antlerboy - Benjamin P Taylor 2:30 am on October 1, 2024
Tags: systems thinking ( 6 )

Updated rough draft systems | complexity | cybernetics reading list

See my post on LinkedIn (replicated below) and join the discussion there:
https://www.linkedin.com/posts/antlerboy_rough-draft-systemscomplexitycybernetics-activity-7246779585235664896-64Xz

pdf: https://www.dropbox.com/scl/fi/85zlt0t6ph8qarx7d7gic/2024-09-27-rough-draft-systems-thinking-reading-list-v1.1BT.pdf?rlkey=3rfavacsy4n6sl8j0pyedph1q&st=qagh1418&dl=0
Commentable Google Doc: https://docs.google.com/document/d/1Tt8GgQQj4Qw4HnR7DxKeF370o_HlDlpv/edit?usp=sharing&ouid=115526108239573817578&rtpof=true&sd=true

How do you get into systems | complexity | cybernetics?

Here’s my rough reading list.

There are a lot of answers to the question, many of them connecting with some kind of disjointing break from ‘normal’ ways of seeing and being. Anything from being bullied at school to being dyslexic. Being in an outsider group. Naively applying thinking from one domain to another. Studying a technical problem long enough to suddenly see it in a completely different light – then either have your breakthrough celebrated or rejected.

It isn’t some mystic thing and it doesn’t require to you break from polite society. But it is one of the richest, weirdest, most diverse and challenging, inspiring and confounding, confronting and validating things you can study.

I’m often asked for a reading list for people interested in the field, and I usually suck my teeth. Some of the books are engaging, insightful, humorous, relevant. Others are dry as old twigs but less likely to kindle a spark.

Really, it depends on you and your context – as David Ing says, it’s better to talk of the thinkers and their individual constellations of interests, history, learning, and personal tendencies than it is to talk of schools and fields and separate places.

And even presenting this reading list, I’d say that I’d recommend Terry Pratchett, Douglas Adams, Ursula K Le Guin, Italo Calvino, Jorge Luis Borges, Star Trek, old 20th Century Sci-Fi and Apartheid-era South African writing, art movies and music more – if you happen to be a bit like me. You’ll find your thing, if you’re interested.

But. The books are there – and many of them are *really good*. Top ones I’d recommend came out this decade

Hoverstadt’s Grammar of Systems
Jackson’s Critical Systems Thinking: A practitioner’s Guide
Opening the box – a slim little thing from SCiO colleagues
Essential Balances by Velitchkov

The attached list is a bit systems-practice focused. It is also too long and incomplete and partial simply for lack of time and energy.

There are *so many* flavours of systems thinking / complexity / cybernetics – do yourself a favour and don’t flog through stuff that doesn’t work for you, find things that bring your mind alive. Start with the articles and skim through.

But do start, because you will find in here the thinking and tools to find better ways of doing things for organisations, societies, the ecosystem, for people – and a lot of fun.

Tip: to save the pdf, hover over the image of the first page and find the rectangle bottom right – click that and it should go full screen. Top right you’ll have a download option, which when clicked will then resolve into a download button… (which might then open in your browser, but at least as a proper pdf you can save).

So… deep breath… what would you recommend? What do you think is missing?

#systems-thinking

Jon Awbrey 2:36 pm on February 14, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 6

Differential Expansions of Propositions

Panoptic View • Difference Maps

In the previous post we computed what is variously described as the difference map, the difference proposition, or the local proposition $\mathrm{D}f_x$ of the proposition $f(p, q) = pq$ at the point $x$ where $p = 1$ and $q = 1.$

In the universe of discourse $X = P \times Q$ the four propositions $pq, \, p \texttt{(} q \texttt{)}, \, \texttt{(} p \texttt{)} q, \, \texttt{(} p \texttt{)(} q \texttt{)}$ can be taken to indicate the so‑called “cells” or smallest distinguished regions of the universe, otherwise indicated by their coordinates as the “points” $(1, 1), ~ (1, 0), ~ (0, 1), ~ (0, 0),$ respectively. In that regard the four propositions are called singular propositions because they serve to single out the minimal regions of the universe of discourse.

Thus we can write $\mathrm{D}f_x = \mathrm{D}f|_x = \mathrm{D}f|_{(1, 1)} = \mathrm{D}f|_{pq},$ so long as we know the frame of reference in force.

In the example $f(p, q) = pq,$ the value of the difference proposition $\mathrm{D}f_x$ at each of the four points $x \in X$ may be computed in graphical fashion as shown below.

The easy way to visualize the values of the above graphical expressions is just to notice the following graphical equations.

Adding the arrows to the venn diagram gives us the picture of a differential vector field.

The Figure shows the points of the extended universe $\mathrm{E}X = P \times Q \times \mathrm{d}P \times \mathrm{d}Q$ indicated by the difference map $\mathrm{D}f : \mathrm{E}X \to \mathbb{B},$ namely, the following six points or singular propositions.

