The Law We Quote Is Not the Law Ashby Wrote

Ask whether anything in our tradition is proved, and the answer comes back quickly: Ashby’s law. Only variety can absorb variety. We have quoted it ourselves, many times, with Ashby’s name under it.

Ashby did not write that sentence.

In chapter eleven of An Introduction to Cybernetics, 1956, he wrote: “only variety in R can force down the variety due to D; variety can destroy variety.”1 The version we quote is Beer’s.2 It is the better sentence, good enough to travel on its own, and it left behind the conditions that made Ashby’s result exact.

The good regulator theorem, which we lean on almost as hard, has a different problem. It does not prove what we cite it for, and its authors said so in the paper itself, in print, in 1970.

The law holds, and the sections below say why it holds and how far it reaches. What needs correcting is how we read it and what we have attached to it. The correction asks for no experiment, no fieldwork and no revision of the model. It asks for different footnotes.

None of this is an argument against Ashby, against Beer, or against the Viable System Model. It is an argument about our reading habits.

Two sentences and one verb

Put the two verbs side by side. Destroy describes what a regulator does to the variety that reaches it. Absorb describes what the regulator must be able to hold. With Beer’s verb the law becomes an instruction to a designer: match the varieties, by amplifying the regulator or attenuating what it regulates.3 Ashby’s verb gives no instruction. It states a bound.

A compression is not a falsification. In one sense Beer’s version is faithful to Ashby. Anyone who accepts the theorem should accept the design advice. What the compression drops is the apparatus: the stipulation the proof rests on, the constant that appears when the stipulation is relaxed, and Ashby’s explicit statement that the result holds a priori and so says nothing about any particular organization. Quote the compression and give the 1956 book as its source, and two things happen at once. Beer speaks under Ashby’s name, and a design instruction is read as a bound.

This is ordinary usage. Martin Pfiffner’s The Neurology of Business, 2022, a book on implementing the Viable System Model, sets “Only Variety can absorb Variety” in a box headed “Definition”, under the title “Ashby’s Law of requisite Variety”, with a footnote to the 1956 book.4 We have cited it the same way.

What the law actually says

In logarithmic form the law says that the variety of outcomes cannot be pushed below the variety of disturbances less the variety of the regulator. Three details of the derivation matter for the rest of this chapter.

The first is a stipulation about the outcome table. The proof rests on it, and without it the bound weakens. Ashby’s own generalization patches the gap with a constant, and in practice the constant absorbs the entire empirical content.5

The second is the notation. Ashby derives the whole result in Shannon’s terms and states the homology outright: a regulator’s capacity as a regulator cannot exceed its capacity as a channel of communication, and “his ‘noise’ corresponds to our ‘disturbance’, his ‘correction channel’ to our ‘regulator R’.”6 Requisite variety is channel capacity, applied to management. That gives it a lineage, and the lineage is why this law is secure where the VSM’s looser mathematical claims are not. A result that reduces to information theory inherits its clarity about what is assumed and what is delivered. We say this too rarely. It is the strongest thing we can say about any formal claim we own, and it shows by contrast how little of the rest of the model has anything comparable behind it.

The third is the status of the result. Ashby is explicit: “The law states that certain events are impossible… It has nothing to do with the properties of matter.”7 A designer can use that to rule out an arrangement before building it. Anyone who wants the law to say something about a particular firm on a particular Tuesday gets nothing from it, which explains why almost nobody has tried to measure variety in a real organization. The few attempts that exist have not agreed on what should be measured. Beer saw the limit himself. Could anyone “USE this variety measure in a real-life situation,” he asked, and “say: this is the variety of the chemical industry, say? Of course we could not.” The use he proposed instead “is not the naive use of counting states, but of matching state generators.”8

That last observation is about our literature, and a single counterexample would overturn it: a documented case in which two teams applied a stated counting procedure to the same organization and arrived at comparable numbers. We are not aware of one. Until one appears, the practical consequence stands. The law licenses an argument about whether a proposed arrangement could work. It does not license a number, and diagnostics that report variety figures are reporting the output of a counting convention. Chapter 12 takes up the one lineage in organization theory that did make a comparable argument operational.

