announcing The Necessary Tangle – a living evidence atlas of systems | cybernetics | complexity

I’ve been wanting for years to do a ‘better map’ of systems | complexity | cybernetics, having strongly criticised the Castellani ‘complexity map’ and seen some others – and been involved in the SCiO SysBoK where we tried to map key concepts, their necessary antecedents and dependent thingummies, people, meaning, and so on (- and always inspired by ‘rock family trees’ and the way it’s the constellation of influences and people around individual practitioners that actually makes the difference, as David Ing says).

So with the assistance of ChatGPT, and I’ve been building The Necessary Tangle – a living, evidence-backed atlas of systems | complexity | cybernetics.

It currently maps 411 public entries and 32 developed profiles from 93 registered sources.

The key difference from the usual family tree is that every line has to say what sort of relationship it represents: logical antecedent, historical precursor, documented influence, teaching, collaboration, practical use, and so on.

The eventual ambition to: trace the human as well as conceptual lineages; connect theory to practice; distinguish espoused intellectual genealogy from the clusters the evidence actually produces; and let categories emerge from the resulting network rather than deciding the schools in advance.

It’s very much a public alpha. Some areas are already quite deep; others are little more than markers saying ‘this belongs here’. I’m putting it out now precisely because corrections, missing connections, rival genealogies and ‘surely you can’t say that’ responses are part of building it.

AND I’m very happy to share, collaborate or whatever….

Have a look
https://transduction.systems

Benjamin
www.antlerboy.com

Information = Comprehension × Extension • Comment 7

Let’s stay with Peirce’s example of inductive inference a little longer and try to clear up the more troublesome confusions tending to arise.

Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram.

Figure 2. Disjunctive Term u, Taken as Subject

\text{Figure 2. Disjunctive Term}~ u, \text{Taken as Subject}

Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.

Figure 4. Disjunctive Subject u, Induction of Rule v ⇒ w

\text{Figure 4. Disjunctive Subject}~ u, \text{Induction of Rule}~ v \Rightarrow w

One final point needs to be stressed.  It is important to recognize the disjunctive term itself — the syntactic formula “neat, swine, sheep, deer” or any logically equivalent formula — is not an index but a symbol.‡  It has the character of an artificial symbol which is constructed to fill a place in a formal system of symbols, for example, a propositional calculus.  In that setting it would normally be interpreted as a logical disjunction of four elementary propositions, denoting anything in the universe of discourse which has any of the four corresponding properties.

The artificial symbol “neat, swine, sheep, deer” denotes objects which serve as indices of the genus herbivore by virtue of their belonging to one of the four named species of herbivore.  But there is in addition a natural symbol which serves to unify the manifold of given species, namely, the concept of a cloven‑hoofed animal.

As a symbol or general representation, the concept of a cloven‑hoofed animal connotes an attribute and connotes it in such a way as to determine what it denotes.  Thus we observe a natural expansion in the connotation of the symbol, amounting to what Peirce calls the “superfluous comprehension”, the information added by an “ampliative” or synthetic inference.

In sum we have sufficient information to motivate an inductive inference, from the Fact u \Rightarrow w and the Case u \Rightarrow v to the Rule v \Rightarrow w.

Remark

  • Here, once again, I have departed from using symbol in the precise technical sense Peirce introduced at the beginning of this discussion, reverting to the more ordinary sense all of us, Peirce included, tend to use on other occasions.  Perhaps the best way to smooth the wrinkle in usage is to mark a distinction among symbols, singling out the natural, normal, canonical, or simple symbols within the more general run of artificial, compound, or complex types.  Taking that tack has the beneficial side‑effect of aligning the work of abduction and induction, at least, in a pre‑established universe of discourse, with the mainstream of work in computation which takes us from dubious terms to clear signs for the objects of our interest.

References

  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432.  ArchiveOnline.

Resources

cc: Academia.eduCyberneticsLaws of Form • Mathstodon
cc: Research GateStructural ModelingSystems ScienceSyscoi

#abduction, #c-s-peirce, #comprehension, #deduction, #extension, #hypothesis, #icon-index-symbol, #induction, #inference, #information-comprehension-x-extension, #inquiry, #intension, #logic, #peirces-categories, #pragmatic-semiotic-information, #pragmatism, #scientific-method, #semiotics, #sign-relations

SysPrac26 21-22 September, UK – 12 HOURS LEFT FOR EARLY BIRD TICKETS!