$\begin{array}{rcccc} 1. & p & q & \mathrm{d}p & \mathrm{d}q \\ 2. & p & q & \mathrm{d}p & \texttt{(} \mathrm{d}q \texttt{)} \\ 3. & p & q & \texttt{(} \mathrm{d}p \texttt{)} & \mathrm{d}q \\ 4. & p & \texttt{(} q \texttt{)} & \texttt{(} \mathrm{d}p \texttt{)} & \mathrm{d}q \\ 5. & \texttt{(} p \texttt{)} & q & \mathrm{d}p & \texttt{(} \mathrm{d}q \texttt{)} \\ 6. & \texttt{(} p \texttt{)} & \texttt{(} q \texttt{)} & \mathrm{d}p & \mathrm{d}q \end{array}$

The information borne by $\mathrm{D}f$ should be clear enough from a survey of these six points — they tell you what you have to do from each point of $X$ in order to change the value borne by $f(p, q),$ that is, the move you have to make in order to reach a point where the value of the proposition $f(p, q)$ is different from what it is where you started.

We have been studying the action of the difference operator $\mathrm{D}$ on propositions of the form $f : P \times Q \to \mathbb{B},$ as illustrated by the example $f(p, q) = pq$ which is known in logic as the conjunction of $p$ and $q.$ The resulting difference map $\mathrm{D}f$ is a (first order) differential proposition, that is, a proposition of the form $\mathrm{D}f : P \times Q \times \mathrm{d}P \times \mathrm{d}Q \to \mathbb{B}.$

The augmented venn diagram shows how the models or satisfying interpretations of $\mathrm{D}f$ distribute over the extended universe of discourse $\mathrm{E}X = P \times Q \times \mathrm{d}P \times \mathrm{d}Q.$ Abstracting from that picture, the difference map $\mathrm{D}f$ can be represented in the form of a digraph or directed graph, one whose points are labeled with the elements of $X = P \times Q$ and whose arrows are labeled with the elements of $\mathrm{d}X = \mathrm{d}P \times \mathrm{d}Q,$ as shown in the following Figure.

$\begin{array}{rcccccc} f & = & p & \cdot & q \\[4pt] \mathrm{D}f & = & p & \cdot & q & \cdot & \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \end{array}$

Any proposition worth its salt can be analyzed from many different points of view, any one of which has the potential to reveal previously unsuspected aspects of the proposition’s meaning. We will encounter more and more such alternative readings as we go.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#amphecks, #animata, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #change, #cybernetics, #differential-calculus, #differential-logic, #discrete-dynamics, #equational-inference, #functional-logic, #gradient-descent, #graph-theory, #inquiry-driven-systems, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #propositional-calculus, #time, #visualization

Jon Awbrey 11:32 am on February 12, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 5

Differential Expansions of Propositions

Worm’s Eye View

Let’s run through the initial example again, keeping an eye on the meanings of the formulas which develop along the way. We begin with a proposition or a boolean function $f(p, q) = pq$ whose venn diagram and cactus graph are shown below.

A function like $f$ has an abstract type and a concrete type. The abstract type is what we invoke when we write things like $f : \mathbb{B} \times \mathbb{B} \to \mathbb{B}$ or $f : \mathbb{B}^2 \to \mathbb{B}.$ The concrete type takes into account the qualitative dimensions or “units” of the case, which can be explained as follows.

Let $P$ be the set of values $\{ \texttt{(} p \texttt{)},~ p \} ~=~ \{ \mathrm{not}~ p,~ p \} ~\cong~ \mathbb{B}.$
Let $Q$ be the set of values $\{ \texttt{(} q \texttt{)},~ q \} ~=~ \{ \mathrm{not}~ q,~ q \} ~\cong~ \mathbb{B}.$

Then interpret the usual propositions about $p, q$ as functions of the concrete type $f : P \times Q \to \mathbb{B}.$

We are going to consider various operators on these functions. An operator $\mathrm{F}$ is a function which takes one function $f$ into another function $\mathrm{F}f.$

The first couple of operators we need are logical analogues of two which play a founding role in the classical finite difference calculus, namely, the following.

The difference operator $\Delta,$ written here as $\mathrm{D}.$
The enlargement operator, written here as $\mathrm{E}.$

These days, $\mathrm{E}$ is more often called the shift operator.

In order to describe the universe in which these operators operate, it is necessary to enlarge the original universe of discourse. Starting from the initial space $X = P \times Q,$ its (first order) differential extension $\mathrm{E}X$ is constructed according to the following specifications.

$\begin{array}{rcc} \mathrm{E}X & = & X \times \mathrm{d}X \end{array}$

where:

$\begin{array}{rcc} X & = & P \times Q \\[4pt] \mathrm{d}X & = & \mathrm{d}P \times \mathrm{d}Q \\[4pt] \mathrm{d}P & = & \{ \texttt{(} \mathrm{d}p \texttt{)}, ~ \mathrm{d}p \} \\[4pt] \mathrm{d}Q & = & \{ \texttt{(} \mathrm{d}q \texttt{)}, ~ \mathrm{d}q \} \end{array}$

The interpretations of these new symbols can be diverse, but the easiest option for now is just to say $\mathrm{d}p$ means “change $p$ ” and $\mathrm{d}q$ means “change $q$ ”.