Who counts the states

Ashby introduces variety with a semaphore. It has two arms and 64 positions, but an observer standing far enough away can tell only 36 of them apart, and for that observer the variety is 36. The lesson he draws is general: “a set’s variety is not an intrinsic property of the set: the observer and his powers of discrimination may have to be specified if the variety is to be well defined.”9 Two years later he put it more plainly: “If two observers differ in the distinctions they can make, then they will differ in their estimates of the variety.”10

Variety is a count of distinguishable states, and nothing in the law fixes who does the distinguishing. Change the partition and the count changes; change the count and the law’s verdict changes with it. The observer enters before the arithmetic begins. Ashby saw this and said so, but he did not close the gap. Beer kept the observer. To state a system’s variety, he wrote in 1966, everything depends on “how the system is defined,” and so “on who defines it”; and the system is itself a choice: “A system is not something given in nature, but something defined by intelligence,” and two people “will not necessarily agree on the existence, or nature, or boundaries of any system so detected.”11 What went missing when the law was passed on is the consequence, in the quotations we use and in our practice, along with the stipulation and the constant.

Care will not repair this, and it is not a weakness peculiar to Ashby. Any formalism that starts by counting states has the same opening. What matters for us is that the same choice turns up twice more in the model, and there too we have treated it as a technical detail. Someone draws a system boundary and decides what is inside and what is environment; Chapter 5 shows how much of the recursion argument hangs on that decision. Someone decides what a transducer will preserve as a message crosses a boundary, which is the subject of Chapter 25. Counting states, drawing boundaries, specifying transducers: one political choice, made in three places. Beer connected the first two and grounded both in purpose as someone perceives it. What separates one state of a system from another, he wrote, is “whether the resulting change of state serves, or has no bearing on, the purposes of the system,” and “systemic purpose (as we saw) is a subjective phenomenon.”12 He did not connect the transducer, and neither he nor we supplied a procedure for settling a disagreement between observers.

Naming the choice does not close it. It does stop us from presenting a variety calculation, a boundary or a transducer specification as a finding when it is a decision. And it tells us where to look when two competent analysts, using the same method on the same organization, produce diagnoses that cannot both be right.

The theorem that is not a theorem

Take a regulator that holds its system at one outcome, always the same one, and let that outcome be a catastrophe. There is no variation and no surprise. By the criterion of the paper that System Four, and System Five’s models of Systems Three and Four, stand on, this regulator is optimal.

The paper is Roger Conant and Ross Ashby’s, 1970, and its title states the claim: every good regulator of a system must be a model of that system.13 We invoke it constantly and read it rarely. Beer, on the same page of Brain of the Firm as the absorb sentence, recalls it as “the cybernetic theorem that declares a regulator to be effective only insofar as its model of what is regulated is adequate.”14 The weight in Beer’s sentence rests on adequate. The theorem’s measure of success is the entropy of the outcome set, to be minimized. The paper defines a set of good outcomes at the start and then does not use it again. On that measure the catastrophic regulator scores zero, which is perfect. A good regulator in Conant and Ashby’s sense is a reliable one; whether it is a desirable one lies outside the mathematics. For an organization this is the sharpest point in the paper. The theorem can support System Four’s need for a model only after someone has shown, on other grounds, that the set-point being defended is worth defending.

Beer leaned on the paper well beyond that sentence. In The Heart of Enterprise the principle “Every regulator must contain a model of that which is regulated” is “precisely an explanation of the necessity for System Four,” and “the Conant-Ashby Theorem” returns when System Five has to hold models of Systems Three and Four, in the argument that leads to his Law of Cohesion. In a later lecture he wrote that “the formal proof” of the claim that a regulator is effective only if it “contains a model that exactly reflects the complexity of the system intended” is “available in a theorem devised by Conant and Ashby,” and that “because of the Conant/Ashby theorem, any other approach is doomed.”15 Each time the theorem arrives as a statement about variety: the model “must have requisite variety,” and “if this model has a given level of variety, it will handle only that equivalent variety in the outside world.” Whether the 1970 proof delivers that reading is the question for the rest of this section.

