Routes to Interdisciplinarity 2: Systems

Sir Alan Wilson FBA, FRS, is Director of Research at The London Interdisciplinary School. These blog posts are developed from his books - Knowledge power and Being interdisciplinary. The latter is free to download: www.uclpress.co.uk/beinginterdisciplinary.
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The Foundation of System Thinking in Mathematics and Physics

I have had versions of the idea of a ‘system’ in my toolkit since I was a student.  My subject was mathematics but under the rubric of ‘applied maths’. there was a lot of physics. Virtually every lecture by a physicist, started with something like: “let us define our system of interest”. A key point in doing this was to identify the simplest system –usually a very artificial one – that could be used to illustrate some law of physics.

It was always necessary to define the elements of the system, and how they related, but it also introduced an important principle, one that is important for teaching but also for ‘thinking things through’ more broadly:what is the simplest ‘system if interest’ I can construct to make my point, to illustrate the problem? Since systems in physics can also be thought of as(usually) mathematical models, it also introduced me to the idea of a toy model– a demonstration model – to get started with a problem. The detail and the depth could be added later.

Since we have ‘elements’ – say people or organisations in my case – a starting point is often to place them in categories, and to count them – population by age and sex for instance. These counts can be systematically arranged. In relation to a working population, for example, we will have residential and work locations for each person and thus have locational information but also interaction between two locations. This information can be arranged in a matrix and form the journey to work accounts.

In seeking to define characteristics and categories, we quickly become aware of the need to define scales. We usually have to handle three dimensions of scale:characteristics of elements – how many age groups? – the spatial scale and the temporal scale. Spatial systems for example are made up of area units – from an individual address, a neighbourhood, a city or a country. Temporal units might be minutes of hours at the micro-scale through to light years in cosmology! In each case, there will be a hierarchy of scales from the macro via theme so to the macro.

Navigating Complexity: Weaver's Insight and the STM Framework

As we specify relationships between system elements, it becomes clear very quickly that there are high levels of interdependence, and this in turn means that we will usually be working with complex systems. At this stage, it is worth noting Weaver’s classification of complex systems. Obviously, the number of elements in the systems gives a measure of complexity and this gives us the first of Weaver’s three categories of complex systems: if this number is relatively small, this can be designated as a simple system; if the number is large, the system is complex and he identifies two types of complexity: systems of disorganised complexity and systems of organised complexity.

The first of these has large numbers of elements but they are weakly interacting; the second consists of systems of organised complexity, where the elements are strongly interacting. These distinctions turn out to be very important in developing mathematical and computer models of systems of interest. Weaver, at the time he was developing these ideas, noted that, possibly oversimplifying with hindsight, the first two kinds of system were represented in physics, the third, organised complexity, in biology. He used his analysis as the science vice president of the Rockefeller Foundation to shift funding from physics to biology on the basis that this is where the most challenging research problems lay.

The idea of defining a system of interest is nearly always a good starting point starting point for research, for tackling a complex problem. This is the basis for what I have described as the STM framework – S: system definition; T: theory, what do we know about the system, how can we build on this knowledge; M: what methods can we apply?

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Stay tuned for the next blog of the series, where Alan Wilson will discuss the third route: The Consensus Theory of Truth