Drawing a venn diagram for the differential extension $\mathrm{E}X = X \times \mathrm{d}X$ requires four logical dimensions, $P, Q, \mathrm{d}P, \mathrm{d}Q,$ but it is possible to project a suggestion of what the differential features $\mathrm{d}p$ and $\mathrm{d}q$ are about on the 2‑dimensional base space $X = P \times Q$ by drawing arrows crossing the boundaries of the basic circles in the venn diagram for $X,$ reading an arrow as $\mathrm{d}p$ if it crosses the boundary between $p$ and $\texttt{(} p \texttt{)}$ in either direction and reading an arrow as $\mathrm{d}q$ if it crosses the boundary between $q$ and $\texttt{(} q \texttt{)}$ in either direction, as indicated in the following figure.

Propositions are formed on differential variables, or any combination of ordinary logical variables and differential logical variables, in the same ways propositions are formed on ordinary logical variables alone. For example, the proposition $\texttt{(} \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{))}$ says the same thing as $\mathrm{d}p \Rightarrow \mathrm{d}q,$ in other words, there is no change in $p$ without a change in $q.$

Given the proposition $f(p, q)$ over the space $X = P \times Q,$ the (first order) enlargement of $f$ is the proposition $\mathrm{E}f$ over the differential extension $\mathrm{E}X$ defined by the following formula.

$\begin{matrix} \mathrm{E}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & f(p + \mathrm{d}p,~ q + \mathrm{d}q) & = & f( \texttt{(} p, \mathrm{d}p \texttt{)},~ \texttt{(} q, \mathrm{d}q \texttt{)} ) \end{matrix}$

In the example $f(p, q) = pq,$ the enlargement $\mathrm{E}f$ is computed as follows.

$\begin{matrix} \mathrm{E}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & (p + \mathrm{d}p)(q + \mathrm{d}q) & = & \texttt{(} p, \mathrm{d}p \texttt{)(} q, \mathrm{d}q \texttt{)} \end{matrix}$

Given the proposition $f(p, q)$ over $X = P \times Q,$ the (first order) difference of $f$ is the proposition $\mathrm{D}f$ over $\mathrm{E}X$ defined by the formula $\mathrm{D}f = \mathrm{E}f - f,$ or, written out in full:

$\begin{matrix} \mathrm{D}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & f(p + \mathrm{d}p,~ q + \mathrm{d}q) - f(p, q) & = & \texttt{(} f( \texttt{(} p, \mathrm{d}p \texttt{)},~ \texttt{(} q, \mathrm{d}q \texttt{)} ),~ f(p, q) \texttt{)} \end{matrix}$

In the example $f(p, q) = pq,$ the difference $\mathrm{D}f$ is computed as follows.

$\begin{matrix} \mathrm{D}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & (p + \mathrm{d}p)(q + \mathrm{d}q) - pq & = & \texttt{((} p, \mathrm{d}p \texttt{)(} q, \mathrm{d}q \texttt{)}, pq \texttt{)} \end{matrix}$

This brings us by the road meticulous to the point we reached at the end of the previous post. There we evaluated the above proposition, the first order difference of conjunction $\mathrm{D}f,$ at a single location in the universe of discourse, namely, at the point picked out by the singular proposition $pq,$ in terms of coordinates, at the place where $p = 1$ and $q = 1.$ That evaluation is written in the form $\mathrm{D}f|_{pq}$ or $\mathrm{D}f|_{(1, 1)},$ and we arrived at the locally applicable law which may be stated and illustrated as follows.

$f(p, q) ~=~ pq ~=~ p ~\mathrm{and}~ q \quad \Rightarrow \quad \mathrm{D}f|_{pq} ~=~ \texttt{((} \mathrm{dp} \texttt{)(} \mathrm{d}q \texttt{))} ~=~ \mathrm{d}p ~\mathrm{or}~ \mathrm{d}q$

The venn diagram shows the analysis of the inclusive disjunction $\texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))}$ into the following exclusive disjunction.

$\begin{matrix} \mathrm{d}p ~\texttt{(} \mathrm{d}q \texttt{)} & + & \texttt{(} \mathrm{d}p \texttt{)}~ \mathrm{d}q & + & \mathrm{d}p ~\mathrm{d}q \end{matrix}$

The differential proposition $\texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))}$ may be read as saying “change $p$ or change $q$ or both”. And this can be recognized as just what you need to do if you happen to find yourself in the center cell and require a complete and detailed description of ways to escape it.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

antlerboy - Benjamin P Taylor 4:27 am on February 12, 2026

Request for votes for interactive skills training workshops at Systems Thinking Systems Practice conference, 24-26 March 2026, University of Hull

At Systems Thinking Systems Practice, 24-26 March 2026, University of Hull, we will again run Skills Training Workshops.

These workshops were a huge success at SysPrac25, with many of them oversubscribed.

They will take the form of interactive workshops, which will further develop your skills or introduce you to new approaches you may not have encountered before.

To vote visit https://docs.google.com/forms/d/e/1FAIpQLSfsLoKstfeA5BwI8pK5kAb25abdUAhLeKe2s51Xp4Gmxw_FAg/viewform before 20 February 2026!