The authors’ own concessions are in the text, in the comments that follow the proof. On the universal claim of the title: “Although not all optimal regulators are models of their regulands, the ones which are not are all unnecessarily complex.” On their own account, then, some good regulators are not models. On the proof: it, “by avoiding all mention of the inputs to the regulator R and its opponent S, leaves open the question of how R, S, and Z are interrelated.” There is no sensing in it, no channel, no noise and no dynamics. On the environment: the assumption that the disturbance distribution is constant can be relaxed only to systems where it changes “slowly with time”. That excludes the non-stationary environments that are System Four’s whole reason for existing.16

The second concession should trouble a community whose model is a diagram of channels. A proof that mentions no inputs, no channel and no noise cannot warrant a claim about how an organization senses its environment. Chapter 4 shows that the model’s own channels fare only a little better: Beer stated their principles, and neither he nor the practice that followed specified who owns them or how they are measured.

Others have read the paper closely. In 2016 John Baez observed that the lemma carrying the proof is close to trivial, and that the step from the regulator’s state is a function of the system’s state to the regulator contains a model is never argued.17 In 2021 John Wentworth wrote that it “may be the most misleading title and summary I have ever seen on a math paper”, and showed that on the definition given, the identity function qualifies as a model. His repair adds expected-utility optimality, information arriving over time, and a cost of storage, and it recovers a real result: the internal state of the minimal optimal regulator must be isomorphic to the Bayesian posterior.18 Beer had met the identity function long before, from the other side, and welcomed it: since every regulator must be an effective model, it “ought to consist of an isomorphic mapping of the system,” and “the guaranteed isomorphic mapping is the identity mapping.”19 In 2025 Virgo, Biehl, Baltieri and Capucci gave the scholarly version, in a preprint on good regulators for embodied agents. The 1970 paper, they write, “doesn’t strictly succeed, even in its own terms, in showing what its title claims.”20 Their reconstruction replaces being a model with having one. Through an interpretation map, an observer may attribute belief states to a regulator, provided they update consistently with the system’s dynamics. The price is an admission that the attributed model may be trivial.

From a complaint into a claim

That price is the useful part.

Chapter 2 follows how our teaching reduced System Four to environmental scanning. A practical failure often goes with that picture: a System Four whose scanning nobody’s decisions depend on. The function exists, it produces material, and nothing downstream moves. We have always described this as a complaint, and complaints of this kind are hard to settle. The people doing the scanning point to their output. The people ignoring it point to their workload. Neither side can be shown to be wrong, because there is no shared standard to measure them against.

The reconstruction supplies one. The complaint becomes a claim: the model attributable to this regulator is trivial. Someone can dispute that with evidence, because it says something specific. No assignment of belief states to this regulator does any work in predicting what it does. To our knowledge nobody has yet applied the reconstruction to an organization, and we do not claim otherwise. What it offers is a familiar grievance turned into a proposition people can argue about, which is more than the 1970 theorem ever gave us.

The result Conant and Ashby are believed to have proved does exist, and it belongs to someone else. Francis and Wonham’s internal model principle, 1976, states that a controller achieving asymptotic regulation robust to parameter perturbation must contain a copy of the dynamics generating the exogenous signals. It has a clean scope, it is taught in graduate control, and half a century of engineering stands behind it. The load under System Four is real, and Francis and Wonham carry it.2122

Their scope condition should stay in view, since dropped scope conditions are what this chapter is about. Francis and Wonham prove their result for a class of control problems with stated dynamics, and an organization is not obviously such a system. What their theorem gives us is a rigorous statement of the form we thought we already had, and a standard for judging whether an organizational reading of it is being argued for or merely assumed.

