Recursion

The fivefold viable-system-model nests. Beer states the theorem twice, “from the opposite angle”. overview Draft 0.8 — not project canon.

What Beer says

BOTF: “Hence: Recursive System Theorem. If a viable system contains a viable system, then the organizational structure must be recursive” (BOTF 1981: 228). It “finally validates the five-tier hierarchic model […]. If the viable firm is organized like this, so is its major viable unit” (ibid.).

HOE: “In a recursive organizational structure, any viable system contains, and is contained in, a viable system” (HOE 1979: 118). Beer: “an alternative version of the Theorem as stated in Brain of the Firm, which expressed the same point from the opposite angle” (ibid.). BOTF infers recursion from containment; HOE starts from a recursive structure and states what it contains.

Mathematical, not loose: “They are RECURSIONS OF THE VIABLE SYSTEM” (DTS 1985: 2). Recursion “answer[s] to mathematical criteria”; the definition is “a vast attenuator of the variety” of organizational description (HOE 1979: 308). System-in-focus: embedded units “will be known as SYSTEM ONE of the System-in-focus”; “up to seven or eight: not many more, I hope, or else you may be missing a whole level of recursion” (DTS 1985: 19). Chile: government as viable system (Five = President), System One = major functions; industry nested likewise (BOTF 1981: 249).

Where it sits in the model

Each system-one is a viable system one recursion down; beyond system-five is the next up (HOE 1979: 259). law-of-cohesion balances a recursive pair. State-scale nest: cybersyn.

Textual notes

BOTF 1981: 228 vs HOE 1979: 118 — same point “from the opposite angle”. Glossary repeats HOE (HOE 1979: 566). Chile “concieved” is [sic] (BOTF 1981: 249).

Open points

HOE 1979: 118 announces a later “topological proof”; none is so labelled. Whether HOE ch. 12 (isomorphic mapping, HOE 1979: 307) is that proof is the manuscript’s reading, not Beer’s (ch. 6 todo).

Related

stafford-beer · viable-system-model · law-of-cohesion · viability-identity-and-autonomy · brain-of-the-firm · pure-vsm-part-i-foundations · pure-vsm-part-ii-the-viable-system-model