The conference: https://stream.syscoi.com/2026/01/25/2026-conference-systems-thinking-and-systems-practice-hosted-by-the-university-of-hull-centre-for-systems-studies-css-systems-and-complexity-in-organisation-scio-and-the-or-society-24-26-march/

2026 Conference: Systems Thinking and Systems Practice, Hosted by the University of Hull Centre for Systems Studies (CSS), Systems and Complexity in Organisation (SCiO) and The OR Society, 24-26 March 2026 | University of Hull, UK

antlerboy - Benjamin P Taylor 1:10 pm on February 9, 2026

Complex Systems Frameworks Collection

Complex Systems Frameworks Collection
Frameworks A-Z – Complex Systems Frameworks Collection

Frameworks A-Z

antlerboy - Benjamin P Taylor 1:10 pm on February 9, 2026

The Game

THE GAME
The Game – Birmingham Food Council

The Game

antlerboy - Benjamin P Taylor 4:00 am on February 9, 2026

Storytelling for Systems Change

New website

Storytelling for Systems Change
A story-kit for changemakers
Storytelling for Systems Change – Dusseldorp Forum

Storytelling for Systems Change

Jon Awbrey 4:32 pm on February 8, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 4

Differential Expansions of Propositions

Bird’s Eye View

An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions.

For example, consider a proposition of the form $``p ~\mathrm{and}~ q"$ graphed as two letters attached to a root node, as shown below.

Written as a string, this is just the concatenation $p~q$ .

The proposition $pq$ may be taken as a boolean function $f(p, q)$ having the abstract type $f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},$ where $\mathbb{B} = \{ 0, 1 \}$ is read in such a way that $0$ means $\mathrm{false}$ and $1$ means $\mathrm{true}.$

Imagine yourself standing in a fixed cell of the corresponding venn diagram, say, the cell where the proposition $pq$ is true, as shown in the following Figure.

Now ask yourself: What is the value of the proposition $pq$ at a distance of $\mathrm{d}p$ and $\mathrm{d}q$ from the cell $pq$ where you are standing?

Don’t think about it — just compute:

The cactus formula $\texttt{(} p \texttt{,} \mathrm{d}p \texttt{)(} q \texttt{,} \mathrm{d}q \texttt{)}$ and its corresponding graph arise by replacing $p$ with $p + \mathrm{d}p$ and $q$ with $q + \mathrm{d}q$ in the boolean product or logical conjunction $pq$ and writing the result in the two dialects of cactus syntax. This follows because the boolean sum $p + \mathrm{d}p$ is equivalent to the logical operation of exclusive disjunction, which parses to a cactus graph of the following form.

Next question: What is the difference between the value of the proposition $pq$ over there, at a distance of $\mathrm{d}p$ and $\mathrm{d}q$ from where you are standing, and the value of the proposition $pq$ where you are, all expressed in the form of a general formula, of course? The answer takes the following form.

There is one thing I ought to mention at this point: Computed over $\mathbb{B},$ plus and minus are identical operations. This will make the relation between the differential and the integral parts of the appropriate calculus slightly stranger than usual, but we will get into that later.

Last question, for now: What is the value of this expression from your current standpoint, that is, evaluated at the point where $pq$ is true? Well, replacing $p$ with $1$ and $q$ with $1$ in the cactus graph amounts to erasing the labels $p$ and $q,$ as shown below.

And this is equivalent to the following graph.

We have just met with the fact that the differential of the and is the or of the differentials.

$\begin{matrix} p ~\mathrm{and}~ q & \quad & \xrightarrow{\quad\mathrm{Diff}\quad} & \quad & \mathrm{d}p ~\mathrm{or}~ \mathrm{d}q \end{matrix}$

It will be necessary to develop a more refined analysis of that statement directly, but that is roughly the nub of it.

If the form of the above statement reminds you of De Morgan’s rule, it is no accident, as differentiation and negation turn out to be closely related operations. Indeed, one can find discussion of logical difference calculus in the personal correspondence between Boole and De Morgan and Peirce, too, made use of differential operators in a logical context, but the exploration of those ideas has been hampered by a number of factors, not the least of which has been the lack of a syntax adequate to handle the complexity of expressions evolving in the process.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

antlerboy - Benjamin P Taylor 1:22 pm on February 8, 2026

Harish’s Notebook – When the Map Becomes More Coherent Than the Territory – Jose (2026)

When the Map Becomes More Coherent Than the Territory:

Jon Awbrey 5:20 pm on February 7, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 3

Cactus Language for Propositional Logic (cont.)

Table 1 shows the cactus graphs, the corresponding cactus expressions, their logical meanings under the so‑called existential interpretation, and their translations into conventional notations for a sample of basic propositional forms.

Table 1. Syntax and Semantics of a Calculus for Propositional Logic

The simplest expression for logical truth is the empty word, typically denoted by $\boldsymbol\varepsilon$ or $\lambda$ in formal languages, where it is the identity element for concatenation. To make it visible in context, it may be denoted by the equivalent expression $``\texttt{(())}"$ or, especially if operating in an algebraic context, by a simple $``1".$ Also when working in an algebraic mode, the plus sign $``+"$ may be used for exclusive disjunction. Thus we have the following translations of algebraic expressions into cactus expressions.