SysPrac26 21-22 Sept 2026 | SCiO – Systems and Complexity in Organisation https://www.systemspractice.org/SYSPRAC26

I’ll be at this, and doing a workshop, just to warn you 😉

https://www.systemspractice.org/SYSPRAC26

On Conversational Confluences at the American Society for Cybernetics Conference | Ep. 166

https://cmminstitute.substack.com/p/on-conversational-confluences-at

Hiroki Sayama (@HirokiSayama) on X

ccs26.cssociety.org

Second Law of Technodynamics – by Ivo Velitchkov

Second Law of Technodynamics – by Ivo Velitchkov

Tavistock Institute of Human Relations | Two Traditions, One Living…

https://tavinstitute.org/whats-on/lunchtime-talk-with-dr-lennox-joseph-consultant-and-author-on-wednesday-16-september-2026

Lunchtime Talk with Dr Lennox Joseph, consultant, author & NTL Institute for Applied Behavioural Science practitioner

Date: Wednesday 16 September 2026, 1pm — 2.30pm
Location: Online
Link: Tickets

The Necessary Tangle update tracking – please contribute!

All you need to do to contribute https://transduction.systems/#view=contribute and offer contributions, things to cover (especially collections that are web-accessible), corrections, usability issues etc etc


https://transduction.systems/

v0.17 now live

  • ‘surprise me’ button on home page (surprisingly, in a different font, for now)
  • better tracking https://transduction.systems/submissions/ of contributions https://transduction.systems/#view=contribute

and a start of thoughts and mapping on inclusion/exclusion https://transduction.systems/canon-and-lineage/

RIP Merrely Emery, 1940-2026

Another really significant figure sadly gone, and Merrelyn was still working and contributing very recently. I’ll leave the first brief obituary to the Socio-Technica Systems Round Table, as per their mailing list announcement:

It is with great sadness that we share the news of Merrelyn Emery‘s passing last week, after a long illness.

Anyone who worked with Merrelyn will recognise the feeling right now: that mix of loss and enormous, uncomplicated gratitude. She gave so much, to so many of us, for so long.

Over five decades, Merrelyn — with Fred Emery and then in her own right — developed Open Systems Theory and refined the Search Conference and the Participative Design Workshop into methods that put people back in charge of their own work and their own communities. She was rigorous, direct, generous with her time, and utterly unwilling to accept that people needed to be managed rather than trusted.

Her legacy stays with us. It’s in the practitioners she trained, the communities she helped find their own way, and the organisations still being designed around her ideas today.

Her body of work, decades of papers on the genotypical organization design principles, democratising organisations, education, media and perception, and theory turned into practice, remains freely available at Social Science That Actually Works.  We’d encourage anyone who hasn’t explored it to do so.

Thank you to everyone who supported and worked alongside her over the years.💚 

The work continues — and that is exactly how she would want it.

In gratitude and loss,
all of us at the Socio-Technical Systems Roundtable (STS RT)

This week in systemic design

This week in systemic design

The Porter Ratio and the Systems Survival Theorem

The Porter Ratio (Quinn Porter, AHQ papers) is R = λ_self / λ_env.
λ_self is the rate of internal structure restoration and propagation.
λ_env is the rate of environmental disruption.

When R ≥ R★ (the ostiary/coherence threshold), prior states remain active, forming a self-sustaining interior with temporal depth and recursive coherence. Below it, structure dissipates and the system stays externally driven.

Primary sources:
https://philarchive.org/rec/PORATT-2
https://philarchive.org/rec/PORTCT-15

Some obvious similarities to Hoverstadt’s: “to survive, the system must be capable of a rate of change that is greater than or equal to the rate of change in the environment on which it depends”: ΔS ≥ ΔE. (Grammar of Systems, 2022)

(he also says the strategies to achieve this include moving faster, retarding the environmental change rate, or directing environmental change)

