How can anyone control a system that is too complex to be specified completely? Chapter 1 ended with that problem. Beer’s answer runs through one concept, variety, and through the ways of working with variety when it cannot be counted in detail. One case from the Chile chapters of Brain of the Firm recurs below: an economy whose only acknowledged regulator is the money supply.
2.1 Variety as a measure of complexity
Beer took the concept of variety from W. Ross Ashby, and his definition of it differs only slightly from book to book (see the textual note in chapter 27.2 and appendix B). In Management Science variety is “roughly defined as the possible number of distinguishable states in a situation” (MS 1967: 37). In the Massey Lectures: “The number of possible states of a system is called its variety. […] variety means the number of possible states” (DF 1974, Lecture 1). In The Heart of Enterprise variety is “the measure of complexity” (HOE 1979: 45). In Diagnosing the System: “Variety is the number of possible states of the system” (DTS 1985: 98). In substance the formulations agree: variety counts possible states, not actual ones, and it serves as a measure of how complex something is. Directly after the definition, DTS asks which states are to count at all (DTS 1985: 98). Beer’s example is deliberately trivial: “Today, Fred Bloggs has changed his shirt” (ibid.). This is a change of state, yet no one would count it in assessing the variety of a firm. Beer sets aside the obvious answer, that one should count all relevant variables, and gives a more basic criterion: “What matters in discriminating one ‘state of the system’ from other states is whether the resulting change of state serves, or has no bearing on, the purposes of the system” (DTS 1985: 98). The count of variety therefore depends on the purpose attributed to the system, and always on an observer. This ties the concept to the observer-dependence of the system in chapter 1.2 and to the treatment of purpose in chapter 3.6.
2.2 Variety is the “stuff” of management and proliferates
In Brain of the Firm Beer writes that “variety is the very stuff and substance of modern management in a newly complicated milieu, just as physical matter was the stuff and substance with which our forefathers had to wrestle” (BOTF 1981: 229). Variety, on this account, plays the part in management that physical matter played for earlier generations. The major thread that management cybernetics unravels is accordingly “the thread of variety — its generation and proliferation, its reduction and amplification, its filtering and control” (ibid.). The list in that sentence could serve as a table of contents for what follows. Beer means “proliferation” literally. When elements interact, the number of possible states of the whole grows much faster than the number of elements. The Heart of Enterprise sets the point out as a display: “Variety / the measure of complexity, / itself the STUFF of modern management — / proliferates.” (typeset as a display in the original). Beer continues: “This is the natural law of interactive systems; and the task of the manager is to handle the proliferating variety of his muddy box” (HOE 1979: 57). The “muddy box” is his term for the partly opaque systems that managers deal with; the black box of section 2.5 is, in his words, its “limiting state” (HOE 1979: 40).
2.3 The Law of Requisite Variety
If variety measures complexity, how much variety does a controller need? Beer answers with Ashby’s law, which he treats as the basic law of control. In Brain of the Firm: “Ashby’s Law of Requisite Variety […] says that control can be obtained only if the variety of the controller (and in this case of all the parts of the controller) is at least as great as the variety of the situation to be controlled” (BOTF 1981: 41). Management Science states the same requirement without Ashby’s name: “the control must be capable of generating as much “variety” as the situation to be controlled” (MS 1967: 37; similarly 149). In The Heart of Enterprise Beer builds the law up in two steps, and he begins from an objection to his own earlier calculations of proliferating variety: “who could possibly USE this variety measure in a real-life situation? Could we ever say: this is the variety of the chemical industry, say? Of course we could not” (HOE 1979: 86). The first step is an observation drawn from many kinds of system. In ecological food webs, “enormously potent variety generators have outputs regulated to criteria which relate to the STABILITY of the system”; in team games, “pairs of players contain variety by ‘marking’ each other” (ibid.). From these examples he draws a conclusion: “Thus the first stage of our perception about variety regulation says that VARIETY ABSORBS VARIETY” (ibid.). As the passage presents it, regulation depends on one source of variety being matched against another, and not on knowing the absolute number of states. In the Chile chapters of Brain of the Firm Beer states the law more sharply and draws out its two possible readings: “Only variety can absorb variety: Ashby’s Law can be met either by expanding regulatory variety to absorb evolutionary variety, or by curbing evolutionary learning until variety in the economy matches the regulatory variety” (BOTF 1981: 308). The second reading is his critique of monetarism in that passage. The full sentence goes on to name the regulatory variety in question as the one “disposed by the only regulator — the money supply — that the ideology of the status quo is prepared to acknowledge” (ibid.). Beer’s objection is that “the regulatory tool embodies a model of what must be regulated that denies variety proliferation in pursuit of adaptation and evolution” (ibid.). The example shows that requisite variety is a condition to be met, and that the law itself does not say how to meet it. It can be satisfied by raising the variety of the regulator or by lowering the variety of what is regulated, and the choice between the two is a matter of design and of values.