$\begin{matrix} a + b \quad = \quad \texttt{(} a \texttt{,} b \texttt{)} \\[8pt] a + b + c \quad = \quad \texttt{(} a \texttt{,(} b \texttt{,} c \texttt{))} \quad = \quad \texttt{((} a \texttt{,} b \texttt{),} c \texttt{)} \end{matrix}$

It is important to note the last expressions are not equivalent to the 3‑place form $\texttt{(} a \texttt{,} b \texttt{,} c \texttt{)}.$

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

antlerboy - Benjamin P Taylor 4:18 pm on February 7, 2026

Laws of Form Conference 2026 (LoF26), 10 – 14 August 2026, University of Cambridge, UK

Call for Abstracts

Submissions for presentations of papers, panel discussions, workshops, performance sessions, and creative contributions, inspired by George Spencer-Brown’s work and life, are now warmly invited for the Laws of Form 2026 Conference (LoF26).

There is no charge to attend or present at the conference.

Submission Guidelines

Please submit an extended abstract (up to 300 words) outlining the content and structure of your proposed contribution. Please include:

• Title of your presentation

• Name, affiliation, and contact email address

• Format preference (paper presentation, panel discussion, workshop, creative, etc.)

• Short biographical note (≤ 150 words)

• Any AV / technical / access requirements

• Submission deadline Sunday 1^st March 2026

• Notification of acceptance 31^st March 2026

Facilities for remote video presentations will be available for those unable to attend in person.

Please send submissions as a single PDF or Word file to: conferences@lof50.com

Subject line: “LoF26 Submission – [Your Name]”

If you have a Google account you may prefer to upload your submission here:

https://forms.gle/zknFvXWQXzmfQtn2A

As with previous conferences, and subject to peer review, contributions may be published in Distinction: Journal of Form (College Publications Ltd) or in future volumes of the Spencer-Brown Society book series Marked States.

Venue

University of Cambridge

Faculty of Education

184 Hills Road

Cambridge CB2 8PQ, United Kingdom

Monday 10 August – Friday 14 August 2026

Social & Cultural Events

In addition to the conference, optional events will include:

• Punting on the River Cam

• Evensong at King’s College Chapel

• A meal at the Eagle pub, where, on 28 February 1953, Francis Crick dramatically announced that he and James Watson had “discovered the secret of life.”

Support

LoF26 is entirely free to attend, made possible through the generosity of the Faculty of Education, Cambridge University, sponsors, and individual supporters.

Donations

Contributions toward the costs of running the conference and sharing its results are deeply appreciated and help ensure that participation remains open to all. Every contribution — large or small — directly sustains the continuation of this unique, open, and evolving forum dedicated to the work and life of George Spencer-Brown. If you are able to support this ongoing work, please make a donation through our website: https://lof50.com/

For enquiries concerning LoF26 please email: conferences@lof50.com

Join the Spencer-Brown Society

Membership of the Spencer-Brown Society is open to all and free of charge. To join and receive updates on conferences and publications, please visit https://lof50.com

We look forward to welcoming you to Cambridge in August for LoF26!

Jon Awbrey 10:45 am on February 6, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 2

Cactus Language for Propositional Logic

The development of differential logic is facilitated by having a moderately efficient calculus in place at the level of boolean‑valued functions and elementary logical propositions. One very efficient calculus on both conceptual and computational grounds is based on just two types of logical connectives, both of variable $k$ -ary scope. The syntactic formulas of that calculus map into a family of graph-theoretic structures called “painted and rooted cacti” which lend visual representation to the functional structures of propositions and smooth the path to efficient computation.

The first kind of connective is a parenthesized sequence of propositional expressions, written $\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,} e_{k-1} \texttt{,} e_k \texttt{)}$ to mean exactly one of the propositions $e_1, e_2, \ldots, e_{k-1}, e_k$ is false, in short, their minimal negation is true. An expression of that form is associated with a cactus structure called a lobe and is “painted” with the colors $e_1, e_2, \ldots, e_{k-1}, e_k$ as shown below.

The second kind of connective is a concatenated sequence of propositional expressions, written $e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k$ to mean all the propositions $e_1, e_2, \ldots, e_{k-1}, e_k$ are true, in short, their logical conjunction is true. An expression of that form is associated with a cactus structure called a node and is “painted” with the colors $e_1, e_2, \ldots, e_{k-1}, e_k$ as shown below.

All other propositional connectives can be obtained through combinations of the above two forms. As it happens, the parenthesized form is sufficient to define the concatenated form, making the latter formally dispensable, but it’s convenient to maintain it as a concise way of expressing more complicated combinations of parenthesized forms. While working with expressions solely in propositional calculus, it’s easiest to use plain parentheses for logical connectives. In contexts where ordinary parentheses are needed for other purposes an alternate typeface $\texttt{(} \ldots \texttt{)}$ may be used for the logical operators.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Jon Awbrey 4:00 pm on February 5, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Change ( 8 ), cybernetics ( 21 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Gradient Descent ( 7 ), Graph Theory ( 12 ), Inquiry Driven Systems ( 13 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Visualization ( 16 )

Differential Logic • 1

Introduction

Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition that broad naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models.