A derivation that went almost uncited

On 29 September 2026 OpenAlex recorded 1,065 citations for Conant and Ashby’s paper and 2,879 for Francis and Wonham’s. For a third paper, published in a cybernetics journal, it recorded 44.23

The third paper is A. Y. Aulin-Ahmavaara’s law of requisite hierarchy, published in Kybernetes in 1979, the year The Heart of Enterprise appeared.2425 Aulin argued formally that hierarchy is what compensates when regulatory ability is limited. That is close to Beer’s recursion, though not the same object, and it comes with the kind of formal derivation Beer promised and, as far as we have found, never gave.26

Counts from one database are a crude instrument. Coverage differs by field and by decade, citations in books are badly captured, and no count separates a paper that was read from a paper that was merely listed. The ratio survives all of that. A formal treatment of the structural claim at the center of the VSM, published in the same year as the book that argues for that structure, has been cited tens of times. The two control-theoretic results discussed above have been cited thousands of times. No better instrument is needed to see that we left an available argument lying where it was. Whether Aulin’s derivation actually establishes recursion in the form the VSM needs is a sharper question. It would take a close reading of the paper against Beer’s claim. This book does not do that reading, and we would like to see it done.

Aulin is not an isolated case. Work that would have given our claims formal support has repeatedly been done outside the tradition and gone unread inside it. Chapter 12 follows another instance through Galbraith, who arrived at a variety argument for organization design without citing Ashby at all.

What the law becomes when someone has to measure it

We have said that this tradition quotes a law and uses a vocabulary. There is one place to check that, because one researcher had to turn requisite variety into a question an informed outsider could answer.

Michael D. Pfiffner’s 2017 dissertation states the law at the head of the section that introduces the relevant items. It keeps Ashby’s verb and glosses his noun: “Ashby’s well-known law of requisite variety states that only variety (i.e. complexity) destroys variety.” On the same page, the requisite-variety items of his instrument ask whether the organization’s “ability to react (i.e. the capability to react in a timely, appropriate and formally correct manner), scope of action (the set of suitable behaviours) and the range of offerings (available solutions to a problem)” are “always sufficient to master expected” internal or external challenges. A second item asks the same about unexpected ones.27

Nothing in these items is counted. They enumerate no states of the regulator and none of the regulated system, and they set up no inequality between the two. They ask whether the people concerned can cope, and the answer is a judgment of adequacy on a scale. Ashby’s law has become a question about whether an organization seems equal to what it faces. The step can be followed on one page: variety becomes complexity in the sentence that states the law, and complexity becomes adequacy in the items below it.

The instrument could not have done otherwise. Counting states is not available to a survey of bankers and consultants, and it is barely available to anyone, for the reasons set out under who counts the states. But that is the finding. When a careful researcher had to make the law operational, what came out was the vocabulary, and the vocabulary is what we have been quoting all along. Chapter 18 examines the study’s further use of that item, which is less benign: its near-negation appears on the other side of the same regression.

What this chapter hands forward

Stop citing the good regulator theorem as though it were proved. Cite Francis and Wonham for the rigorous claim and Virgo and colleagues for the modern reconstruction. The authors of the 1970 paper qualified its title inside the paper itself, and we went on invoking it. We take that as evidence that we have not read our own foundations closely enough. It is also the cheapest correction open to us.

Own the partition problem instead of inheriting it three times. Who counts the states, who draws the boundary, and who defines the transducer are one question wearing three coats. Better technical work will not close it. It marks the point at which an observer, and with the observer a politics, enters the model.

Receipt — one corrected citation practice; cost: free. Stop presenting Conant and Ashby’s title as a proved universal. Cite Francis and Wonham for robust regulation through an internal model, and Virgo and colleagues for the modern reconstruction. This is a practice change, not an experiment: it is retired only by a proof that restores the universal claim under conditions relevant to organizational regulation.

This is the smallest receipt in the book, and deliberately so. Chapter 9 asks why so little in this tradition has ever cost us anything, and part of the answer is that we have rarely been anywhere that being wrong was expensive. Changing a citation practice costs no one anything. If we cannot make this correction, the obstacle is not resources.

