---
title: "Ch11 nesting simon koestler jaques content"
description: "Chapter 10 opened on the Select Bibliography of Brain of the Firm; it has no room for Simon, Koestler or Jaques.[1] The earlier Decision and Control names…"
url: "https://wiki.cybernetic-futures.org/punch-and-judy/part-02-outside-the-model/ch11-nesting-simon-koestler-jaques/ch11-nesting-simon-koestler-jaques-content"
modified: "2026-11-12T15:26:25.898Z"
language: "en"
site: "Cybernetic Futures"
---

# The Nesting: Simon, Koestler, Jaques

Chapter 10 opened on the Select Bibliography of *Brain of the Firm*; it has no room for Simon, Koestler or Jaques.[^ch11-botf-bibliography] The earlier *Decision and Control* names none of the three either.[^ch11-decision-control] The name Simon does occur once in *Brain of the Firm*. It belongs to Beer's son, Simon Beer, the electronic engineer who built in England the prototype set of algedonic meters that was taken to Chile.[^ch11-simon-beer]

The secondary literature is just as quiet. Andrew Pickering's *The Cybernetic Brain*, a scholarly history of British cybernetics, has no Koestler in its index and one incidental Simon, on a page about the Logic Theorist.[^ch11-pickering] The silence runs the other way too. Simon's "The Architecture of Complexity" cites Wiener and Ashby and names neither Beer nor Koestler, and the third edition of *The Sciences of the Artificial* mentions none of them.[^ch11-simon-silence] One link runs between any two of these bodies of work, and only one: Koestler read Simon. He says so on the first page of the chapter in which he coins the holon, where the parable of the two watchmakers comes with the words "I owe it to Professor H. A. Simon", and he credits him again in the book's appendix, for the word *span*.[^ch11-koestler-span]

The five do not form a tradition. Four people besides Beer arrived at the nesting of systems within systems, and they arrived separately. Three of them were working within about fifteen years of one another and of Beer: Jaques in 1956, Simon in 1962, Koestler in 1967. Two of them worked in the same country and in overlapping industrial worlds. The fourth, C. S. Holling, came after Beer's first statement of the model, so his work is convergence rather than prior art, and for that reason a different kind of evidence. Independent arrival is stronger news than influence would have been. When five people working from ecology, from economics and administration, from psychoanalytic industrial fieldwork, from evolutionary biology and from operational research all end up describing systems nested inside systems, the structure is unlikely to be an artifact of any one of their vocabularies.

That is good news for the model. The less comfortable news is why the four entries below share one form. Each arrival came with an account of what a level is. None came with a way of measuring where one level ends and the next begins. Simon has a threshold he cannot set. Koestler has propositions he cannot test. Jaques has a genuine ruler whose construct validity his own side concedes is thin. Holling has a phase nobody has shown they can identify in the present tense. And Beer, as Chapter 5 argued at length, has a criterion for a level of recursion that resolves in practice to a judgment call.

Chapter 5, *The Ladder Without a Ruler*, made that charge against our own side and named these neighbors in passing. Here the neighbors get their own hearing: what each of them claimed, on what evidence, with what admitted limits, and what the VSM↗[^ch11-glossary] would have gained by reading them. Where the material overlaps with Chapter 5 we send the reader there and go further here. Panarchy has a place in a chapter named for three earlier authors because the question in this part of the book goes beyond who named hierarchy first. It asks who made cross-scale nesting operational, and how far they got.

One caution applies to all four entries. Beer's criterion, set out in Chapter 10, is a criterion for a recursion and not for a level in general: a viable system inside a viable system, which is neither an organizational level nor a layer of management.[^ch11-beer-criterion] Simon's blocks, Koestler's holons, Jaques's strata and Holling's scales are each a related object. Where their boundaries meet Beer's, the finding is convergence on a related but not identical object, and whether they meet at all is what the receipt at the end of this chapter tests.

:::: {.how-we-looked}
**How we looked**

Several of this chapter's claims are claims about an absence, and an absence is the easiest thing in scholarship to get wrong. Where a full-text search was possible we ran one: Simon's 1962 paper and his 2002 one, and Koestler's Alpbach appendix. Where only an index was available we say so. *Decision and Control*, the second edition of *Brain of the Firm* and *The Heart of Enterprise* we searched in full text; the Pickering result is an index result rather than a concordance. The Select Bibliography we checked as a printed list and then against the running text of the book, where none of the three men is named either.

The same caution applies to the count of holonic systems that reached day-to-day production, which this book makes in Chapter 15 rather than here. That count rests on three sources that would have reported a deployment if one existed, and it is exactly the kind of claim we are asking other people to make about us. One counterexample retires it, and we would like to be sent it.
::::

## Simon — a level is a rate separation

**What he found ·** Near-decomposability: interactions are stronger or faster within a level than between levels. **When ·** 1962, revisited in 2000–2002. **Who cited whom ·** The searches reported above found no Beer–Simon exchange on this claim. **Evidence base ·** An analytical argument whose watchmaker arithmetic is withdrawn two paragraphs later. **What it costs us ·** The epsilon that distinguishes a level remains unset.

"The Architecture of Complexity" was read to the American Philosophical Society and published in December 1962, ten years before *Brain of the Firm*.[^ch11-arch-complexity] Most readers remember it as the parable of the two watchmakers, and remember the parable in a way that misses what Simon was doing with it.

Hora builds in subassemblies of ten, three levels deep. Tempus builds each watch of a thousand parts in one sitting and loses everything whenever the telephone rings. At an interruption probability of one in a hundred, Tempus takes about four thousand times as long. Two paragraphs later comes the comment almost nobody quotes: "These assumptions are not particularly realistic… Although we cannot, therefore, take the numerical estimate seriously the lesson for biological evolution is quite clear and direct. The time required for the evolution of a complex form from simple elements depends critically on the numbers and distribution of potential intermediate stable forms."[^ch11-watchmakers] The four thousand is a rhetorical prop, and Simon says so in the same breath. The theorem is the final sentence. It is a claim about the availability of stable intermediates, and ratios play no part in it.