To the extent a logical inquiry makes use of a formal system, its differential component governs the use of a differential logical calculus, that is, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

Simple examples of differential logical calculi are furnished by differential propositional calculi. A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe. Such a calculus augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Dr. Steffen Roth 9:41 am on February 4, 2026

CFP | Luhmann Conference 2026

Call for Papers

Luhmann Conference 2026

Theme: Meaning. Observed with …

Venue: Inter-University CentreDubrovnik, Croatia

Conference dates: 14–18 September 2026
Pre-conference dinner: 14 September 2026

Submission Deadline: 15 May 2026

Conference Theme

Coded as the distinction between actual and potential, meaning (Sinn) occupies a central position in Niklas Luhmann’s theory programme. As the shared medium in which both psychic and social systems operate, meaning enables observation, selection, and the continuous opening of horizons of possibility. As a medium without an outside (Luhmann, 1995a; 1995b, 62), meaning is notoriously inescapable for meaning-processing observers (Morales, 2025), and such are the blind spots and paradoxes it entails (Tække, 2025).

In his major theoretical works, Luhmann (1995b; 2012; 2013) distinguished three dimensions of meaning—the factual (this/that), the temporal (before/after), and the social (ego/alter). Each of these dimensions relates to a distinct sub-theory of his systems-theoretical programme: the factual dimension grounds the theory of social differentiation, the temporal dimension the theory of social evolution, and the social dimension the theory of communication (Roth 2009; Sohn, 2021). As shown by Andersen (2003), each of these meaning dimensions moreover corresponds to a dedicated strategy of deparadoxifying the inescapable paradox of observation, while they also allow for analytically differentiating forms of social systems, depending on how meaning is stabilised as semantics and processed across objects, time, and social relations (Harste, 2021; Jönhill, 2012).

What Luhmann did not adequately address, however, is how these dimensions of meaning come about, and why meaning should be structured into precisely three dimensions rather than more—or fewer (Roth, 2021). While the triadic architecture of meaning has become canonical in systems theory, its underlying logic remained explicitly unresolved.

More recent contributions have returned to this problem by reconstructing meaning dimensions in relation to the basic questions of observation—such as what, when, and who—and by exploring whether additional questions (where, how, why, and possibly others) may correspond to further, systematically expandable dimensions of meaning (Roth and Kaczmarczyk, 2026).

Meaning Dimension	Basic Question	Code	Focus
Spatial	Where?	here/there	The locus of observation
Temporal	When?	before/after	The process of observation
Factual	What?	this/that	The object of observation
Social	Who?	ego/alter	The observer
Modal	How?	thus/otherwise	The manner of observation
Motivational	Why?	intent/accident	The purpose of observation
…	…	…	…

Table: Six (or more?) dimensions of meaning as oriented by basic questions, codes, and observational foci (adapted from Roth and Kaczmarczyk, 2026)

From this perspective, Luhmann’s triad appears not as a closed architecture but as a reduced form of a broader, potentially open framework for analysing meaning and—tentatively—deparadoxifying the paradox of observation.

Against this backdrop, the Luhmann Conference 2026 invites contributions that revisit, rethink, and extend the concept of meaning under contemporary conditions of complexity. Under the guiding theme Meaning. Observed with …, the conference foregrounds meaning not as a static concept but as a dynamic medium of observation—one that allows for distinctions to be drawn, alternatives to be imagined, and contingency to be processed.

As such, the ellipsis in this year’s conference title is intentional. It signals an openness to different observational standpoints, theoretical instruments, and empirical domains. Rather than prescribing a single perspective, the conference asks how meaning is observed, transformed, stabilised, and contested when observed with different distinctions, media, and systems.

Key Orientations

Building on ongoing debates within social systems theory and beyond, the conference particularly welcomes contributions engaging with one or more of the following orientations:

Meaning and observation: second-order observation, reflexivity, and the observation of observation in social and psychic systems.
Psychic systems, consciousness, personality, and personhood: renewed engagement with consciousness, sense-making, psychology, psychotherapy, and their relation to identity formation across psychic and social systems.
Artificial and technological mediation of meaning: AI, artificial communication, algorithmic decision premises, and their implications for meaning-processing systems and structures of expectation.
Possibility, contingency, and alterity: forms of meaning that resist closure, reduction, or authoritarian simplification; imagination, counterfactuals, and non-necessary social orders.
Meaning and society: values, polarisation, populism, inter-systemic relations, pathologies of meaninglessness, and strategies of complexity reduction.
Expanding architectures of meaning: theoretical work that revisits or extends established three-dimensional models of meaning, including novel distinctions, questions, or sub-programmes within systems theory.

These themes are not exhaustive. Contributions from sociology, organisation studies, political theory, economics, education, cultural studies, literary studies, communication and media studies, cybernetics, philosophy, and related fields are explicitly encouraged, provided they engage meaning as a central analytical concern.