Notes

  1. W. Ross Ashby, An Introduction to Cybernetics (Chapman & Hall, 1956), 207. The sentence is in section 11/7, where the law is stated in logarithmic form and Ashby introduces it as the way to put that law “more picturesquely”; it does not close the section — one sentence follows it before 11/8. Section 11/6 has already proved the non-logarithmic version and closes on a near-identical sentence: “Only variety in R’s moves can force down the variety in the outcomes.” ↩
  2. “Only variety can absorb variety” is Beer’s compression rather than Ashby’s sentence. See Stafford Beer, Brain of the Firm, 2nd ed. (John Wiley & Sons, 1981), in the chapters on the Chilean project: “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 disposed by the only regulator… that the ideology of the status quo is prepared to acknowledge.” The sentence is at page 308, in the section “Externalities”; page checked 22 September 2026 against a scan of the Wiley second edition. Beer had quoted Ashby’s own verb in 1966: the law “may be expressed (in Ashby’s own words) ‘picturesquely: only variety can destroy variety'” (Stafford Beer, Decision and Control (John Wiley & Sons, 1966; Stafford Beer Classic Library reprint, 1994), 279, page as in the 1994 reprint). Beer’s quotation has “only”; the reprint of Ashby’s page 207 cited in the note above does not. By 1979 the verb is Beer’s: in The Heart of Enterprise (John Wiley & Sons, 1979) he introduces “VARIETY ABSORBS VARIETY” as “the first stage of our perception about variety regulation” (86), writes of “the natural law that variety absorbs variety” (88), and twice sets the absorb form under Ashby’s name: “These diagrams are embodiments of Ashby’s Law. They say: only variety can absorb variety” (286); “Ashby’s Law: ONLY VARIETY CAN ABSORB VARIETY” (497). Pages read 29 September 2026 in the PDFs. ↩
  3. Beer, Brain of the Firm, 308, in the sentence quoted in the note on Beer’s compression above: the 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.” In The Heart of Enterprise the design task is put the same way: “it is management’s job to DESIGN the necessary amplifiers and attenuators” (97), followed there by the First Principle of Organization. Pages read 29 September 2026 in the PDFs. ↩
  4. Martin Pfiffner, The Neurology of Business: Implementing the Viable System Model, trans. Mark Kyburz (Springer, 2022), 143, https://doi.org/10.1007/978-3-031-14260-4. The box is in chapter 9, “Mastering Complexity (Excursus),” section 9.2, “Coping with Complexity”; its footnote 6 reads “W. Ross Ashby, An Introduction to Cybernetics (London: Chapman & Hall, 1956).” Page checked 29 September 2026 in the Springer PDF. ↩
  5. Ashby, An Introduction to Cybernetics, 204–8. The stipulation is at section 11/5: “let us consider, then, only those tables in which no column contains a repeated outcome.” Section 11/8 shows what survives when the tabular form is abandoned; section 11/9 replaces the stipulation with the assumption that each element is repeated k times in a column, and the bound becomes V(O) ≥ V(D) − log k − V(R), or in entropy terms H(D) − K − H(R). K is Ashby’s constant, and it is unbounded by anything in the theory. ↩
  6. Ashby, An Introduction to Cybernetics, 209–11. The capacity sentence (“R’s capacity as a regulator cannot exceed R’s capacity as a channel of communication”) is at 209, section 11/11; the Shannon homology at 211. Ashby’s reference is to Claude E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal 27, no. 3 (1948): 379–423, and 27, no. 4 (1948): 623–56, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x; the correction-channel result Ashby calls Theorem 10 is in Part II, section 12, at 409. ↩
  7. Ashby, An Introduction to Cybernetics, 208 (section 11/10). Unelided: “The law states that certain events are impossible. It is important that we should be clear as to the origin of the impossibility. Thus, what has the statement to fear from experiment? It has nothing to do with the properties of matter.” ↩
  8. Stafford Beer, The Heart of Enterprise (John Wiley & Sons, 1979), 86–87. The question and the answer are on page 86, the proposal on page 87. ↩