2.4 Variety engineering: attenuation, amplification, transduction
The variety of the environment always exceeds that of the operation, and the variety of the operation exceeds that of its management. If control requires matching variety, management must either reduce the variety that reaches it or increase its own. Beer calls “the manipulation of varieties by design” variety engineering (DTS 1985: 26). It has three components.
- Attenuation: High variety “is necessarily cut down, or attenuated, to the number of possible states that the receiving entity can actually handle” (DTS 1985: 23). Attenuation happens whenever information passes to a system of lower variety, and it becomes a failure only when it goes too far. In the exercises of DTS two quite different examples lead to the same finding: “each attenuator has reduced variety below the threshold of the required response. We say that the responding system does not exhibit REQUISITE VARIETY” (DTS 1985: 26).
- Amplification: Management has to raise its own variety towards the operation and the environment. Beer warns against assuming that information-gathering amplifies automatically, and takes market research as his example: “Many people suppose (without much thought) that because market research ‘finds things out’ it must be an amplifier of managerial variety” (DTS 1985: 25). In his example it does the opposite. It reduces an impractical range of customer demand to a range the works can handle, and so acts as an attenuator (ibid.). Whether a device amplifies or attenuates depends on the direction of the flow and on the system from whose point of view it is described.
- Transduction: Where a channel crosses a boundary, the message has to be translated. The Heart of Enterprise gives the reason: “Because the ‘language’ of each subsystem is unique to it, messages have to be ‘translated’ when a boundary is crossed” (HOE 1979: 101). The mechanism that does this “is called a transducer, because it ‘leads across’” (ibid.). For Beer, the balancing of varieties is both a natural tendency and a task. Over time the varieties of management, operation and environment come to equal one another. The way in which they do so may be damaging, and that is where the task arises: “if this is not to occur by happenstance, because a natural law is operating, then it is management’s job to DESIGN the necessary amplifiers and attenuators” (HOE 1979: 97). The monetarism of section 2.3 is one way of reaching the balance: curbing evolutionary learning in the economy attenuates what is regulated until its variety matches that of the regulator. At this point in HOE Beer formulates the First Principle of Organization, discussed with the other rules in chapter 3.
2.5 The black box
Anyone who has had a new baby, Beer writes in The Heart of Enterprise, knows “what it is like to be in charge of a black box”: one sees its outputs and controls some of its inputs. “So the solution is to manipulate the inputs in order to regulate the outputs. This can be done without much knowledge of what is happening inside the baby” (HOE 1979: 40). The systems of chapter 1.3 cannot be specified completely, and Beer treats them in the same way, as black boxes that cannot be fully entered. Two “regulatory aphorisms” follow from this (HOE 1979: 40, 47; wording in chapter 3). The first concerns the function of the box, which can be understood from input and output alone. The second concerns its variety. With a series of combinatorial examples Beer shows that the variety of even simple boxes reaches very large numbers, and concludes that “we can measure the intrinsic variety of a black box, or even of a cascade of black boxes, by studying the mathematical implications of the interactions of their input and output schemata” (HOE 1979: 47). Together the aphorisms release the manager from having to understand the inside of a system before regulating it. The inside still matters. Regulation simply does not have to wait for it.
2.6 Heuristics rather than algorithms
In Brain of the Firm Beer contrasts algorithms, which specify every step towards a fully specified goal, with heuristics, which specify only a direction: “in dealing with unthinkable systems it is normally impossible to give a full specification of a goal, and therefore impossible to prescribe an algorithm. But it is not usually too difficult to prescribe a class of goals” (BOTF 1981: 53). Hence: “To think in terms of heuristics rather than algorithms is at once a way of coping with proliferating variety. Instead of trying to organize it in full detail, you organize it only somewhat; you then ride on the dynamics of the system in the direction you want to go” (ibid.). Proliferating variety that cannot be specified completely cannot be controlled by a complete set of instructions either. Beer observes that people already live this way, and that institutions tend to reverse it: “The strange thing is that we tend to live our lives by heuristics, and to try and control them by algorithms” (BOTF 1981: 53). Heuristic control is therefore no relaxation of rigor, since it follows from the law of requisite variety. A controller that tries to prescribe everything would have to match the full variety of what it controls, while a controller that sets a direction and relies on the system’s own dynamics needs far less.