See

https://researchgate.net/profile/Patrick-Hoverstadt/publication/332082232_Organisational_agility_and_its_measurement/links/5c9e5a9da6fdccd460438dae/Organisational-agility-and-its-measurement.pdf?utm_source=chatgpt.com&__cf_chl_rt_tk=PIder.UzjUOsdZLeNwyBUII3oE1kRQb3Sc7_6SoFK7E-1786986626-1.0.1.1-E2LwoKpdqyPkvzAMkczO8p92KOHOQ5zW0hRzdRDJOJM (2018)

https://mesg.ch/en/organisational-agility/ (2021)

https://systemspractice.org/system/files/2022-03/2022.2%20hoverstadt.pdf (2022)

The 2018 measurement paper and 2021 MESG piece turn ΔS ≥ ΔE into a practical diagnostic: quantify environmental change rate, then assess scanning, orientation, decision speed and pivot capacity. Those levers directly raise the effective internal rate, matching the three strategies and the quantitative Porter threshold.

VSM7 Walkthrough – Intelligent Organisations

Information = Comprehension × Extension • Comment 6

Returning to Peirce’s example of inductive inference in Comment 2, let’s try to get a clearer picture of why he connects it with disjunctive terms and indicial signs.

At this point in time I can’t say I’m entirely satisfied with my understanding of the relationship between disjunctive terms, indicial signs, and inductive inferences as presented by Peirce in his early accounts.  What follows is just one of the simplest and least question‑begging attempts at rational reconstruction I’ve been able to devise.

Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram.

Figure 2. Disjunctive Term u, Taken as Subject

\text{Figure 2. Disjunctive Term}~ u, \text{Taken as Subject}

Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.

Figure 4. Disjunctive Subject u, Induction of Rule v ⇒ w

\text{Figure 4. Disjunctive Subject}~ u, \text{Induction of Rule}~ v \Rightarrow w

If there is any distinguishing feature shared by all the instances under the disjunctive description “neat, swine, sheep, deer” then sign users may take that feature as a predictor of being herbivorous, precisely because all the things under the disjunctive description are herbivorous.  But everything under the disjunctive description is cloven‑hoofed, so the cases under the disjunctive description serve to indicate, support, or witness the utility of the induction from cloven‑hoofed to herbivorous.

References

  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432.  ArchiveOnline.

Resources

cc: Academia.eduCyberneticsLaws of Form • Mathstodon
cc: Research GateStructural ModelingSystems ScienceSyscoi

#abduction, #c-s-peirce, #comprehension, #deduction, #extension, #hypothesis, #icon-index-symbol, #induction, #inference, #information-comprehension-x-extension, #inquiry, #intension, #logic, #peirces-categories, #pragmatic-semiotic-information, #pragmatism, #scientific-method, #semiotics, #sign-relations

Kyla Avis: Have you ever tried to work with a group of people to do system mapping?

Linkedin post from Kyla Avis: https://www.linkedin.com/posts/kylaavis_have-you-ever-tried-to-work-with-a-group-activity-7493696398811598848-MI6E?utm_source=share&utm_medium=member_desktop&rcm=ACoAAACuq-oBecVFDW6PCf3lkoG-peMeuLBeoho

Have you ever tried to work with a group of people to do system mapping? Maybe you tried it on Kumu or MIro or even on a whiteboard. It gets very messy, very fast. Even when the dialogue is powerful, the map can be useless at the end.

Gene Bellinger has created a really interesting tool with AI. His program will ask you/your team a series of questions to understand the problem and create a system map for you complete with highlighted feedback loops and system archetype descriptions. I’ve only started playing with it but it’s a very valuable tool if you like system thinking.

Here is a link to the tool: https://lnkd.in/gSTZ4SAB
Here is an explainer video: https://lnkd.in/gkuzvMaB

Requisite Variety for safety – Jun 6, 2026 Todd Conklin’s PreAccident Podcast 601 – Rethinking Safety: AI, Pre-Jobs, and the Power of Listening Ron Gantt about the future of safety

I enjoy this podcast and – underprisingly perhaps – it’s quite systems | cybernetics | complexity – ish.
In this interview with Ron Gantt I was just thinking ‘hmm this is Requitie Variety for safety – that’s insightful/obvious’ and sure enough, Ron Gantt actually uses the phrase ‘the requisite variety necessary to manage a construction site’.
https://preaccidentpodcast.podbean.com/e/rethinking-safety-ai-pre-jobs-and-the-power-of-listening/

So I asked my chat j’ai pété to do a dive into RV as a concept in Safety. It said:

His argument has a recognisable lineage, but he gives it a particularly useful inter-organisational and political twist.