The definition underneath the parable matters more for us. Simon defines hierarchy by *near-decomposability*, not by authority, and he states the exclusion outright: "We shall want to include systems in which there is no relation of subordination among subsystems. (In fact, even in human organizations, the formal hierarchy exists only on paper…)"[^ch11-nd-definition] A level exists where interaction rates separate: the parts within a block interact with each other much faster, or much more strongly, than the blocks interact with one another. Any reader of Beer will recognize the epistemological payoff: "we can study the equilibrium at any given level without much concern for the slow dynamics at the levels above, and we can study the dynamics at any level without much concern for the rapid return to equilibrium at the levels below."[^ch11-nd-payoff] That is the license to model one level at a time, and the VSM exercises it on every page.

Beer spent his career insisting that recursion was not the organization chart. Simon had got there in 1962, from a different direction, and with something Beer claimed and never supplied: a criterion that is in principle computable. Beer wrote that the levels of recursion "answer to mathematical criteria" and then, since his was "not a book for mathematicians", discussed them in words and diagrams.[^ch11-beer-math] An interaction matrix either has block structure or it does not, and whether it does depends on observable rates, not on the analyst's reading of a system's identity. Had the two literatures met, the obvious joint project would have been to test whether the boundaries a VSM diagnostician draws coincide with the blocks a rate matrix finds. As far as we can establish, that project was never proposed, let alone run.

*In principle* carries a great deal of weight there, and Simon knew it. His own admissions are more damaging than most of his critics'. Near-decomposability is "a rather strong property for a matrix to possess, and the matrices that have this property will describe very special dynamic systems — vanishingly few systems out of all those that are thinkable." He defends its usefulness on purely empirical grounds: the world we happen to live in is full of such systems. Worse for our purposes, the property is threshold-relative, and the analyst chooses the threshold: "How few they will be depends, of course, on how good an approximation we insist upon." Simon offers no principled way to set it. When he applies the idea to a whole economy, he has to qualify it at once. The input-output matrix is nearly decomposable "with one qualification. There is a consumption subsystem of the economy that is linked strongly to variables in most of the other subsystems."[^ch11-nd-limits] One hub, and the property degrades. The networks organizations actually run on are made of hubs: shared services, enterprise systems, a finance function that touches everything.

The criterion is therefore computable and underdetermined at once, which is a more interesting position than being simply right or simply wrong. It turns a question about identity into a question about a number, and then leaves the number to judgment. Beer's defect is a different one, and larger. Two analysts who disagree about an epsilon can show each other their matrices and see exactly where they part company. Two analysts who disagree about whether a unit has an identity of its own have little to show.

There is a second Simon paper, and keeping the two apart is the most useful thing anyone can do with him. In the work published in 2002 he conceded that the 1962 composition argument does not carry over to multicellular life. He takes bacterial complexity as its limit and writes that existing multi-celled organisms are unlikely to have been formed by the combination of single-celled ones. In its place he built a different argument: among systems of comparable complexity, the nearly decomposable ones adapt faster, because feedback on a part is not scrambled by everything else the system is doing.[^ch11-simon-2002] The claim is better, closer to what a management cybernetician would want, and much less famous. It concerns the rate of adaptation rather than the possibility of assembly, which makes it testable in settings where assembly arguments are not.

What would settle Simon's side is a demonstration, on real organizational interaction data, that the block structure is robust across a reasonable range of thresholds, or that it is not. The data required (who talks to whom, how often, about what) is the kind most organizations now generate as a byproduct of their own communications infrastructure. That is a change in the world since 1962, and this field has not exploited it.

## Koestler — the word, and the propositions

**What he found ·** The holon and a proposition set for self-regulating hierarchy. **When ·** 1967, restated in 1969. **Who cited whom ·** Koestler cites Simon, for the watchmakers' parable and for “span”; Beer and Koestler do not cite one another in the material checked. **Evidence base ·** About sixty-five propositions, not a validated measurement program. **What it costs us ·** A better vocabulary and explicit channel rules still leave the claims untested.

*The Ghost in the Machine* appeared in 1967, and Koestler's first contribution was a name: the holon, the unit that is a whole to what it contains and a part to what contains it. "Parts and wholes in an absolute sense do not exist in the domains of life."[^ch11-ghost] Beer's noun for the thing that recurses is "viable system", and he used the mathematical term itself as a count noun: the embedded systems "are themselves viable systems. They are RECURSIONS OF THE VIABLE SYSTEM."[^ch11-beer-noun] That noun names the recursing thing only if it is viable. Koestler's holon names any part that is also a whole, which is wider than Beer's term and easier to use, and the difference matters more than style. It is one reason VSM diagrams are hard to read aloud and holonic ones are not. It is also one reason our diagrams are so often mistaken for organization charts, since the nouns practitioners reach for to label them are the nouns of the org chart. Naming was Koestler's contribution, and a considerable one.

The technical apparatus came in the same book, as its first appendix: propositions on the "General Properties of Open Hierarchical Systems", across ten headed sections. Two years later Koestler restated them, some sixty-five in all, in the appendix to his Alpbach paper, and the quotations below follow that version.[^ch11-soho] Anyone trained in this model who reads that appendix beside *The Heart of Enterprise* has a strange experience.

Koestler has the autonomy-cohesion↗ tension, and states it as a dual tendency belonging to every holon rather than as a management problem: "Every holon has the dual tendency to preserve and assert its individuality as a quasi-autonomous whole; and to function as an integrated part of an… larger whole." He has attenuation↗ and amplification without either word: "Output hierarchies spell, concretize, particularize. Input hierarchies digest, abstract, generalize", with filters on every echelon stripping noise from the input on its way up. He has the prohibition on skipping levels, stated as a structural rule rather than as etiquette: "The higher echelons in a hierarchy are not normally in direct communication with lowly ones, and vice versa; signals are transmitted through 'regulation channels', one step at a time". He also names the pathology that follows from short-circuiting them. He has recursion as representation, the formally exact version of the idea: a holon is "a system of relata which is represented on the next higher level as a relatum." And he has the answer to the objection every VSM presentation still meets, that hierarchy must mean a tree. Hierarchies, in his account, are "'vertically' arborizing structures whose branches interlock with those of other hierarchies at a multiplicity of levels and form 'horizontal' networks."