2.7 Feedback, ultrastability, self-organization
Riding on the dynamics of a system presupposes that the system has dynamics that tend towards stability. Beer’s account starts from negative feedback, which “corrects output in relation to fluctuating inputs from any cause”; with it “we are now well on to the track of that normally desirable systemic property, ultrastability” (BOTF 1981: 36). His own glossary defines ultrastability as “the capacity of a system to return to an equilibrial state after perturbation by unknown or unanalysed forces (against the intervention of which the system was therefore not explicitly designed)” (BOTF 1981: 403). The Heart of Enterprise puts it more briefly: “An ultrastable system, that is, will operate in the face of perturbations that have not been envisaged in advance — at the design stage” (HOE 1979: 62). The weight falls on unforeseen perturbations. A system that can cope only with the disturbances its designers anticipated has, in effect, the variety of its designers’ foresight. An ultrastable system can absorb disturbances nobody predicted. Self-organization has, in Beer’s account, a structural precondition: “the redundancy of potential command turns out to be the prerequisite capability of any self-organizing system, and […] given this prerequisite the system will indeed organize itself” (BOTF 1981: 233). Redundancy of potential command means that the capacity to take control is distributed rather than reserved to a single center. Control built into the operation of the system itself is a constant theme: “Control is integral and control is intrinsic” (BOTF 1981: 86). In HOE the engine governor serves as the example: it is designed so “that in the very process of going out of control, it is brought back onto control. This regulatory process of INTRINSIC CONTROL sees to it that Ashby’s Law is automatically obeyed” (HOE 1979: 91). Management Science calls the same principle implicit control (MS 1967: 145–147; see chapter 27.7) and defines ultrastability in its own words (MS 1967: 155; see chapter 27.9). The connection to section 2.4 is direct: intrinsic control absorbs variety where it arises, so that it does not have to be transmitted to a manager at all.
2.8 The algedonic signal
In Brain of the Firm Beer introduces the algedonic signal with a trainer and a dog. The trainer tries to extinguish responses he dislikes by a rebuke and to reinforce those he approves by a reward, and so creates a mode of communication “between two systems which do not speak each other’s language” (BOTF 1981: 59). Beer takes the term “algedonic” from the Greek algos (pain) and hedos (pleasure). The trainer does not need to know how the dog’s brain works; pain and pleasure change the dog’s behavior without a shared language. Not every signal can wait for the normal channels. In the VSM the algedonic signal is a special alarm signal that bypasses the normal filters on the way to System Five (DTS 1985: 133). Its function is to make sure that the attenuation described in section 2.4 does not filter out the message that matters most. According to Brain of the Firm, the algedonic controller is “the biggest variety reducer of them all”, both in the brain and in the firm (BOTF 1981: 233). Its place in the model is discussed in the chapters on System Five and the algedonic channel.
2.9 Every regulator needs a model: Conant–Ashby
The monetarism passage of section 2.3 already relies on a further theorem. There Beer recalls “the cybernetic theorem that declares a regulator to be effective only insofar as its model of what is regulated is adequate” (BOTF 1981: 308). This is the theorem of Conant and Ashby, which says in substance that every good regulator must be a model of the system it regulates, and it links variety to knowledge. For Beer it is also the formal basis for saying that self-regulation needs a model of the self: “Because of the Conant/Ashby theorem, any other approach is doomed: we should find ourselves or our social units moving blindly and incontinently in unknown territory” (TBYT 2009: 111). The step from requisite variety to the theorem can be stated briefly (this is an explanatory reconstruction, not Beer’s wording). A regulator must match the variety of the system it regulates; to do so selectively, it must represent the relevant states of that system; a representation of the relevant states is a model. A system that regulates itself must therefore contain a model of itself. In the VSM the model of the self later becomes the task of System Four (chapter 10).
References
- MS — Beer, Stafford (1967). Management Science: The Business Use of Operations Research. Garden City, NY: Doubleday, in association with Aldus Books, London.
- DF — Beer, Stafford (1974). Designing Freedom. London: John Wiley. Cited by lecture from a transcript edition.
- HOE — Beer, Stafford (1979). The Heart of Enterprise. Chichester: John Wiley & Sons.
- BOTF — Beer, Stafford (1981). Brain of the Firm. 2nd ed. Chichester: John Wiley & Sons. (1st ed. London: Allen Lane, 1972.)
- DTS — Beer, Stafford (1985). Diagnosing the System for Organizations. Chichester: John Wiley & Sons.
- TBYT — Beer, Stafford (2009). Think Before You Think: Social Complexity and Knowledge of Knowing. Edited by David Whittaker. Charlbury: Wavestone Press.
- Ashby, W. Ross. 1956. An Introduction to Cybernetics. London: Chapman & Hall.
- Conant, Roger C., and W. Ross Ashby. 1970. “Every Good Regulator of a System Must Be a Model of That System.” International Journal of Systems Science 1, no. 2: 89-97.