Seven objects in Decision and Control (1966) have a variety of 7, of 2, of 21, of 42 or of 2 to the power 42, depending on what the observer takes them to be (DC 1966: 247–252). The demonstration stands in Part III of the book, where Beer applies the view of models from chapter 24 (homomorphic mappings that keep a chosen structure and discard the rest) to the concept of system itself. Chapter 11 (“About Systems”) and chapter 12 (“Coping With Complexity”) contain his most careful statement of what a system is, of the role of the observer, and of variety as the measure of complexity. Several ideas that later carry the VSM are already fully present there, in the language of 1966: requisite variety, the variety sponge, and the black box as a source of variety.
25.1 Coherence, pattern, purpose
Chapter 11 of DC (“About Systems”) begins with the system the manager faces: “It is exceedingly complex. It is highly probabilistic. It is, at least in certain ways, self-regulating (otherwise it would be chaotic)” (DC 1966: 241). Before these features can be discussed, Beer asks what a system is in the first place. “To speak of a system is to speak of the coherence of a number of entities called parts of that system” (DC 1966: 241). The objects themselves do not say what makes them coherent. “A system is not something given in nature, but something defined by intelligence” (DC 1966: 242). Beer’s argument goes through relations. Calling a collection a system means acknowledging that its parts are related; “But everything is related to everything else” (DC 1966: 242). He cites Hegel’s Axiom of Internal Relations, by which things “would not be the things that they are if they were not related to everything else in the way that they are” (ibid.). Since everything is related, relatedness alone cannot pick out a system. The selection comes from the observer: “In practice, however, we acknowledge relatedness only when we are ready to declare its relevance” (ibid.). A collection is recognized as a system in three steps, coherence, pattern and purpose, and it “is not dignified by the unitary notion of a system until some unifying purpose is devised for it” (ibid.). Beer spells the steps out. We acknowledge obtrusive relationships, and “this turns a mere collection into something that may be called an assemblage”; we detect a pattern, which gives “a systematically arranged assemblage”; and “Thirdly, we perceive a purpose served by this arrangement: and there is a system” (DC 1966: 242). “But coherence and pattern and purpose are, all three, acts of mental recognition rather than characteristics of physical things” (DC 1966: 243). The consequences follow at once. “It follows that the detection of system in the world outside ourselves is a subjective matter. Two people will not necessarily agree on the existence, or nature, or boundaries of any system so detected” (DC 1966: 243). Consequently: “Nor is it possible to prove that a system exists, or is thus and thus; it is possible to say only that the treatment of a certain collection of things as a system is helpful” (ibid.). Beer ties this directly to the theory of models from chapter 24. The account of systems “is highly reminiscent of the account given earlier of models” (ibid.), and a recognized system is tested the way a model is tested, “by checking on the predictive capability of the insight” (ibid.). The management example is market share. When two market research firms produce different estimates of a company’s share, managers assume one of them is wrong. Beer’s diagnosis is different: “the two organizations have not identified identical systems” (DC 1966: 244). What matters is the comparison within one system over time, and here he credits Locke: “The relation is more important than the things related” (DC 1966: 245). Classical science had handled large systems by isolating pairs of variables; “It dealt with this problem by making big systems little” (ibid.). It also claimed that its laws were independent of the observer, and “The discoveries of Einstein ruined that claim” (ibid.). The OR scientist should therefore “not gaily accept the system delineated by the conventions of management structure” (DC 1966: 246). One sentence links the section to the rest of the book: “This act of recognition is precisely the formulation of a conceptual model of system” (DC 1966: 246). Making such a model rigorous is the job of “the tool called General Systems Theory” (ibid.). A chemical analysis of a man is correct but “says nothing of any use to the observer concerned with man-the-system”; “Equally one might ask how much a balance sheet, which is correct and factual, tells about the system that is a firm” (ibid.). Beer repeated the point in 1980, in his preface to Maturana and Varela: “A system is not something presented to the observer, it is something recognized by him” (TBYT 2009, “Preface to Autopoiesis”: 68). In the same preface he draws the consequence for boundaries: “the labelling of connections between the system and its environment as either inputs or outputs is a process of arbitrary distinction” (ibid.). On purpose he goes further than DC: “I myself have for a long time been convinced that purpose is a mental construct imported by the observer to explain what is really an equilibrial phenomenon of polystable systems” (TBYT 2009, “Preface to Autopoiesis”: 67–68). In DC purpose is the third act of recognition; in 1980 it is explicitly a construct of the observer. Chapter 26 follows the later texts further.