  9. Ashby, An Introduction to Cybernetics, 125 (section 7/5). The example that precedes it is the two-armed semaphore: 64 arm positions, of which a distant observer can distinguish only 36, “so to the distant observer … the variety is 36, not 64.” ↩
  10. W. Ross Ashby, “Requisite Variety and Its Implications for the Control of Complex Systems,” Cybernetica 1, no. 2 (1958): 83–99, in the opening section “Variety.” The sentence is parenthetical in the original, and Ashby adds that he will “not, however, have to treat this complication.” We read the retyped Principia Cybernetica version, which does not carry the journal pagination; page to be taken from the journal. ↩
  11. Stafford Beer, Decision and Control (John Wiley & Sons, 1966; Stafford Beer Classic Library reprint, 1994), 242–43 and 247–52, pages as in the 1994 reprint. The boundary sentences are at 242 and 243, where Beer adds that “it is possible to say only that the treatment of a certain collection of things as a system is helpful,” to be tested “by checking on the predictive capability of the insight.” The variety sentence is at 247, where Beer warns that “the lessons of the last section are already being forgotten”; pages 247–52 then show seven things whose variety is 7, 2, 21, 42 or 2^42, depending on what they are taken to be elements of. Pages read 29 September 2026 in the PDF. ↩
  12. Stafford Beer, Diagnosing the System for Organizations (John Wiley & Sons, 1985), 98; Stafford Beer, The Heart of Enterprise (John Wiley & Sons, 1979), 158. The sentence at 158 continues: “rather than a property of the system independent of its instigators, participants, and observers.” It is a step in the argument whose conclusion, on the same page, is that “Freedom is in principle a computable function of systemic purpose as perceived.” Beer also links his account of systems to his account of models: it “is highly reminiscent of the account given earlier of models” (Decision and Control, 243). Pages read 29 September 2026 in the PDFs. ↩
  13. Roger C. Conant and W. Ross Ashby, “Every Good Regulator of a System Must Be a Model of That System,” International Journal of Systems Science 1, no. 2 (1970): 89–97, https://doi.org/10.1080/00207727008920220. The optimality criterion is declared at 91: “In this paper we shall use the last measure, H(Z), and we define ‘successful regulation’ as equivalent to ‘H(Z) is minimal’.” The paper does define a set of good outcomes, “(2) The set G, a sub-set of Z, consisting of the ‘ good ‘ events, those ensured by effective regulation” (90), and names membership of a goal-set G as one criterion of success, beside a small root-mean-square and a small entropy (91). It then chooses H(Z), and G plays no part in the theorem. Nothing in the theorem distinguishes a low-entropy outcome set that is good from a low-entropy outcome set that is fatal. Baez noticed the same gap: “Where did the subset … of ‘good’ outcomes go? Shouldn’t that play a role?” (see the note on Baez below). ↩
  14. Stafford Beer, Brain of the Firm, 2nd ed. (John Wiley & Sons, 1981), 308. The sentence opens: “Remembering the cybernetic theorem that declares a regulator to be effective only insofar as its model of what is regulated is adequate, we see in monetarism a diminution in variety of the real economic world entailed by a regulatory model that cannot encompass more.” The next sentence is the one quoted in the note on Beer’s compression above. Beer does not name Conant and Ashby here. Page checked 29 September 2026 in the scan of the Wiley second edition. ↩
  15. Beer, The Heart of Enterprise, 234–35 and 352. At 234 the principle is set as a displayed statement, followed by “This is precisely an explanation of the necessity for System Four”; the variety sentence is at 235. At 352 Beer names “the Conant-Ashby Theorem” and continues: “Every regulator contains a model of whatever is regulated. This model must have requisite variety”; “System Five, then, must necessarily contain models of System Three and Four.” The Law of Cohesion is stated at 355. Stafford Beer, Think Before You Think: Social Complexity and Knowledge of Knowing, ed. David Whittaker (Wavestone Press, 2009), 110–11, in “The Will of the People”: the “formal proof” sentence is at 110, “any other approach is doomed” at 111. Pages read 29 September 2026 in the PDFs. ↩
