Homomorphism

A homomorphism is a many-one mapping, not an isomorphism, arranged so that “certain operational characteristics concerning the relationship of elements are preserved” (DC 1966: 108). “A scientific model is a homomorphism on to which two different situations are mapped, and which actually defines the extent to which they are structurally identical” (DC 1966: 113).

What Beer says

A model is the “mental representation of the world that is not direct perception” (DC 1966: 100); “explicitly made available for experimentation” (DC 1966: 101). Mapping: each element has an “image” (DC 1966: 107). Isomorphism: one-one correspondence that also “preserves operational characteristics” (DC 1966: 108). First comparison is analogy, “always open to disputation” (DC 1966: 112); both models then mapped homomorphically — “completely free of the bedevilling disputation that attends analogy” (DC 1966: 113). Dropped elements cost utility, not validity. The manager “can at best settle for a homomorph” (DC 1966: 124). Precursor of the viable-system-model: “a homomorphic mapping of the brain which is by definition a simplification” (DC 1966: 136).

Where it sits in the model

Why brain–firm is not analogy: the VSM maps structure (brain-of-the-firm; pure-vsm-part-ii-the-viable-system-model). Recognizing a system is forming a conceptual model (observer-and-recognition; DC 1966: 246).

Textual notes

Jacket vs body vs method (pure-vsm-appendix): jacket “should not be thought of as ‘analogy’” (BOTF 1981, jacket); body “Models are more than analogies” (BOTF 1981: 75); method: scientific model as homomorphism (DC 1966: 113). MS restates for a general readership (MS 1967: 63–69).

Open points

DC 1966: 136 e-book reads “simplificationand”; print character unchecked. Draft not canon (overview).

Related

pure-vsm-part-v-method-and-epistemology · decision-and-control · management-science-1967 · stafford-beer