information, Epistemology, ontology or semantics, Methodology or model |
Isomorphisms should be carefully distinguished from homomorphisms.
According to R. VALLÉE, the pluridisciplinary, (or better, transdisciplinary) character of systems theory “… is a result of one of its fundamental goals, i.e. to show, in the best case, structural isomorphisms between systems pertaining to different disciplines (or between representations of these systems). Such isomorphisms, which most generally, if not always, are merely homomorphisms, were already heralded by cybernetics, as in the title of WIENER's work…
- “This search for isomorphisms, or more modestly, homomorphisms, leads to the concept of model, which allows for the representation of a category of systems. The ideal of an isomorphic representation is however misleading. As KORZYBSKI reminded us, ”the map is not the territory“ (1990, p.56).
St. BEER enounces a similar opinion: “Having refined the conceptual models, the contents of mind, … the scientist produces two deeper-level homomorphic models — and these may well be isomorphic with each other” (1968, p.113).