content

13 min read

In Appendix One of The Heart of Enterprise Beer brings together all the rules developed in the book in a “Glossary of Rules for the Viable System” (HOE 1979: 565–567). Those three pages are the most compact authorized summary of his theory, and they collect the rules he derives from the concepts of chapters 1 and 2. The wording below follows that appendix. The page references in brackets are Beer’s own references to the place in the text where each rule is developed, and where the wording in the body of the book differs from the appendix, this is noted. In the synopsis at the start of HOE Beer says that a science is expected to deliver “precepts” as well as concepts, “the rules that apply to the exercise of any art” (HOE 1979: 4). The glossary sorts its precepts into kinds: aphorisms, principles, a theorem, axioms and a law. The labels mark different degrees of generality and different ways in which Beer claims to have arrived at each rule, and they reflect his view (chapter 1.1) that cybernetics is a science that delivers invariant principles.

3.1 Aphorisms

  • First Regulatory Aphorism: “It is not necessary to enter the black box to understand the nature of the function it performs.” (HOE 1979: 565; developed on p. 40)
  • Second Regulatory Aphorism: “It is not necessary to enter the black box to calculate the variety that it potentially may generate.” (HOE 1979: 565; p. 47) The two aphorisms follow from the treatment of complex systems as black boxes (chapter 2.5). The first rests on the observation that “The nature of the function can be deduced from those relationships between input and output schemata that turn out to be invariant” (HOE 1979: 40). Beer’s example is a box observed in four operations (his Figure 4): the missing output, 26, can be supplied without difficulty because the box demonstrates an invariant transformation, which he names “times two” (ibid.). The box never has to be opened. Two pages later Beer gives the first aphorism a practical edge. Managers, he writes, tend to disregard it in action: “They are prone to enter the box, hunting down ‘causes’ with the jawbone of an ass” (HOE 1979: 42). His example is industrial relations. A manager who explains his staff’s behavior with a theory such as “All that interests them is the pay packet” has reduced the variety of a human being to the few states his theory allows, and is blinded to the input-output regularities he might otherwise observe (ibid.). The second aphorism extends the argument from function to variety: the variety of a system can be estimated from the combinatorics of its inputs and outputs (HOE 1979: 47). Both are called aphorisms, not laws: they are rules of method for the observer rather than statements about the system.

3.2 Principles of Organization

  • First Principle: “Managerial, operational and environmental varieties, diffusing through an institutional system, tend to equate; they should be designed to do so with minimum damage to people and to cost.” (HOE 1979: 565; p. 97)
  • Second Principle: “The four directional channels carrying information between the management unit, the operation, and the environment must each have a higher capacity to transmit a given amount of information relevant to variety selection in a given time than the originating subsystem has to generate it in that time.” (HOE 1979: 565; p. 99)
  • Third Principle: “Wherever the information carried on a channel capable of distinguishing a given variety crosses a boundary, it undergoes transduction; the variety of the transducer must be at least equivalent to the variety of the channel.” (HOE 1979: 566; p. 101)
  • Fourth Principle: “The operation of the first three principles must be cyclically maintained through time without hiatus or lags.” (HOE 1979: 566; p. 258)

Textual note: In the body of the book the principles are worded slightly differently. The First reads “with minimal damage” (HOE 1979: 97); the Second reads “the management unit, the operation and the environment” and “originating sub-system” (HOE 1979: 99); the Third reads “it undergoes transduction; and the variety of the transducer” (HOE 1979: 101); the Fourth reads “cyclically maintained through time, and without hiatus or lags” (HOE 1979: 258). None of these differences changes the meaning.

