One other feature of syntactic recursion deserves to be brought into higher relief. Evidence of it can be found in the recursion diagram by examining the places where three paths meet. On the descending side there is the point where three paths diverge. On the ascending side there is the point where the middlemost of the three divergent paths joins the upshot arrow in medias res.
The arrows of the diagram represent functions, a species of dyadic relations, but nodes of degree three signify aspects of triadic relations somewhere in the mix.
The three arrows from the initial node represent a function such that
The three arrows at the penultimate node represent a function such that
For the sake of a first approach, many questions about triadic relations which might arise at this point can be safely left to later discussions, since the current level of generality is comprehensible enough in functional terms.
Kristof Van Assche, Department of Earth and Atmospheric Sciences, University of Alberta, Canada, Gert Verschraegen, Professor of Sociology, Department of Sociology, University of Antwerp, Belgium and Monica Gruezmacher, University of Alberta, Canada
In this Concise Introduction, Kristof Van Assche, Gert Verschraegen and Monica Gruezmacher provide an accessible explanation of the complex genealogy of systems thinking. Covering both social and natural sciences, the authors present the key implications of this perspective for the understanding and transformation of systems and their context.
For those interested, there is a particular systems methodology called (for rather obscure reasons) Cultural-Historical Activity Theory, or CHAT for short. CHAT was developed by Mike Cole and Yrjö Engestrom. Etienne Wenger later of Communities of Practice and Situated Learning fame, was also involved in the early days. CHAT is based on the idea that if systems approaches are intended to be opportunities for learning, then why not develop a systems methodology based on learning theories. In this case, it was based on Vygotsky’s ideas of learning as a social process. CHAT is a fascinating approach that has strongly influenced my practice, but in essence is based on the idea that an individual’s journey to fulfilling a need is mediated by the tools they use (including language), the rules of the community they are part of and the roles that they play in that community. How an individual learns how to fulfill that need is dependent on how they addresses and resolve the contractions within and between tool, rules, roles and needs. Now expand this into a work setting (ie a community of practice) where people are working on the same activity but fullfilling different needs, and you have a whole bunch more contradictions that need to be addressed, as this article so succinctly describes. CHAT is frequently used in high risk environments especially concerning health and safety issues, where contradictions abound. If anyone is interested to find out more, there is a description of CHAT in my book System Diagrams, along with the questions that CHAT addresses. The book is donationware (ie free but you can pay something if you wish) and can be downloaded from https://bobwilliams.gumroad.com
This inspired me to do a little run on CHAT – and also links to
From Heraclitus’s river to second-order cybernetics — twenty-five centuries of ideas about wholes, parts, flux, feedback, and the organised complexity of the living world.
SYSTEMSLITERACY.ORG The History of Systems Thinking From Heraclitus’s river to second-order cybernetics — twenty-five centuries of ideas about wholes, parts, flux, feedback, and the organised complexity of the living world.
The 19th International Conference of Sociocybernetics will take place in Oaxaca, Mexico, from August 3rd to August 7th, 2026. This event is organized under the theme “Glocal Intersections”
19TH INTERNATIONAL CONFERENCE OF SOCIOCYBERNETICS
Glocal Intersections Oaxaca, Mexico, 3-7 August 2026 (Hybrid Format)
The 19th International Conference of Sociocybernetics will take place in Oaxaca, Mexico, from August 3rd to August 7th, 2026. This event is organized under the theme “Glocal Intersections”
Turning to the form of a simple recursive function the clause we used to define it earns the title of “syntactic recursion” due to the way the function name occurring in the defined phrase re‑occurs in the defining phrase
It needs to be clear there is no circle in the definition — each instance of the type is defined in terms of an instance one step simpler until the base case is reached and fixed by fiat. Instead of a circle then we have two gyres, the gyre down via the precedent function and the gyre up via the modifier function
such that
such that
Systems Community of Inquiry 
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