All of that was in print in 1967, five years before Beer set out the same structure in *Brain of the Firm* and twelve before *The Heart of Enterprise*, and neither man appears to have known of the other's work.[^ch11-beer-dates] Several of the pieces were Beer's before they were Koestler's: *Decision and Control*, in 1966, already has subsystems of greater and lesser autonomy, a many-one reduction of variety through an echelon of small filters, and an algedonic loop that can short-circuit the whole machinery.[^ch11-dc-pieces] What Koestler had first is the proposition set and the name. That is a claim about citation, and it goes no further: neither cites the other, and we found no correspondence or third-party report that they had read one another. One letter in one archive would overturn it.

What Koestler lacks is a theory, and the gap can be stated exactly. The propositions predict nothing and forbid nothing. Between them, the self-assertive and the integrative tendencies can be made to account for any observed behavior of any part of any system, which amounts to accounting for none. Nothing in the appendix would tell an observer that a putative holon is not one, and no quantity in it could come out wrong. The VSM has the same difficulty, here reached by a writer with no organizational data at all, and the resemblance runs all the way down: a rich generative vocabulary, immediate intuitive assent from readers, and nothing that could fail.

The container has aged badly as well. *The Ghost in the Machine* argues that the human brain is an evolutionary botch and that the species may need chemical correction. The holon survived its vehicle, which is more than the vehicle deserved, and the survival is instructive. What carried was the part that named a structure people could see in their own material. The claims about the world were left behind.

What would settle Koestler's side is narrower than it looks. Two of his propositions are close to testable as they stand. The rule that signals pass one step at a time, together with the pathology he attributes to short-circuiting it, is a claim about observable communication traffic and observable consequences. Anyone with a year of routing data and a record of escalations could put it at risk. Nobody in our tradition has done so, in the half-century during which we have taught the same rule as the algedonic↗ exception, and that says something about us rather than about him.

## Jaques — a ruler

**What he found ·** Time-span of discretion as an empirical criterion for organizational strata. **When ·** 1956–1989. **Who cited whom ·** Beer and Jaques worked in adjacent British industrial worlds without a citation trail between them. **Evidence base ·** Mixed replications and an advocate bibliography that records its own gaps. **What it costs us ·** The available ruler has weak construct-validity evidence.

Elliott Jaques worked the same ground as Beer, in the same country, in the same decades: British industry, the structure of the firm, the shape of authority inside a manufacturing company. His fieldwork was at the Glacier Metal Company while Beer was head of operational research at United Steel. *Measurement of Responsibility* appeared in 1956, three years before *Cybernetics and Management*.[^ch11-jaques-1956] Beer never cites him. Of the documented silences in this chapter, this is the one we find hardest to account for, because it is the only one that distance of discipline or of geography cannot explain. Two men were asking what distinguishes one level of a firm from the next, in different senses of the word level, in the same industrial economy, at the same time, and the record we can reach shows no contact.

Jaques claims that the level of work in a role is measurable by a single quantity, the time-span of discretion: the longest period over which a subordinate exercises discretion before the results of that discretion become reviewable. He also claims that organizational strata are discrete rather than continuous, with boundaries falling at roughly three months, one year, two years, five, ten and twenty.[^ch11-timespan] Set beside Beer's criterion, the difference is not one of rigor or ambition but of what the criterion produces. Beer's produces a judgment about a system's identity. Jaques's produces a number attached to a role, obtained by asking a manager a question about a task. Two analysts who disagree about whether a unit is viable in its own right and one of the units that do what the containing system does, which is Beer's test in our paraphrase, have no procedure for settling it, and Beer supplies none.[^ch11-beer-paraphrase] Two analysts who disagree about a time-span can go and ask.

Beer did leave a rule of thumb for a missing level: "up to seven or eight: not many more, I hope, or else you may be missing a whole level of recursion." In *The Heart of Enterprise* he also published an identity exercise, marked on cards, of which he wrote that "maybe (one day) thresholds will be established, to exceed which will predict collapse."[^ch11-beer-rules] Neither locates a boundary. The second is the nearest thing to a ruler in Beer's own work, and nobody in the tradition built on it.

A ruler does not make a theory right, and the evidence for Jaques's ruler sorts into three unequal piles.

The strongest pile supports the claim Jaques started from, which concerns felt-fair pay rather than structure. Roy Richardson's Minnesota doctorate found a correlation of about 0.86 between the time-span of discretion of a role and what incumbents independently judged to be fair pay for it, on 180 managers at three Honeywell facilities.[^ch11-richardson] That is a serious number, obtained from outside the movement, on a sample large enough to take seriously. The movement's own bibliography records its limitation: neither the dissertation nor the book contains the raw data or a graph, so the figure has to be taken as reported.

The middle pile is the discreteness of the strata. This is the part the VSM would actually want, since a boundary is what we are short of. Here the support comes largely from Jaques's own circle and is reprinted in his own edited volumes, which makes it a research program citing itself rather than an independent replication. The one genuinely independent corroboration we found is Rowbottom and Billis. In 1977, from action research in social services departments in England and Wales, they derived five qualitative work strata and reported that the boundaries coincided with Jaques's.[^ch11-rowbottom] The word independent needs one qualification, and we would rather enter it ourselves. Rowbottom and Billis worked inside Jaques's framework of strata while dropping time-span of discretion as the measure. That is convergence from a different method within a related tradition, short of corroboration by strangers. It is still the best thing in this pile.

The thinnest pile is the later work on cognitive maturation curves. We could find no independent psychometric validation of it at all, and the movement's own annotated bibliography points to no such study.[^ch11-maturation] That is a negative result of our own searching, and the absence of a study we could find does not prove that none exists.

Three lines of criticism stand against the theory. Only one of them is fatal to the use we would want to make of it.

Alan Fox's 1966 appraisal makes the deepest objection, and it concerns pluralism rather than measurement. On Fox's account a firm is a coalition of divergent interests rather than a single team, so a norm of equitable payment is the residue of a power relation, not a fact waiting to be discovered. On that reading, a correlation between time-span and felt-fair pay may show only that both quantities track an internalized and contested status order.[^ch11-fox] We were not able to obtain the thirty-page pamphlet itself and read Fox's argument through the accounts of others. The characterization above is therefore a reconstruction from his position elsewhere in the same year, not a report of the appraisal's own words.