The four principles form a sequence. They apply the variety concepts of chapter 2 to Beer’s elementary model of three boxes: environment, operation and management unit, connected by channels. The First Principle has two halves. The first is descriptive: the three varieties “tend to equate”, which is a statement about what happens anyway. The second is normative: they “should be designed” to do so, with minimum damage to people and to cost. The passage discussed in chapter 2.4 links the two halves: if the equalization is not to happen by chance, “it is management’s job to DESIGN the necessary amplifiers and attenuators” (HOE 1979: 97). The criterion of design is not efficiency alone; damage to people is named first. The Second Principle concerns the channels. Requisite variety at each box is not enough if the channels between the boxes cannot carry it. The principle is formulated in terms of rates, and Beer explains why: variety “counts the number of possible states of the system. Clearly, in a dynamic system, there is a minimal time in which all possible states could be exhibited, and therefore there is a rate of variety generation possible per unit time” (HOE 1979: 99). A channel must be able to carry information faster than the originating subsystem generates the variety it has to report. The Third Principle concerns the boundaries. Each subsystem has its own “language”, so every channel that crosses a boundary needs a transducer (chapter 2.4). The principle adds that the transducer itself must have at least the variety of the channel. A channel of high capacity is useless if the translation at its end reduces what it carries. The Fourth Principle comes much later in the book, in the discussion of the relation between Systems Three and Four. Beer says that it “was there all the time” and was entailed in the first three, but that it took the analysis of the Three-Four loops to show it “with sufficient force” (HOE 1979: 258). His reason for stating it separately is practical: “Breaks in flow, and especially time lags, are dangerous to the entire management process”, and yet “orthodox managerial procedures appear to rely, almost wholly, on ‘snapshot’ accounts of the situation” (ibid.). The first three principles describe a balance. The fourth requires that the balance be maintained continuously rather than checked at intervals.

3.3 Theorem

  • Recursive System Theorem: “In a recursive organizational structure, any viable system contains, and is contained in, a viable system.” (HOE 1979: 566; p. 118). Beer notes that this is “an alternative version of the Theorem as stated in Brain of the Firm, which expressed the same point from the opposite angle” (HOE 1979: 118). Beer quotes the earlier version in the same place: “if a viable system contains a viable system, then the organizational structure must be recursive” (HOE 1979: 118). The two versions run in opposite directions. The BOTF version starts from the fact of containment and infers recursion; the HOE version starts from a recursive structure and states what it contains. Beer calls this rule a theorem because he intends to prove it: “Theorems, no doubt, ought to be proved. The proof offered later will be a topological proof” (HOE 1979: 118). The claim to be proved is that all viable systems, drawn as systems diagrams, look alike, and that the way they are connected between levels of recursion is invariant as well (ibid.). The theorem is the basis of the recursive structure discussed in chapter 6.

3.4 Axioms of Management

  • First Axiom: “The sum of horizontal variety disposed by n operational elements equals the sum of vertical variety disposed on the six vertical components of corporate cohesion.” (HOE 1979: 566; p. 217)
  • Second Axiom: “The variety disposed by System Three resulting from the operation of the First Axiom equals the variety disposed by System Four.” (HOE 1979: 566; p. 298)
  • Third Axiom: “The variety disposed by System Five equals the residual variety generated by the operation of the Second Axiom.” (HOE 1979: 567; p. 298)

Textual note: In the body of the book the First Axiom is set with an equals sign (“= the sum of vertical variety”, HOE 1979: 217), and the Second and Third Axioms say “equivalent” rather than “equals”: “The variety disposed by System Three, resulting from the operation of the First Axiom, and the variety disposed by System Four, are equivalent”; “The variety disposed by System Five is equivalent to the residual variety generated by the operation of the Second Axiom” (HOE 1979: 298).

The three axioms are balance equations. Each states that one variety must match another, which is the Law of Requisite Variety applied to a specific pair of components in the model. The First Axiom balances the variety generated by the operational elements (System One) on the horizontal plane against the variety absorbed by the vertical channels of the model. Beer summarizes the reasoning in HOE: there are six vertical loops, “three determined by the nature of the enterprise, and three designed for metasystemic, managerial reasons”, and “These six vertical loops (of which only one, the command loop, is customarily acknowledged in management theory) must absorb the total variety generated by the horizontal loops of the elemental units, according to Ashby’s Law. This requirement leads to the designation of The First Axiom of Management” (HOE 1979: 143). The remark in parentheses states one of Beer’s main criticisms of conventional organization: it recognizes only the line of command, and so provides one channel where the balance requires six. The Second Axiom concerns the metasystem. Systems Three and Four must balance each other, and Beer explains why no one else can do it for them: “it is necessary for Systems Three and Four to absorb each other’s variety: System Five cannot do it” (HOE 1979: 298). The Third Axiom assigns to System Five the variety left over from that interaction. Beer admits that the two axioms are hard to elucidate further, “because everything has already been said in the exposition of the viable system”, and that a great deal of thought is needed before their full meaning is understood (ibid.). The axioms are therefore summaries of the preceding analysis, not independent starting points. The systems they refer to are described in Part II.