  16. Conant and Ashby, “Every Good Regulator,” 96. All three passages are in the four comments that follow the proof (“First… Second… Third… Last”): “although not all optimal regulators are models of their regulands, the ones which are not are all unnecessarily complex”; “the proof of the theorem, by avoiding all mention of the inputs to the regulator R and its opponent S, leaves open the question of how R, S, and Z are interrelated”; and, on relaxing the constancy of p(S), “if the statistics of S change slowly with time, the theorem holds over any period throughout which p(S) is essentially constant.” ↩
  17. John Baez, “The Internal Model Principle,” Azimuth (blog), January 27, 2016, https://johncarlosbaez.wordpress.com/2016/01/27/the-good-regulator-theorem/. The post’s title and its URL slug disagree; the title above is the one the post carries. Having stated the lemma, Baez asks: “What in the world does this have to do with a good regulator containing a model of the system it’s regulating? Well, I can’t explain that as well as I’d like—sorry.” Further down he restates Conant and Ashby’s conclusion as “the state of the regulator should be completely determined by the the [sic] state of the system” and adds: “this, I believe, is what they mean by” the paper’s title. On the lemma, in his own comment on the post of January 28, 2016: “the proof of this lemma is so easy that I can’t imagine the theorem, whatever it is, is very helpful for actually doing practical things.” Baez’s wording is more tentative than our summary in the text. He does not say the step is never argued; he says he cannot explain the connection well, offers a rough version of it himself, and takes the function reading to be what the title means. ↩
  18. John Wentworth (posting as johnswentworth), “Fixing the Good Regulator Theorem,” AI Alignment Forum, February 9, 2021, https://www.alignmentforum.org/posts/Dx9LoqsEh3gHNJMDk/fixing-the-good-regulator-theorem. The judgement quoted in the text is his opening: “This may be the most misleading title and summary I have ever seen on a math paper.” His repair adds expected-utility optimality, information arriving in more than one chunk and having to be stored until decision time, and a cost on what is stored; the recovered result is that the model “is isomorphic to the Bayesian posterior.” ↩
  19. Beer, Think Before You Think, 52, in “An Open Letter to Heinz von Foerster.” The passage opens: “Since every regulator must be an effective model of the system regulated, it ought to consist of an isomorphic mapping of the system,” and continues, “it is evident but not trivial that the guaranteed isomorphic mapping is the identity mapping.” Beer draws the opposite moral from Wentworth: he proposes to approach an identity mapping of a large system with a network of microprocessors. Page read 29 September 2026 in the PDF. ↩
  20. Nathaniel Virgo, Martin Biehl, Manuel Baltieri, and Matteo Capucci, “A ‘Good Regulator Theorem’ for Embodied Agents,” arXiv preprint arXiv:2508.06326 (August 4, 2025), https://doi.org/10.48550/arXiv.2508.06326. Published as “A ‘Good Regulator Theorem’ for Embodied Agents,” in ALIFE 2025: Ciphers of Life: Proceedings of the Artificial Life Conference 2025 (MIT Press, 2025), paper 46, https://doi.org/10.1162/isal.a.874; we cite the preprint because that is the version we read. Version 2 (21 August 2025) keeps the quoted sentence unchanged (checked 26 September 2026). In the original the quoted sentence reads “(C&A) doesn’t strictly succeed, even in its own terms, in showing what its title claims,” where (C&A) is the paper’s own abbreviation for Conant and Ashby. The authors credit Baez and Wentworth with having made the point first. ↩
  21. Bruce A. Francis and W. Murray Wonham, “The Internal Model Principle of Control Theory,” Automatica 12, no. 5 (1976): 457–65, https://doi.org/10.1016/0005-1098(76)90006-6. ↩