Programme Committee:

Nico Buitendag, University of the Free State, South Africa
Lars Clausen, UCL University College, Odense, Denmark
Michal Kaczmarczyk, University of Gdansk, Poland
Vincent Lien, University of Cambridge, United Kingdom*
Steffen Roth, Excelia Business School, La Rochelle, France, and University of Cambridge, United Kingdom
Augusto Sales, Brazilian School of Public and Business Administration (FGV-EBAPE), Rio de Janeiro, Brazil, and Yale University, New Haven, United States of America
Tilia Stingl de Vasconcelos Guedes, University of Applied Sciences for Management & Communication, Vienna, Austria
Krešimir Žažar, University of Zagreb, Croatia*

*Corresponding members: vwsl2@cam.ac.uk and kzazar@m.ffzg.hr

Publication opportunities

The organising committee is currently negotiating dedicated publication opportunities for the Luhmann Conference 2026. A considerable number of Luhmann Conference Community members are supporting Kybernetes, an important forum for research in cybernetics and systems thinking. Previous Luhmann Conferences have been or are currently being published in edited volumes or special issues of journals such as

Roth S., Stingl T., and Zazar K. (in progress). Coding society. Programmatic encounters between information systems and social theory, Information Technology & People.
Roth S. and Valentinov V. (in progress). Reprogramming. Observed with social systems theory, Journal of Organizational Change Management.
Roth S. and Sales A. (in progress). Programmes in management and organisation. Observed with social systems theory, Management Decision.
Roth S., Watson S., Dahms H., and Atanesyan A. (2025). Guiding distinctions of social theory. Current Sociology.
Steffen Roth, Lars Clausen, Margit Neisig, and Augusto Sales (2025): Guiding Distinctions of Management and Organisation Research, Managment Revue.
Roth S. (2025), Environments and Guiding Distinctions. Observed with social systems theory, Systems Research and Behavioral Science.
Roth S., Zazar K., Clausen L., and Stingl de Vasconcelos Guedes T. (2024, Scientific Communication. Observed with social systems theory, Systemic Practice and Action Research.
Roth S., Laursen K., and Harste G. (2021), Moral communication. Observed with social systems theory, Kybernetes 51(5).
Roth S., Heidingsfelder M., Clausen L., and Laursen K. (2021), George Spencer Brown’s “Design with the NOR”. With related essays, Bingley: Emerald.
Febbrajo A. and Harste G. (2013). Law and Intersystemic Communication. Understanding “Structural Coupling”. London: Ashgate 2013.

Historical background

In the 1980s, Hans-Ulrich Gumbrecht and Ludwig Pfeiffer co-organised a number of conferences at the Inter-University Centre of Post-Graduate Studies (IUC) in Dubrovnik in the former Yugoslavia, now Croatia. Starting in 1981, Luhmann attended several of these conferences. Conference proceedings were published in a series of five rather big volumes at the important Suhrkamp Verlag (Der Diskurs der Literatur- und Sprachhistorie, 1983; Epochenschwellen und Epochenstrukturen im Diskurs der Literatur- und Sprachhistorie, 1985; Stil, 1986; Materialität der Kommunikation, 1988; Paradoxien, Dissonanzen, Zusammenbrüche, 1991). Many of these works were dedicated to semantic history and to a system theory of art.
The IUC was shelled during the siege of Dubrovnik in 1991, and for some years the conferences could not take place. Today, the IUC has been completely restored both physically and in spirit.
The series resumed subsequent to the complete restoration of the IUC premises and, in turning increasingly international, became known under the sub-headlines “Observed with Niklas Luhmann’s systems theory” or “Observed with social systems theory”, respectively.

Practical information

The conference fee is EUR 200 for early career scholars (PhD students and post-Docs two years from their first PhD) and EUR 250 for everybody else. The amount is due in advance by bank transfer once your submission is accepted and registration confirmed. Once transferred, the fee is not refundable.
The IUC is located in the vicinity of the famous medieval city of Dubrovnik. Accommodation is available in one of the many Dubrovnik hotels (Hotel Imperial is the closest to the IUC, but rather expensive. Hotel Lero is more affordable and located about 1.5 kilometres (1 mile) from the IUC. Another popular form is one of the many private accommodations (Room or “Sobe”) which are relatively cheap and can be found everywhere. Do make sure to book well in advance to get the best price. The IUC also provides affordable but limited accommodation in the building itself.
The conference fee includes catering during coffee breaks. All other meals are taken at restaurants and cafés in town.
The Dubrovnik airport is situated about 20 kilometres south of Dubrovnik and connected to the town by regular shuttle busses. Travel by car and ferryboat is somewhat more complicated, though beautiful.
The weather in September is normally sunny and 25-30° C, though rain is not impossible. Whereas the weather is perfect for beach activities, buildings do still heat up considerably at this time of the year. The air conditioning systems in the conference rooms are therefore set at temperatures around 21° C, which implies that they are in continuous operation. Persons who get cold easily are therefore advised to bring a jacket and a light scarf.

Luhmann community groups and supporters @socialmedia

Anglophone Facebook Group: https://www.facebook.com/groups/2834060864/
Germanophone Facebook Group: https://www.facebook.com/groups/132998763464111
Scandinavian Facebook Group: https://www.facebook.com/groups/147050955334098/
Next Society Institute: https://twitter.com/nexsocinstitute
Inter-University Centre Dubrovnik: https://twitter.com/IUCDubrovnik
Luhmann Conference: https://twitter.com/Luh_Con

This CFP is available for download here.

