This is a short post prompted by my Bristol colleague Oliver Johnson‘s excellent 2024 piece, “The Final Cut“, which I came across again after it was recently reshared on LinkedIn. It is well worth reading in full.
Oliver starts with the max-flow min-cut theorem, formalised by Lester Ford and Delbert Fulkerson in the 1950s: in a network, the maximum possible flow from one point to another is determined by the capacity of the smallest cut that separates them. The mathematics is elegant, but what makes Oliver’s post particularly interesting is what happens when he applies the intuition beyond the abstract network. Electricity grids, NHS pathways, military logistics, vaccine delivery and organisational management can all be viewed, with appropriate caveats, by asking where the critical constraints actually sit.
His practical advice is to “focus on your cuts”. Increasing capacity elsewhere in a system may achieve remarkably little if another part remains the binding constraint. More generation does not necessarily produce more usable electricity if the transmission capacity is not there; increasing activity at one stage of a healthcare pathway may simply move the queue somewhere else. What matters is not only the capability of individual components, but how they are connected and what constrains the performance of the system as a whole.
That caught my attention because it provides a neat mathematical lens for something I have been returning to repeatedly in my own work on complex socio-technical systems. That perspective sits within a much wider tradition of systems thinking in engineering and public policy, concerned not simply with individual components but with their interactions, dependencies, feedback and constraints. Nancy Leveson’s Engineering a Safer World (2012), for example, develops precisely this kind of systems perspective for complex, software-intensive socio-technical systems, where failures can arise from interactions rather than simply from broken components.
There is also a connection here to Donella Meadows’ Thinking in Systems (2008), which I read in 2024 and have found myself returning to since, especially her work on leverage points: understanding where intervention in a system might actually make a difference. This is not quite the same thing as finding a minimum cut, of course, but the underlying discipline is similar: before reaching for an intervention, understand the structure, flows, feedback and constraints of the system you are trying to change.
That is also why systems thinking has become increasingly relevant to public policy. The Government Office for Science systems thinking guidance for civil servants, developed in collaboration with the Policy Profession, Royal Academy of Engineering and others, encourages policymakers to understand the wider system before choosing interventions, rather than disaggregating complex problems until the interactions that matter disappear. This sits within a longer engineering tradition: the Royal Academy of Engineering’s Creating Systems That Work emphasises purpose, people, relationships, interfaces and interdependencies rather than optimising components in isolation, while its later Engineering Better Care (2017) applies that systems approach directly to health and social care — neatly complementing Oliver’s NHS example.
The interesting constraints in socio-technical systems are not necessarily physical, or even technical. They can lie in institutional capacity, organisational processes, skills, human attention, governance, assurance, authority, or in the interfaces between organisations and technologies.
This becomes particularly visible with AI. As I reflected earlier this year in “Seven years of AI research“, introducing an increasingly capable technical component into an organisation does not automatically increase the capability of the wider system. Institutions, people, infrastructure and governance have to change with it. More recently, “Which games not to play” considered a related problem from another direction: what happens as automated systems can act increasingly quickly and autonomously, while the human capacity to understand, challenge and exercise meaningful authority over those actions remains necessarily constrained.
The same intuition applies to resilience. Systems can appear robust when viewed component by component while remaining vulnerable because of dependencies, bottlenecks or apparently minor connections on which much larger flows depend. David Woods’ work on resilience engineering (2015) is useful here because it distinguishes resilience from simple robustness: systems also need the capacity to adapt when pressures move beyond the conditions for which they were designed. Redundancy, alternative pathways and spare capacity can therefore matter precisely because they change how a system responds when particular routes or resources become constrained.
There are obvious limits to pushing a mathematical analogy too far. Real socio-technical systems are dynamic, adaptive and full of feedback, conflicting objectives and human behaviour; their important constraints are rarely as cleanly visible as the edges of a network diagram. Nor is maximising “flow” necessarily the objective of a public system. But that may make the question more useful rather than less so.
Where, in the system we are actually trying to improve, is the cut?
I suspect there is rather more to unpack in that question, and I expect to return to it in more detail in a future post. For now, Oliver’s post is a very good place to start.
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