3.5 Law

  • Law of Cohesion for Multiple Recursions of the Viable System: “The System One variety accessible to System Three of Recursion x equals the variety disposed by the sum of the metasystems of Recursion y for every recursive pair.” (HOE 1979: 567; p. 355)

Textual note: In the body of the book the law is set with an equals sign and ends earlier: “The System One variety accessible to System Three of Recursion x = the variety disposed by the sum of the metasystems of Recursion y” (HOE 1979: 355). The words “for every recursive pair” are added in the appendix.

The law connects two levels of recursion. “Recursion x” is the level on which the analysis is focused and “Recursion y” the viable system contained in it (HOE 1979: 320). What System Three at the upper level can see of System One must match the variety managed by the metasystems at the lower level. The law is a balance equation like the axioms, applied across levels rather than within one. Beer’s overview of the argument of HOE places the law in the context of planning. The planning process is “perceived as the cohesive ‘glue’ that holds the embedments of viable systems in place”, and the examination of that process “leads to the ennunciation [sic] of the Law of Cohesion for multiple recursions of the viable system” (HOE 1979: 276). Of all the rules in the glossary, this is the only one Beer calls a law.

3.6 Other key statements

The glossary ends there, but Beer uses three further statements as rules:

  • “The purpose of a system is what it does.” In HOE it first appears in the bar dialogue (HOE 1979: 25). In DTS it is introduced as the “key aphorism”: a good observer imputes the purpose of a system from its actions, because “there is, after all, no point in claiming that the purpose of a system is to do what it consistently fails to do” (DTS 1985: 99).
  • “Information is what changes us.” (PFC 1975: 223; quoted again in HOE 1979: 337). In PFC it goes with the distinction between data and information: “Data are the very latest kind of pollution” (PFC 1975: 223).
  • Freedom as a computable function: “Freedom is in principle a computable function of systemic purpose as perceived” (HOE 1979: 158). Beer calls this “the explosive conclusion”, “explosive precisely because it sounds heartless” (ibid.). The first statement is often quoted on its own, but in DTS it is part of an argument about how purpose is established. The purpose of a system is stated for it by the higher recursion; the system acts and reaches a new state; and “A GOOD OBSERVER will impute the purpose of the system from its actions and thus from the resultant state” (DTS 1985: 99). The declared purpose and the imputed purpose can differ. Beer describes a comparator that “continuously compares the declared purpose with the purpose imputed from the results that the system delivers”, with the result that “THIS SYSTEM WILL CONVERGE ON A COMPROMISE PURPOSE” (ibid.). Like the regulatory aphorisms of section 3.1, the statement is a rule for the observer: judge purpose by outputs, not by declarations. The second statement belongs to Beer’s argument about regulation. In PFC the sentence stands in a sequence: “The purpose is regulation. And that means translating data into information. Information is what changes us” (PFC 1975: 223). Data that change nothing have, in Beer’s words, no value “of themselves” (ibid.). In the terms of chapter 2, information is what alters the state of a receiving system, whereas data that change nothing add to the variety to be handled without contributing to regulation. The third statement concludes a numbered argument in HOE about the autonomy of the operational elements. Two steps of that argument explain why Beer calls the result explosive. First, “The metasystem must make some intervention, and should make only that degree of intervention that is required to maintain cohesiveness in a viable system” (HOE 1979: 158). Second, cohesiveness depends on purpose, “But systemic purpose (as we saw) is a subjective phenomenon, rather than a property of the system independent of its instigators, participants, and observers” (ibid.). Freedom is computable because the necessary degree of intervention can in principle be calculated; it is relative to purpose “as perceived” because the purpose is not given. Beer restates the result later as “freedom for the operational unit is a computable function of the purposes of the system as perceived” (HOE 1979: 200). The phrase connects the rules of the glossary to the discussion of autonomy and cohesion in Part II, and back to the observer-dependence of the system concept in chapter 1.2.

References

  • PFC — Beer, Stafford (1975). Platform for Change. Chichester: John Wiley & Sons. Cited from the Stafford Beer Classic Library reprint, 1994.
  • HOE — Beer, Stafford (1979). The Heart of Enterprise. Chichester: John Wiley & Sons.
  • DTS — Beer, Stafford (1985). Diagnosing the System for Organizations. Chichester: John Wiley & Sons.