  22. A second route from the law to the need for a model, which does not pass through Conant and Ashby, is the law of requisite knowledge: having enough actions is not sufficient, since the regulator must also be able to select the one that fits the disturbance. In entropy form, H(E) ≥ H(D) + H(R|D) − H(R) − K. E stands for the essential variables, the ones the regulator has to keep within bounds; K, as in Ashby, is the variety removed by passive buffering; and H(R|D) measures the regulator’s uncertainty about which action to take given the disturbance. Heylighen and Joslyn credit this extension to Aulin: “Aulin has shown that the law of requisite variety (4) can be extended to include knowledge or ignorance by simply adding this conditional uncertainty term.” They give no reference for it. The same term appears in Aulin-Ahmavaara’s 1979 paper, where H_D(R) “represents the ignorance of the regulator about how to react correctly to each appearance of a disturbance D” (260). Francis Heylighen and Cliff Joslyn, “Cybernetics and Second-Order Cybernetics,” in Encyclopedia of Physical Science & Technology, 3rd ed., ed. R. A. Meyers, vol. 4 (Academic Press, 2001), 155–70; we read the preprint; the page range matches the Vrije Universiteit Brussel record of the chapter, and we have not seen the printed volume. We cite it as a formulation that makes the knowledge requirement explicit, not as a proof. ↩
  23. On 29 September 2026, OpenAlex recorded 44 citations of Aulin-Ahmavaara’s paper, against 1,065 for Conant and Ashby (1970) and 2,879 for Francis and Wonham (1976); on 7 August 2026 the counts were 43, 1,040 and 2,838. Citation counts from one database are a crude instrument and we use them only for the order of magnitude. ↩
  24. A. Y. Aulin-Ahmavaara, “The Law of Requisite Hierarchy,” Kybernetes 8, no. 4 (1979): 259–66, https://doi.org/10.1108/eb005528; the law is stated at 262. Stafford Beer, The Heart of Enterprise (John Wiley & Sons, 1979). ↩
  25. The 1979 paper is not the first statement of the law. Aulin-Ahmavaara writes that its content “seems to have been published in English for the first time in an article of the present writer published in 1975 in Cybernetica,” and his reference list gives A. Y. Ahmavaara, “Cybernetics as the foundational science of action,” Cybernetica 3 (1975): 171–200 (“The Law of Requisite Hierarchy,” 262; reference 1 at 266). We have not read the 1975 paper. The coincidence of dates with The Heart of Enterprise holds for the Kybernetes paper, not for the idea, which was in print four years earlier. ↩
  26. This identification may be overstated. Aulin-Ahmavaara’s hierarchy is a hierarchy of control: governors placed above the regulators compensate for the regulators’ ignorance of which action fits which disturbance. His law says that “the lack of regulatory ability can be compensated for, up to a certain amount, by a greater hierarchy in organization” (262), and he applies it to social classes and the organization of society as a whole. The paper does not mention Beer, recursion or viability. The law maps at least as naturally onto the metasystem above System One as onto recursion, the nesting of viable systems inside viable systems. Beer stated his Recursive System Theorem in 1979 and wrote that “the proof offered later will be a topological proof” (Stafford Beer, The Heart of Enterprise, John Wiley & Sons, 1979, 118); a full-text search of the book found no passage presented as that proof. ↩
  27. Michael Dominik Pfiffner, System viability of organizations and the aetiology of organizational crisis: A Quantitative Assessment of Stafford Beer’s Viable System Model (PhD diss., Universiteit Utrecht, 2017), section 4.6.3.10, “Principle of Requisite Variety,” Table 18 (Questionnaire Principle Requisite Variety), items P.3 and P.4 (Principles Repertoire), 165. The items are also reproduced in the dissertation’s appendix. The statement of the law quoted in the text is the first sentence of section 4.6.3.10, on the same page as Table 18. Read in full text 14 September 2026; page checked 22 September 2026 against the Utrecht PDF, and the statement of the law on 29 September 2026 in the Utrecht repository (publisher) version. ↩

Related reading

This chapter is part of a cumulative research programme on the viable system model. For the general statement, see the law of requisite variety.

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