### The closest precedent: high reliability organising

The nearest match I have found is Karl Weick, Kathleen Sutcliffe and David Obstfeld’s 1999 paper, [‘Organizing for High Reliability: Processes of Collective Mindfulness’](https://www.theisrm.org/documents/Weick%20%281999%29%20Organizing%20for%20High%20Reliability%20-%20Processes%20of%20Collective%20Mindfulness.pdf).

They say that high-reliability organisations:

‘cultivate requisite variety and assume that it takes a complex system to sense a complex environment’.

Their mechanisms include diverse perspectives, overlapping checks, job rotation, adversarial review and what Schulman called ‘conceptual slack’: disagreement and alternative interpretations that prevent the organisation from collapsing complexity too soon.

Even closer to Gantt, they describe safety as depending on ‘negotiated complexity’: informal and continually renewed relationships between organisations. Those relationships are not peripheral niceties. They form part of the machinery through which safe operation is produced.

That is almost exactly Gantt’s construction-site problem. The expertise needed to regulate the work is dispersed among client, principal contractor, subcontractors, supervisors, trades and workers. No single organisation contains enough of the relevant variety.

### The direct safety literature

There is also a paper whose title answers your question almost comically directly:

Vanessa Becker Bertoni, Tarcisio Abreu Saurin and Flávio Sanson Fogliatto, [‘Law of requisite variety in practice: Assessing the match between risk and actors’ contribution to resilient performance’](https://doi.org/10.1016/j.ssci.2022.105895), published in *Safety Science* in 2022.

It applies Ashby’s law to the relationship between the variety of risks and the contribution of different actors to resilient performance, using social-network analysis in a healthcare setting. The practical proposition is that safety depends not just on possessing expertise somewhere in the organisation, but on whether the network makes the necessary people and capabilities available to one another.

A related paper by Hirose and colleagues, [‘Functional Analysis of Law of Requisite Variety’](https://doi.org/10.1016/j.ifacol.2022.10.231), links Ashby explicitly with resilience engineering and FRAM. Their modelling suggests that strategies with a greater repertoire of possible actions cope better with variability in working conditions.

So there is an identifiable, if still rather small, literature explicitly joining requisite variety and safety.

### Safety-II and resilience engineering

A much larger body of safety work makes essentially the same argument without always naming Ashby.

The early resilience-engineering formulation defines resilience as the capacity to adjust functioning before, during or after disturbances so that required operations continue under expected and unexpected conditions. The [EUROCONTROL resilience-engineering white paper](https://www.eurocontrol.int/archive_download/all/node/11591) says, in effect, that the less completely work can be specified in advance, the more performance variability is needed.

That is requisite variety translated into safety language:

  • Work generates more states and disturbances than procedures can enumerate.
  • People therefore have to notice differences, interpret them and adjust.
  • A safe system needs a sufficiently differentiated repertoire of responses.
  • Attempts to remove all variation from human performance can remove the very capacity that keeps the system safe.

Todd Conklin’s formulation that safety is ‘the presence of capacity’, rather than merely the absence of accidents, belongs in this family. Dekker and Tooma develop that idea more systematically in [‘A capacity index to replace flawed incident-based metrics for worker safety’](https://sidneydekker.com/wp-content/uploads/2024/12/ilr.12210.pdf). Among the capacities they identify are operational knowledge, resources, diversity of voices, local decision authority and the ability to respond to emerging risk.

### What Gantt is adding

Gantt’s point is not simply ‘we need more perspectives’. It is that the variety already present on a construction site is prevented from becoming usable regulatory variety.

| Construction-site feature | Cybernetic reading |
| ———————————————————— | —————————————————————– |
| Changing conditions, interacting trades and emerging hazards | Disturbance variety |
| Local knowledge and different contractors’ capabilities | Potential response variety |
| Contracts, liability anxiety and organisational silos | Attenuated communication and action channels |
| Hierarchy and power differences | Suppression of signals and reduction of actors’ effective options |
| ‘The right people at the right time’ | Appropriate selection plus sufficiently rapid response |
| Trust and joint problem-solving | Coupling distributed variety into a functioning regulator |

This makes power a cybernetic variable. A worker or contractor may perceive a dangerous condition and know how to respond, but anticipated blame, contractual exposure or lack of authority can remove that response from the system’s effective repertoire.