Writing in *Personnel Psychology* in 1969, Michael Gordon charged the theory with unfalsifiability: it leans on unconscious concepts that can be used to nullify what people actually say about their own work. He proposed three concrete validation routes. Decades later, the movement's own annotated bibliography concedes that they "have yet to be explored".[^ch11-gordon] Paul Goodman's 1967 study reported low correlations between time-span and hierarchical level. The movement's bibliography disputes the result on two grounds, and we report it without adjudicating.[^ch11-goodman]

The advocates themselves report the internal weakness, and it is the one that matters most here. In Richardson's data, time-span correlated with felt-fair pay at 0.86 and with actual freedom to act at 0.41.[^ch11-freedom-to-act] The measure predicts what people think a role should pay considerably better than it predicts the discretion the role is named after. For a theory of remuneration that is a curiosity. For our purposes it comes close to disqualifying, because the quantity we would be borrowing is discretion, and discretion is the half the instrument tracks least well.

Jaques then left the refereed journals and published through his own imprint and a practitioner network, and the movement maintains its own annotated bibliography.[^ch11-craddock] None of that makes the theory false. The bibliography is also more honest than a partisan compilation has any obligation to be: the 0.41 figure, the unexplored validation routes and the limits of Richardson's reporting are all in it, entered by advocates rather than extracted by critics. It does mean the citation record cannot be read like a normal literature. Inside a network that publishes and cites itself, a count of citations measures the network rather than the claim. We enter that caution with no comfort at all. It describes a position one recursion level away from our own.

For the use the VSM would make of the ruler, a further study of pay would settle nothing. What would settle it is a construct-validity study of the boundaries: does the stratum a role falls into by time-span predict anything about the role other than what people think it should earn? Gordon named three such routes in 1969 and nobody ran them. We did not run them either, and we had as much reason to want the answer as the requisite-organization community did.

## Holling and panarchy — the thing Beer's diagram cannot show

**What they found ·** Phase-specific adaptive cycles nested across scales, coupled by revolt and remember. **When ·** 1973–2002. **Who cited whom ·** This literature postdates Beer's first VSM statement; it is convergence, not prior art. **Evidence base ·** A review finds substantial metaphorical and retrospective use. **What it costs us ·** Recursion without phase cannot show what panarchy's unequal couplings are meant to show.

Holling's adaptive cycle is the one member of this group that comes after Beer rather than before him: resilience in 1973, the cycle itself in 1986, panarchy proper at the turn of the century. Systems pass through exploitation, conservation, release and reorganization. The cycles nest across scales that differ in speed and extent. And the levels are coupled in both directions. In *revolt*, a fast collapse at a small scale cascades upward into a slower and larger level. In *remember*, the slow large level supplies accumulated structure downward to reconstitute a small one after its collapse.[^ch11-holling]

The contrast with Beer is the sharpest in this chapter, and it concerns time. Beer's recursion is structurally invariant: the same five systems at every level, and the diagram of a level looks the same whatever phase it is in. Beer did make intervention depend on purpose, since "Viable systems of concentrated purpose will be closely-knit" and those of general purpose "more loosely coherent", and in *Brain of the Firm* he distinguished modes of behavior for a whole firm, sustained activity, growth, retrenchment and crisis among them.[^ch11-beer-modes] He has no phase that differs between levels at the same moment, and no coupling that changes with phase. Panarchy's nesting is temporal. Each level sits somewhere in a cycle, different levels are in different phases at once, and the coupling between them changes with phase. A System One↗ in release does not need the System Three↗ that a System One in conservation needs, and imposing the second on the first is a recognizable way to kill a unit that is trying to reorganize. A VSM diagram cannot represent that situation, and every restructuring produces it.

The channels are the second contrast. Beer's inter-recursion couplings (the command axis with its resource bargain, the planning he called the "glue" of cohesion, the cross-recursion coordination of System Two and Three-Star, and the algedonic signal) are all regulatory relations in his sense of the word.[^ch11-beer-couplings] Neither revolt nor remember is a regulatory relation. Revolt is contagion; remember is inheritance. The algedonic signal is arguably a degenerate revolt, a pain report that bypasses levels, though it is a report rather than a cascade, and it is addressed rather than propagated. Nothing anywhere in the model corresponds to remember. We therefore have no account of how a destroyed unit is reconstituted out of the memory held by its container, and the case is far from exotic. It follows every closure, every failed subsidiary and every team that is stood down and later stood up again.

On evidence, the panarchy community has done something the cybernetics community has not: it has audited itself in public. Its founders describe the framework as "not a theory of what it is, but a metaphor of what might be".[^ch11-metaphor] In 2022 a systematic review by resilience insiders coded a sample of the literature. Roughly half of it used panarchy purely as a metaphor, the empirical applications are dominated by qualitative and retrospective studies, and many papers confirm the framework's expectations without testing alternatives. Their central admission, as they wrote it: "There remains a lack of testable mechanistic theories to explain the dynamics of panarchy and, consequently, there are a lack of methods to measure or observe it in real social-ecological systems."[^ch11-rocha] Nearly every application is retrodiction.

The parts of the framework in actual use are also, for our purposes, the wrong parts. The adaptive cycle appears in about four fifths of the coded papers, the rigidity trap in a fifth, the poverty trap in a seventh. Cross-scale interaction, the nesting that makes panarchy *panarchy* rather than the adaptive cycle, ranks second, behind the cycle, and the review records that papers did not engage in measurement or observation to test revolt and remember.[^ch11-nesting] The component we would most want to borrow is the one that community has tested least.

There is also one real test, and it went against the framework. In 2020 zu Castell and Schrenk built an information-theoretic method for identifying the phases and applied it to the European financial crisis and to grassland ecosystems. They recovered the phases, and reported: "We cannot confirm a generally short duration of the Ω- and α-phase compared to the r- and K-phase."[^ch11-castell] The fast back loop and slow front loop drawn into every version of the diagram did not appear in the data. The authors also warn that their method cannot be used in a black box fashion and depends on the analyst's choice of parameters. That is Simon's threshold problem, arriving at the other end of the chapter under a different name.