25.2 The observer and the relatively isolated system
Chapter 12 of DC begins with a difficulty: science needed the idea of an absolutely isolated system, and yet no real system is one. Beer’s answer is the notion of the “relatively isolated system”: “a set of entities […] that is separable from the rest of the world except for two specially chosen sets of relationships with things outside, called its inputs and outputs” (DC 1966: 273). He attributes the technical term to “the Polish cybernetician Henryk Greniewski” (ibid.). Only relations that matter are counted. A company’s relation to the sun is real but unchanging and cannot be influenced, so “it will be disregarded” (DC 1966: 272). Beer at once admits that the division into inputs and outputs is arbitrary, “just another of those dichotomies on which the author is fond of pouring scorn” (DC 1966: 273). Feedback already breaks it: in a feedback loop “an input is an output, and an output is an input” (ibid.). The deeper problem is that the direction of an interaction depends on how the system is drawn. With a teacher and a class, either the pupils’ questions are the input and the teacher’s answers the output, or the teacher’s words are the input and passed examinations the output. Which relations count as inputs and outputs depends on the observer: “Everything depends on how the system is defined, and this in turn depends on who is the observer: the dilemma of modern physics appears once again” (DC 1966: 274). The inputs and outputs of a relatively isolated system “may not be easy to nominate; moreover, which is which depends upon the observer’s point of view and the conventions he unconsciously adopts” (ibid.). Beer draws a practical conclusion for industrial relations. Management treats effort as input and wages as output; the workforce treats wages as input and effort as output. An incentive scheme that management sees as a reward is then seen by the workforce as a sanction. “The systems are formally the same, the one being a mirror image of the other, but the standpoint of each observer causes him to see the system in a totally different light” (DC 1966: 275). Beer advises assuming two-way interaction between subsystems, as a recognition that viable systems depend on richer interactions “than the analyst customarily assumes” (DC 1966: 275). The systems management deals with are of a specific kind: “It is exceedingly complex (to the point where full definition becomes impossible); it is extremely probabilistic (to the point where causal relationships are discernible as no more than tendencies); and it is internally self-regulating to some extent” (DC 1966: 275). Later in the chapter Beer returns to closure. When an environmental disturbance arrives that no one in the system can interpret, management brings in someone who can “speak the language” of that environment and in this way closes the system again, and the process can repeat indefinitely (DC 1966: 287–288). Beer links this to the Incompleteness Theorem and to his own earlier book: “In Cybernetics and Management, I tried to show that this theorem underlies the whole problem of organizing control in a large system such as an industrial company” (DC 1966: 288). To discuss control, the open system has to be closed “by an artificial convention”; “I have called this the principle of completion from without”; and “the closure of the system is artificial” (DC 1966: 288). Beer counts this as fortunate. He cites Bertalanffy’s result that closed systems cannot behave equifinally: “Therefore viable systems are not closed” (ibid.).
25.3 Variety depends on the observer
To discuss the magnitude of the manager’s problem, Beer needs a measure. “A clearly-formulated concept of complexity is needed, and its scientific name is variety” (DC 1966: 247). The first definition seems simple: “The variety of anything is its number of distinguishable elements” (ibid.). But its measurement depends on definition: “For if the intention is to measure the complexity of a system, to state its variety, everything will depend on how the system is defined”, “in short, on who defines it” (ibid.). “In particular, it will be vital to know how deeply the observer’s insight has penetrated into the nature of the system” (ibid.). Here the seven objects come in, described successively at the levels of section 25.1 (DC 1966: 247–252). As a collection of dissimilar things, their variety is 7. If four of them are identical and the other three are identical, the variety is 2: “The seven-ness is illusory” (DC 1966: 248). As an assemblage in which every thing is related to every other, the variety is the number of connections, 21 (DC 1966: 249). If the relations are oriented, so that B→F differs from F→B, it is 42 (DC 1966: 249–250). If the seven things form a dynamic system in which each of the 42 connections can be on or off, the variety is 2 to the power 42, “well over 1,000,000,000,000” (DC 1966: 251–252). The objects stay the same throughout. Only the observer’s account of them changes, and with it the variety. Variety proliferates: “Every conceptual step which enriches the nature of a system under study increases the information about it, increases the uncertainty informing it, and proliferates its variety” (DC 1966: 252). Because interacting varieties multiply rather than add, Beer recommends the logarithmic measure to base 2 (DC 1966: 252–253). He then draws the conclusion for method that also closes chapter 24: “The erroneous idea that the problem could in principle be contained by nominating the most important variables in the system, and writing down some kind of equation to show how they are connected, has surely been demolished by now” (DC 1966: 253). “The reason is that what makes control difficult is precisely the proliferation of variety” (DC 1966: 253). The later definitions of variety in BOTF, HOE and DTS are compared in chapter 2.1 and in Appendix B.