In other words, nominal variety is not enough. It has to be:

  • perceptible;
  • communicable;
  • authorised;
  • resourced;
  • co-ordinated;
  • available quickly enough to matter.

Gantt’s suggestion that the more powerful client should accept some liability risk and actively earn trust is therefore not merely a cultural recommendation. It is an attempt to alter the control structure so that distributed knowledge can participate in regulation.

### One important qualification

Requisite variety is a necessary condition for regulation, not a complete theory of safety.

More variety is not automatically better. Unstructured diversity may produce noise, conflict or paralysis. Systems also achieve safety by attenuating disturbance variety: guarding machinery, separating traffic, simplifying interfaces, providing physical buffers and standardising genuinely repeatable work.

The useful question is therefore not simply ‘How do we increase variety?’ It is:

Which disturbances should we prevent or attenuate, and what remaining variety must the system be able to detect, interpret and respond to?

So my short answer is: yes, several traditions have done this. The strongest explicit precursor to Gantt is Weick, Sutcliffe and Obstfeld’s combination of requisite variety, collective mindfulness and ‘negotiated complexity’. What seems particularly sharp in Gantt’s version is the application to the client–contractor boundary: liability, hierarchy and mistrust can leave a construction system full of expertise while making that expertise cybernetically unavailable.

Information = Comprehension × Extension • Comment 5

Let’s stay with Peirce’s example of abductive inference a little longer and try to clear up the more troublesome confusions tending to arise.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

Figure 1. Conjunctive Term z, Taken as Predicate

\text{Figure 1. Conjunctive Term}~ z, \text{Taken as Predicate}

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

Figure 3. Conjunctive Predicate z, Abduction of Case x ⇒ y

\text{Figure 3. Conjunctive Predicate}~ z, \text{Abduction of Case}~ x \Rightarrow y

One thing needs to be stressed at this point.  It is important to recognize the conjunctive term itself — namely, the syntactic string “spherical bright fragrant juicy tropical fruit” — is not an icon but a symbol.‡  It has its place in a formal system of symbols, for example, a propositional calculus, where it would normally be interpreted as a logical conjunction of six elementary propositions, denoting anything in the universe of discourse with all six of the corresponding properties.

The symbol “spherical bright fragrant juicy tropical fruit” denotes objects which may be taken as icons of oranges by virtue of their bearing those six properties in common with oranges.  But there are no objects denoted by the symbol which aren’t already oranges themselves.  Thus we observe a natural reduction in the denotation of the symbol, consisting in the absence of cases outside of oranges which have all the properties indicated.

The above analysis provides another way to understand the abductive inference from the Fact x \Rightarrow z and the Rule y \Rightarrow z to the Case x \Rightarrow y.  The lack of any cases which are z and not y is expressed by the implication z \Rightarrow y.  Taking that in conjunction with the Rule y \Rightarrow z gives the logical equivalence y = z.  But that reduces the Case x \Rightarrow y to the Fact x \Rightarrow z and so the Case is justified.

Viewed in the light of the above analysis, Peirce’s example of abductive reasoning exhibits an especially strong form of inference, almost deductive in character.  Do all abductive arguments take that form, or may there be weaker styles of abductive reasoning which enjoy their own levels of plausibility?  That must remain an open question at this point.

Remark

  • Readers will notice I have slipped at this point from using symbol in the precise technical sense Peirce introduced at the beginning of this discussion to the more ordinary sense all of us, Peirce included, tend to use on other occasions.  Should it become a big problem we can always find a way to mark the distinction but so far it seems context has usually sufficed to resolve any likely confusion.

References

  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432.  ArchiveOnline.

Resources

cc: Academia.eduCyberneticsLaws of Form • Mathstodon
cc: Research GateStructural ModelingSystems ScienceSyscoi

#abduction, #c-s-peirce, #comprehension, #deduction, #extension, #hypothesis, #icon-index-symbol, #induction, #inference, #information-comprehension-x-extension, #inquiry, #intension, #logic, #peirces-categories, #pragmatic-semiotic-information, #pragmatism, #scientific-method, #semiotics, #sign-relations