The VSM's own epistemic position is very nearly the same: a rich generative model, wide uptake, thin falsification. The difference is the one this book is about. Somebody built an instrument, the instrument returned a negative result, and the community published it.

## What the four have in common

Taken together, the four entries yield a single result, and it has nothing to do with any one author's carelessness.

Simon has a threshold nobody can set, and says so. Koestler has propositions nobody can test, and does not say so. Jaques has a ruler whose construct validity his own side concedes is weak, and records the concession in his own bibliography. Holling has a phase nobody has yet shown they can identify in the present tense, and the review that establishes this was written by insiders. Beer has a criterion that resolves to a judgment call, which is the finding of Chapter 5.

Four people saw related structures independently, and Beer saw his own version a fifth time. None of the five could measure it. The instrument has been missing for six decades in five literatures at once, in fields with different data, different methods, different funding and different standards of proof. That distribution is itself evidence, and it points away from the explanation each community reaches for first. The difficulty is unlikely to lie in cybernetics, or in requisite organization, or in resilience ecology. It lies in the structure, and whoever builds the instrument will have done something considerable for all five.

Two readings of the situation hold up, and Beer held both. In the first, levels are real and hard to measure, as many real things are, and the convergence of five independent traditions on related objects that none of them can measure is a reason to keep working. In the second, levels are an artifact of how observers parse continuous systems: five traditions converged because five sets of humans parse in the same way, and the instrument is missing because there is nothing for it to measure. Beer wrote the second as method: "A system is not something given in nature, but something defined by intelligence"; two people "will not necessarily agree on the existence, or nature, or boundaries of any system so detected"; and it is possible to say only that treating a collection of things as a system "is helpful." He wrote the first when he said that levels of recursion "answer to mathematical criteria."[^ch11-beer-readings] Neither half has been put to a test. We believe the first. We cannot presently show that the second is wrong, and no one in the other four literatures can either. That is why the instrument matters more than another round of exposition.

This part of the book is no priority dispute, and the four neighbors do not compete for our territory. Each offers the model something specific that it lacks. Simon offers a boundary criterion stated over observable rates rather than over identity. Koestler offers a noun for the recursing thing and a set of channel rules stated sharply enough to be broken. Jaques shows that a level, in his sense of the word, can be attached to a number at all, and leaves an honest record of what that number does and does not predict. Holling offers phase, and the two cross-scale couplings we have no counterpart for. We did not read this literature, and it cost us four opportunities to test our own central construct against somebody else's.

## The priced receipt

**Receipt — one registered blind comparison of level boundaries, in one organization.** Build an interaction matrix from observed rates of interaction. Record time-span of discretion for the roles that head each candidate recursion's management, at the boundaries an experienced VSM diagnostician independently selects. As a third and cheap boundary reading, have the heads of each candidate recursion complete Beer's identity exercise at the same boundaries, which puts Beer's own nearest thing to a ruler beside time-span; Beer called what it asks for "subjective judgments."[^ch11-beer-identity-receipt] Then give the matrix and the VSM account to two analysts who do not know which method produced which boundaries, and ask each to reconstruct the level structure. Register the protocol and the criterion of agreement before any of it is run. Agreement is measured as the adjusted Rand index between the matrix-derived and the VSM-derived partitions of units; chance is estimated by a permutation test against 1,000 random partitions with the same block sizes, and convergence requires p below 0.05 and an index of at least 0.5, both registered before the run. Ten interview-days, five observation-days and five analysis-days make this approximately twenty working days.

The design stands or falls on a negative result being publishable in advance. If the boundaries do not converge beyond chance, the claim that recursion identifies an observable level structure is weakened, and so is the assumption that Jaques's strata and Beer's recursions can be read off the same boundaries. We should say so in print. If they do converge, the field has the beginning of a ruler, and the first evidence in sixty years that the thing five literatures have been pointing at can be seen twice, by two methods.

[^ch11-decision-control]: Stafford Beer, *Decision and Control: The Meaning of Operational Research and Management Cybernetics* (John Wiley & Sons, 1966). The negative claim is ours. It rests on a full-text search, run on 23 September 2026, of the Stafford Beer Classic Library reprint (John Wiley & Sons, 1994), which reproduces the 1966 text: neither Simon, Koestler nor Jaques is named anywhere in the book, index and apparatus included. A search of a digital text layer is as good as the text layer, and we report it as that.

[^ch11-botf-bibliography]: Stafford Beer, *Brain of the Firm*, 2nd ed. (John Wiley & Sons, 1981), Select Bibliography, 405–10. The named works are Beer's own listing; *The Pauper's Cookbook* is Jocasta Innes, *The Pauper's Cookbook* (Penguin Books, 1971), entered under “D. Explicit References” (p. 410) and quoted in the preface to the second edition (p. xii): “brains need gentle handling or they are apt to disintegrate”. The absence of Simon, Koestler and Jaques from the Select Bibliography is a check of a printed list; a full-text search of the same edition, run on 23 September 2026, finds none of the three in the running text either.

[^ch11-simon-beer]: Stafford Beer, *Brain of the Firm*, 2nd ed. (John Wiley & Sons, 1981), 284: “A prototype system of ten algedonic meters, linked by a single wire in a loop through a large summation meter, was built in England by my son Simon Beer (an electronic engineer), and taken to Chile for experimental purposes.” The book's index has the single entry “Beer, Simon, 284”, and a full-text search of the edition finds no other occurrence of the name.

[^ch11-pickering]: Andrew Pickering, *The Cybernetic Brain: Sketches of Another Future* (University of Chicago Press, 2010). The claim rests on the book's index. We were unable to run a full-text search of the volume, and the reader should treat "no Koestler at all and one incidental Simon" as an index result rather than a concordance.

[^ch11-simon-silence]: Herbert A. Simon, "The Architecture of Complexity," *Proceedings of the American Philosophical Society* 106, no. 6 (1962): 467–82. Verified in full text: the paper's notes cite Shannon and Weaver and W. R. Ashby's *Design for a Brain* and "Design for an intelligence amplifier," and Wiener once; Beer, Koestler and Jaques do not appear (search of the text layer of the JSTOR scan, repeated on 29 September 2026). For the third edition, Herbert A. Simon, *The Sciences of the Artificial*, 3rd ed. (MIT Press, 1996); we have not been able to search that volume in full text and rest the claim on its index and bibliography.