25.4 The Law of Requisite Variety and the variety sponge in DC
Beer introduces the law with a rugby match. One can try to stop fifteen men in red jerseys with an elaborate computer and automata, but “the best way in which to control the system of fifteen men in red jerseys, is to put fifteen men in white jerseys on to the field” (DC 1966: 278). The plain onlooker knows this without theory, but the manager does not have his advantage: “He is playing a game of incomplete information, in which only a few of the rules are known” (DC 1966: 279). DC gives Ashby’s law in Ashby’s words: “‘picturesquely: only variety can destroy variety’” (DC 1966: 279). Beer does not dwell on the formal statement. He expects the reader to find it obvious and replies: “if the law of requisite variety is a truism, how is it that we try to disobey it all the time?” (DC 1966: 280). His example is a predator population controlling its prey. If there is one hawk for every hundred prey animals, each hawk must take a hundred. The general statement reads: “Requisite variety must be there; it does not have to exist on the basis of a raw count of items, but the purposive and systematic assemblage that is identified as a system must be capable of proliferating requisite variety” (DC 1966: 280). Communications matter too, but Beer considers the deeper point to be that “the capacity to proliferate variety within the control box must be as great or greater than the capacity of the situation box to proliferate variety” (DC 1966: 282). An environmental disturbance that cannot be explained or foreseen increases the variety of the situation further. Neither the manager who looks for recurrent patterns nor the analyst who seeks a full explanation can deal with it. The cybernetician can, because he claimed neither (DC 1966: 284). From this Beer derives a different idea of control: “The orthodox notion of control is frankly fascist; it is mandatory; it is a bully. Orders are issued and it is expected that they will be carried out. But by now we have put on nature’s spectacles” (DC 1966: 284). The image of the variety sponge, used later for the Three–Four homeostat (chapter 11), already appears here: “We see that the fundamental nature of the self-regulatory control implicit in a viable system is that it can absorb proliferating variety like a sponge” (DC 1966: 284). The mechanism is the self-vetoing homeostat, in which each of two coupled subsystems rejects any state of the other that does not suit it, until both are in acceptable states (DC 1966: 292). It “has a plan for ultrastability” (ibid.; on ultrastability see chapter 27.9). Even with disturbances nobody understands, control that has requisite variety can go on vetoing unacceptable states: “Requisite (control) variety absorbs proliferating (world) variety like a sponge” (DC 1966: 293). Beer names the limitation in the same passage: “the length of time taken to reach homeostatic equilibrium may be far too long” (ibid.). If control is slower than the arrival of disturbances, the system oscillates without end (ibid.).
25.5 Black box and variety generator
A practical question remains. Variety proliferates naturally in the situation, but the control system is artificial, “and we are simply not accustomed to the idea of a machine or an office which is meant to be a variety proliferator” (DC 1966: 293). Beer’s answer is the black box, “a box to which inputs are observed to lead and from which outputs are observed to emerge”, with nothing known about the connections inside (ibid.). A transparent box has constrained variety, because its internal arrangement is fixed. The black box “is assumed to be able to take on any internal arrangement of input–output connectivity at all; it can therefore proliferate maximal variety” (DC 1966: 293). For control, that makes it a resource. Beer shows how quickly this variety grows. A box with two binary inputs and one binary output can be sixteen distinguishable machines (DC 1966: 294–295). In general the variety is 2 raised to 2 to the power n, where n is the number of inputs. With eight inputs the result is 2 to the power 256, a number with seventy-eight figures, close to Eddington’s number of particles in the universe (DC 1966: 296). The seven objects of section 25.3 reached only 2 to the power 42. The conclusion is reassuring: “it is not necessary to be over-awed by the task of trying to supply requisite variety for its control” (ibid.). “This immense variety is the raw material of a control mechanism competent to handle real-life situations” (DC 1966: 296). Against this, “The plain man, and especially the classical scientist, copes with complexity by suppressing the proliferation of variety, by killing off variety until almost none is left” (ibid.). The task is the reverse: “We have to learn how to fabricate systems from this raw material without de-naturing it” (ibid.). Beer distinguishes two verbs. In natural situations variety proliferates; in the control element of an artificial system it must be generated, which means that “deliberate ‘black box engineering’ can be undertaken in the design of managerial systems” (DC 1966: 296–297). A “variety generator” is a device “deliberately organized to generate it for a purpose” (DC 1966: 297). Beer’s example is two friends who want to find a place on the same map by telephone. The map has upwards of 20,000 grid squares. Numbering every square would meet the law of requisite variety but take about seventeen hours; the map’s coordinates achieve the same by handling only 2 × 144 = 288 elements, which can generate 20,736 combinations (DC 1966: 297). “So, for the expense of recording and handling a variety equal to twice the square root of the requisite variety, the law has been met” (ibid.). The opposite case is a classification that destroys variety. Divide people into Scotsmen and Englishmen, kilts and bowler hats, and then meet an Englishman in a kilt and a trilby: “Before we know what has happened, 95 per cent of our records are in the miscellaneous file. The arrangements lack requisite variety” (DC 1966: 298). The two chapters of DC give a consistent picture. A system is a conceptual model formed by an observer (25.1). Its boundary and the direction of its inputs and outputs are conventions (25.2). Its variety depends on how it is defined, as the seven objects show (25.3). Control means matching that variety, not suppressing it (25.4), and the variety needed for control can be generated by design (25.5). The VSM of the 1970s gives these points an organizational structure, and the observer-dependence of the concepts remains in it.
References
- DC — Beer, Stafford (1966). Decision and Control: The Meaning of Operational Research and Management Cybernetics. Chichester: John Wiley & Sons. Cited from the Stafford Beer Classic Library reprint, 1994.
- TBYT — Beer, Stafford (2009). Think Before You Think: Social Complexity and Knowledge of Knowing. Edited by David Whittaker. Charlbury: Wavestone Press.