Jon Awbrey 12:48 pm on February 3, 2026
Tags: Amphecks ( 9 ), Animata ( 11 ), Boolean Algebra ( 9 ), Boolean Functions ( 10 ), C.S. Peirce ( 29 ), Cactus Graphs ( 10 ), Category Theory ( 4 ), Change ( 8 ), cybernetics ( 21 ), Differential Analytic Turing Automata ( 2 ), Differential Calculus ( 8 ), Differential Logic ( 10 ), Discrete Dynamics ( 8 ), Equational Inference ( 10 ), Functional Logic ( 9 ), Graph Theory ( 12 ), Hologrammautomaton ( 2 ), Indicator Functions, Inquiry Driven Systems ( 13 ), Leibniz ( 2 ), logic ( 31 ), Logical Graphs ( 11 ), Mathematics ( 30 ), Minimal Negation Operators ( 10 ), Propositional Calculus ( 10 ), Time ( 7 ), Topology, Visualization ( 16 )

Differential Logic • Overview

A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions. Indeed, one of the first lessons I learned when I set about implementing Peirce’s graphs and Spencer Brown’s forms on the computer is that 2‑dimensional representations of logic quickly become death traps on numerous conceptual and computational counts.

Still, venn diagrams do us good service at the outset in visualizing the relationships among extensional, functional, and intensional aspects of logic. A facility with those connections is critical to the computational applications and statistical generalizations of propositional logic commonly used in mathematical and empirical practice.

All things considered, then, it is useful to make the links between various styles of imagery in logical representation as visible as possible. The first few steps in that direction are set out in the sketch of Differential Logic to follow.

Part 1

Introduction

Cactus Language for Propositional Logic

Differential Expansions of Propositions

Bird’s Eye View

Worm’s Eye View

Panoptic View • Difference Maps

Panoptic View • Enlargement Maps

Part 2

Propositional Forms on Two Variables

Transforms Expanded over Ordinary and Differential Variables

Enlargement Map Expanded over Ordinary Variables

Enlargement Map Expanded over Differential Variables

Difference Map Expanded over Ordinary Variables

Difference Map Expanded over Differential Variables

Operational Representation

Part 3

Field Picture

Differential Fields

Propositions and Tacit Extensions

Enlargement and Difference Maps

Tangent and Remainder Maps

Least Action Operators

Goal-Oriented Systems

Document History

Differential Logic • Ontology List 2002

Dynamics And Logic • Inquiry List 2004

Dynamics And Logic • NKS Forum 2004

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#amphecks, #animata, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #category-theory, #change, #cybernetics, #differential-analytic-turing-automata, #differential-calculus, #differential-logic, #discrete-dynamics, #equational-inference, #functional-logic, #graph-theory, #hologrammautomaton, #indicator-functions, #inquiry-driven-systems, #leibniz, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #propositional-calculus, #time, #topology, #visualization

antlerboy - Benjamin P Taylor 9:51 am on February 3, 2026

PhD Studentship: A Systems Thinking Approach to Understanding and Preventing Male Suicide – SHORT DEADLINE

via Steve Hales at SCiO, who says:

Please be aware of this opportunity. Unfortunately the deadline I only a couple of weeks off. Please click on the link to apply:

PhD Studentship: A Systems Thinking Approach to Understanding and Preventing Male Suicide

University of Birmingham – School of Psychology

Qualification Type:	PhD
Location:	Birmingham
Funding for:	UK Students, EU Students, International Students
Funding amount:	Not Specified
Hours:	Full Time

Placed On:	19th January 2026
Closes:	17th February 2026

The Centre for National Training and Research Excellence in Understanding Behaviour (Centre-UB) is inviting applications for a Doctoral Studentship in association with our collaborative partner Sandwell Council to start in October 2026.

Male suicide is a major global public health challenge, accounting for around 75% of suicide deaths worldwide. In the UK, it remains the leading cause of death among men under 50, with persistently high rates despite sustained prevention efforts. Traditional research has focused on individual risk factors (e.g., depression, substance misuse, relationship breakdowns), but these approaches often overlook the complex, systemic nature of suicide.

This PhD will apply systems thinking to male suicide in the UK, recognising the dynamic interactions between individual, social, cultural, and structural factors.

The PhD aims to develop and test a novel systems-based framework to inform both policy and practice, identifying leverage points for more effective intervention. The successful candidate will use a combination of methodological approaches and techniques including realist review, co-production of complex systems map and case study analysis. They will work closely with stakeholders and experts by experience to ensure the research is meaningful, accessible and co-produced with the communities it aims to benefit.

We are looking for a highly talented and dedicated PhD student with a 1st class or 2:1 degree in the field of psychology, health sciences or related field. An MSc degree in a relevant area is desirable though not necessary. Applicants should demonstrate experience in both quantitative and qualitative data analysis. Prior experience working with vulnerable or marginalised populations is highly valued, as is familiarity with stakeholder engaged research, co production approaches, and systems thinking frameworks.

To be considered for this PhD, please follow the instructions, click the ‘Apply’ button above.

Application deadline: February 17 2026

Interviews for this studentship are expected to take place on Friday 20 March 2026.

Centre-UB studentships cover tuition fees, a maintenance stipend, support for research training, as well as research activity support grants. Due to funding stipulations set by UKRI, we are able to recruit up to 30% of international applicants to the cohort each year. You can find further details at https://www.centre-ub.org/studentships/call-for-applicants/

Informal enquiries about the project prior to application can be directed to Dr Maria Michail (m.michail@bham.ac.uk).