[^ch11-koestler-span]: Arthur Koestler, *The Ghost in the Machine* (Hutchinson, 1967), 45 for the parable ("I owe it to Professor H. A. Simon"), 47 for Simon's conclusion on stable intermediate forms, quoted at length, 52 n. for Simon's decomposable hierarchies, 342 for proposition 2.2 with *span* credited to Simon, and 364 for "The Architecture of Complexity" in the bibliography (read in the Internet Archive scan of the Hutchinson first edition on 2 October 2026; page 45 checked against the page image). The Alpbach appendix repeats the credit: Arthur Koestler, "Beyond Atomism and Holism—The Concept of the Holon," in *Beyond Reductionism: New Perspectives in the Life Sciences*, ed. Arthur Koestler and J. R. Smythies (Hutchinson, 1969), appendix, "Some General Properties of Self-Regulating Open Hierarchic Order," proposition 2.2: "The number of levels which a hierarchy comprises is a measure of its 'depth', and the number of holons on any given level is called its 'span' (Herbert Simon)." The link is a debt declared in the book that coins the holon, not only an attribution in the technical apparatus. We found no reciprocal citation, and no citation in either direction between any other pair among the five.

[^ch11-arch-complexity]: Simon, "The Architecture of Complexity," 467–82. Read to the American Philosophical Society and published in the issue dated 12 December 1962.

[^ch11-watchmakers]: Simon, "The Architecture of Complexity," 470 for the watchmakers and the four-thousand estimate, 471 for the retraction: "These assumptions are not particularly realistic. They undoubtedly underestimate the decrease in probability of achieving the assembly with increase in the size of the assembly… Although we cannot, therefore, take the numerical estimate seriously the lesson for biological evolution is quite clear and direct." The ellipsis in the text stands for a sentence in which Simon says the assumptions understate the advantage of hierarchy.

[^ch11-nd-definition]: Simon, "The Architecture of Complexity," 468. Simon's parenthesis reads in full: "(In fact, even in human organizations, the formal hierarchy exists only on paper; the real flesh-and-blood organization has many inter-part relations other than the lines of formal authority.)"

[^ch11-nd-payoff]: Herbert A. Simon, "Near Decomposability and the Speed of Evolution," *Industrial and Corporate Change* 11, no. 3 (2002): 587–99. The sentence quoted is from the later paper, not from "The Architecture of Complexity" — we searched the 1962 text and it is not there. It reads in full: "In fact — and this property is used continually by the sciences — we can study the equilibrium at any given level without much concern for the slow dynamics at the levels above, and we can study the dynamics at any level without much concern for the rapid return to equilibrium at the levels below, or for the (very slowly moving) disequilibrium states at the levels above." We verified the wording against Simon's own working paper, Complex Information Processing Working Paper #549, dated 4 April 2000, in the Carnegie Mellon collection of his papers.

[^ch11-nd-limits]: Simon, "The Architecture of Complexity," 475, for all three quotations: the "vanishingly few" concession, "How few they will be depends, of course, on how good an approximation we insist upon," and the consumption-subsystem qualification.

[^ch11-simon-2002]: Simon, "Near Decomposability and the Speed of Evolution," 587–99. The concession is explicit: having taken bacterial complexity as the limit of the composition argument, Simon writes that "it is highly unlikely that existing living multi-celled organisms were formed by the combination of single-celled organisms," and builds the fitness-rate argument in its place. On his age: the paper appeared posthumously in 2002, Simon having died in February 2001; the working-paper version is dated 4 April 2000, when he was eighty-three. He turned eighty-four in June 2000. We have not been able to date the final revision and therefore cannot confirm "at eighty-four" as more than approximate.

[^ch11-ghost]: Arthur Koestler, *The Ghost in the Machine* (Hutchinson, 1967), 48, where the holon is coined. The sentence quoted is proposition 1.3 in both of Koestler's proposition sets, and we give it in the form of the 1969 Alpbach appendix. The 1967 book prints it in its own Appendix I, 341, with "domain" for "domains" (read in the Internet Archive scan of the Hutchinson first edition on 2 October 2026; proposition 1.3 checked against the page image).

[^ch11-soho]: Arthur Koestler, *The Ghost in the Machine* (Hutchinson, 1967), Appendix I, "General Properties of Open Hierarchical Systems (O.H.S.)," 341–48, in ten headed sections from "The Janus Effect" to "Regeneration"; the propositions quoted in this paragraph appear there as 4.1 (343), 5.6 and 5.8 (344), 5.11 and 6.1 (345) and section 7 (346), with the short-circuiting pathology as 7.2, in British spelling ("concretise, particularise", "arborising") (read in the Internet Archive scan of the Hutchinson first edition on 2 October 2026). We quote the 1969 restatement: Koestler, "Beyond Atomism and Holism—The Concept of the Holon," appendix, "Some General Properties of Self-Regulating Open Hierarchic Order." The propositions run to about sixty-five across ten headed sections; the ones quoted in this paragraph are, in order, 4.1 (the dual tendency), 5.11 (output hierarchies spell, input hierarchies digest) with 5.8 for the filters that strip the input of noise, 7.1 (regulation channels, one step at a time) with 7.3 for the pathology of short-circuiting them, 5.6 (a system of relata represented on the next higher level as a relatum), and 6.1 (arborization and reticulation). The paper was given at the Alpbach Symposium in 1968 and published in 1969; a version of the essay was also reprinted as Arthur Koestler, "Beyond Atomism and Holism—the Concept of the Holon," *Perspectives in Biology and Medicine* 13, no. 2 (1970): 131–54. We verified the propositions against a full transcription of the appendix and cite them by number because we could not confirm page numbers in the Hutchinson printing.

[^ch11-dc-pieces]: Stafford Beer, *Decision and Control* (John Wiley & Sons, 1966), 104–5 (control systems in the enterprise and the body are both hierarchical and redundant, and "both incorporate sub-systems of greater and lesser autonomy"), 384 (the "many-one transformation" by "an echelon of small, rather simple black boxes"), 388 (the importance filter) and 396 (the algedonic loop, "which can effectively short-circuit the total machinery"), paginated after the Stafford Beer Classic Library reprint (John Wiley & Sons, 1994), which reproduces the 1966 text.

[^ch11-beer-dates]: Stafford Beer, *The Heart of Enterprise* (John Wiley & Sons, 1979), and *Brain of the Firm* (Allen Lane, 1972), the first edition; the second edition of 1981 is the one whose Select Bibliography is described above. The claim that neither man knew of the other is a claim about citation, not about acquaintance: neither cites the other, and we found no correspondence or third-party report that they had read one another. A full-text search of *The Heart of Enterprise* and of the second edition of *Brain of the Firm* finds no mention of Koestler or of the holon.

[^ch11-jaques-1956]: Elliott Jaques, *Measurement of Responsibility: A Study of Work, Payment, and Individual Capacity* (Tavistock Publications, 1956); Stafford Beer, *Cybernetics and Management* (English Universities Press, 1959). Jaques's fieldwork was at the Glacier Metal Company, reported in Elliott Jaques, *The Changing Culture of a Factory* (Tavistock Publications, 1951); Beer was head of operational research at United Steel over the same years: “In the mid 1950s, I was directing management sciences for the largest steel company in Britain, United Steel”, in a department called “The Department of Operational Research and Cybernetics” (Stafford Beer, *Brain of the Firm*, 2nd ed. [John Wiley & Sons, 1981], 384). That Beer does not cite Jaques rests on full-text searches of *Decision and Control*, *Brain of the Firm* (2nd ed.) and *The Heart of Enterprise*; that Jaques does not cite Beer we take from Jaques's reference apparatus.

[^ch11-timespan]: Jaques, *Measurement of Responsibility*, for the derivation of time-span of discretion, and Elliott Jaques, *Requisite Organization: The CEO's Guide to Creative Structure and Leadership* (Cason Hall, 1989), for the stratum boundaries at three months, one year, two years, five, ten and twenty years in their settled form. The lowest five of those boundaries are the ones Rowbottom and Billis test below; the twenty-year boundary is not independently corroborated in anything we found.

[^ch11-richardson]: Roy Richardson, "An Empirical Study of Fair Pay Perceptions and Time Span of Discretion" (PhD diss., University of Minnesota, 1969), published as *Fair Pay and Work: An Empirical Study of Fair Pay Perception and Time Span of Discretion* (Southern Illinois University Press, 1971). The correlation is +0.862, significant at the 0.001 level, on 180 managers at three Honeywell facilities. We take the figure from Ken Craddock, *Requisite Organization Annotated Bibliography on Elliott Jaques, Wilfred Brown, and Requisite Leadership (Covering 1942 to 2009)*, 5th ed. (August 2009), https://globalro.org/system/files/documents/RO-Biblio.pdf, which reports it from the dissertation and the book; neither contains the raw data or a graph, a limitation the bibliography itself notes.

[^ch11-rowbottom]: Ralph Rowbottom and David Billis, "The Stratification of Work and Organizational Design," *Human Relations* 30, no. 1 (1977): 53–76. Five successive levels derived from action research in social services departments in England and Wales — prescribed output work, situational response work, systematic service provision work, comprehensive service provision work, comprehensive field coverage work — with the paper stating that Jaques's "critical time-span boundaries between strata — 3 months, 1 year, 2 years, 5 years, and 10 years — will correspond to the boundaries between successive strata" they identify. One qualification on the word *independent*: Rowbottom and Billis used Jaques's framework of strata while dropping time-span of discretion as the measure, so this is convergence from a different method inside a related research tradition, not corroboration by strangers.

[^ch11-maturation]: The negative finding is ours and it is a negative: searching the psychometric literature we found no independent validation of the cognitive-maturation curves, and the annotated bibliography of the movement itself points to no such study. Absence of a result we could find is not proof that none exists.

[^ch11-fox]: Alan Fox, *The Time-Span of Discretion Theory: An Appraisal*, Research Paper No. 1 (Institute of Personnel Management, 1966), 30 pp. Fox's pluralist position — that a firm is a coalition of divergent interests rather than a single team, so that norms of equitable payment express a power relation — is set out in the same year in his *Industrial Sociology and Industrial Relations*, Research Paper 3 for the Royal Commission on Trade Unions and Employers' Associations (HMSO, 1966). We were not able to obtain the thirty-page appraisal itself and read Fox's argument in it through the accounts of others; the characterization in the text is therefore a reconstruction from his position elsewhere, and a reader wanting the appraisal's own words will have to find the pamphlet.

[^ch11-gordon]: Michael E. Gordon, "An Evaluation of Jaques' Studies of Pay in the Light of Current Compensation Research," *Personnel Psychology* 22, no. 4 (1969): 369–89. The three routes are at 386–87: the behavior of pay over time, statistical models of pay, and the relationship between pay and other job-satisfaction variables. The concession is in Craddock's *Requisite Organization Annotated Bibliography*, in the entry for this article: "Gordon's other research suggestions have yet to be explored." Craddock adds "HINT, HINT," which we have not quoted but which is the tone of the concession.

[^ch11-goodman]: Paul S. Goodman, "An Empirical Examination of Elliott Jaques' Concept of Time Span," *Human Relations* 20, no. 2 (1967): 155–70. The movement's own bibliography disputes the finding on two grounds — that Goodman obtained strong correlations when managerial roles alone were used, and that the low result was not replicated in six later studies — and records that Goodman himself stepped back from the article in a 1973 book review, Paul S. Goodman and Robert L. Miller, review of *Fair Pay and Work*, by Roy Richardson, *Administrative Science Quarterly* 18, no. 1 (1973): 135–37. The six studies it lists are the Berkeley dissertations of Kvålseth (1971) and Wirth (1976), three Canadian studies by Hansen (1973, 1974, 1975), and Vinton's dissertation (1995). The text reports what Goodman reported; it does not adjudicate the dispute.

[^ch11-freedom-to-act]: Craddock, *Requisite Organization Annotated Bibliography*, entry for Richardson 1969 and 1971: the correlation of time-span with felt-fair pay is +0.862 and with freedom to act +0.407. Both figures come from the movement's own annotated bibliography, which is the point being made about them: the weaker number is reported by the advocates, not extracted by critics.

[^ch11-craddock]: Craddock, *Requisite Organization Annotated Bibliography*. Jaques's later imprint was Cason Hall, publisher of *Requisite Organization*; the practitioner network is the Global Organization Design Society, which hosts the bibliography.

[^ch11-holling]: C. S. Holling, "Resilience and Stability of Ecological Systems," *Annual Review of Ecology and Systematics* 4 (1973): 1–23; C. S. Holling, "The Resilience of Terrestrial Ecosystems: Local Surprise and Global Change," in *Sustainable Development of the Biosphere*, ed. William C. Clark and R. E. Munn (Cambridge University Press, 1986), 292–317, where the adaptive cycle first appears; Lance H. Gunderson and C. S. Holling, eds., *Panarchy: Understanding Transformations in Human and Natural Systems* (Island Press, 2002), and C. S. Holling, "Understanding the Complexity of Economic, Ecological, and Social Systems," *Ecosystems* 4, no. 5 (2001): 390–405, for revolt and remember.

[^ch11-metaphor]: Gunderson and Holling, *Panarchy*, 32.

[^ch11-rocha]: Juan C. Rocha, Linda B. Luvuno, Jesse T. Rieb, Erin T. H. Crockett, Katja Malmborg, Michael Schoon, and Garry D. Peterson, "Panarchy: Ripples of a Boundary Concept," *Ecology and Society* 27, no. 3 (2022): art. 21, https://doi.org/10.5751/ES-13374-270321. The coded sub-sample is N = 42: "Roughly half (20/42) of the papers used panarchy as a metaphor"; "Empirical papers predominantly used qualitative methods (17) and were primarily retrospective historical reviews"; "Many of the papers we read confirmed but did not challenge the expectations that panarchy put forward." A correction the reader is owed: earlier drafts of this chapter attributed to this paper the sentence "we still lack the theory and methods to gather observations and be able to decide in which phase of the adaptive cycle a system currently is." That sentence is not in the paper. We searched the full text of the article and of the one other work it could plausibly have come from, zu Castell and Schrenk's, and searched for the phrase in the open literature, and we could not source it anywhere. It has been replaced above by the review's own statement of the same admission, and the earlier sentence should not be quoted by anyone as Rocha and colleagues' words.

[^ch11-nesting]: This is a correction. Rocha and colleagues report the adaptive cycle at 81 per cent of the coded sample (34 of 42), the rigidity trap at 19 per cent and the poverty trap at 14 per cent, and they rank cross-scale interactions second: "the most common feature of panarchy in the literature was the adaptive cycle (81%, 34 out of N = 42) followed by cross-scale interactions." Earlier drafts of this chapter called the nesting the least-used component of all, which the review contradicts. The review's conclusion nonetheless supports the weaker claim now made — "Cross-scale dynamics, structure, and traps have received less attention" — and it records that papers "did not engage in measurement or observation to test… revolt and remember cross-scale interactions." The review's figure 5, which breaks the coding down further, has no separate code for nestedness: hierarchy and cross-scale interactions are coded together, at about three quarters of the sub-sample, second only to the adaptive cycle.

[^ch11-castell]: Wolfgang zu Castell and Hannah Schrenk, "Computing the Adaptive Cycle," *Scientific Reports* 10 (2020): art. 18175, https://doi.org/10.1038/s41598-020-74888-y. The method is information-theoretic, built on transfer entropy in a network representation, and is applied to a Tangled Nature model, to the European financial crisis and to an ecological succession experiment in Kansas grassland. The quotation is verified verbatim, and its context is worth keeping: "Some of the details that Gunderson and Holling draw on cannot be supported by our study. For example, we cannot confirm a generally short duration of the Ω- and α-phase compared to the r- and K-phase." The authors also warn that the method "can not be used in a black box fashion" and depends on the analyst's choice of parameters — which is Simon's epsilon problem, arriving at the other end of the chapter.

[^ch11-glossary]: Terms marked ↗ are defined in the Glossary at the back of the book. The mark is set on the first appearance of each term in each chapter, and not afterwards.

[^ch11-beer-criterion]: Stafford Beer, *Diagnosing the System for Organizations* (John Wiley & Sons, 1985), 1–2; Stafford Beer, *The Heart of Enterprise* (John Wiley & Sons, 1979), 118, 308 and 411. The quotations are given in Chapter 10.

[^ch11-beer-paraphrase]: The wording is our paraphrase of Beer and not a quotation. His nearest statements: the operational elements of a viable system exhaust its "basic activities, namely those which exist to do what the system does" (Beer, *Heart of Enterprise*, 116); a division that "could in principle be hived-off as a separate business" is a viable system, and the accounting system that prepares the group accounts is not (ibid., 118); and "the viable system is necessarily a producer of the organization, and not just an adjunct to it, however important" (Beer, *Diagnosing the System*, 8).

[^ch11-beer-math]: Beer, *Heart of Enterprise*, 308.

[^ch11-beer-noun]: Beer, *Diagnosing the System*, 2.

[^ch11-beer-identity-receipt]: Beer, *Heart of Enterprise*, 417–33, "Identity: an exercise"; the caution is at 419: "These are subjective judgments for which we ask."

[^ch11-beer-rules]: Beer, *Diagnosing the System*, 19; Beer, *Heart of Enterprise*, 417–33, with the sentence quoted at 432. Beer introduces the scoring with a caution of his own: "we are entering ground where it would be bogus to pretend that proper measurements can be made. These are subjective judgments for which we ask" (419).

[^ch11-beer-modes]: Beer, *Heart of Enterprise*, 158; Stafford Beer, *Brain of the Firm*, 2nd ed. (John Wiley & Sons, 1981), 234–35.

[^ch11-beer-couplings]: Beer, *Heart of Enterprise*, 336 and 407; Beer, *Diagnosing the System*, 38–39 and 135.

[^ch11-beer-readings]: Stafford Beer, *Decision and Control* (John Wiley & Sons, 1966), 242 and 243, paginated after the Stafford Beer Classic Library reprint (John Wiley & Sons, 1994); Beer, *Heart of Enterprise*, 308.