Exploring the science of complexitySystems & complexity

Exploring the science of complexity series (part 14): Concept 5 – Sensitivity to initial conditions

This article is part 14 of a series of articles featuring the ODI Working Paper Exploring the science of complexity: Ideas and implications for development and humanitarian efforts.

Complexity and systems – Concepts 4, 5, 6, and 7

The next four concepts relate to different aspects of how complex systems – those characterised by Concepts 1-3 – change over time. The causal relationships that play out within complex systems are explained using the concept of nonlinearity (Concept 4) and the sensitivity of complex systems to their starting conditions is highlighted (Concept 5). The overall shape of the system and its future possibilities are described using the idea of phase space (Concept 6). The patterns underlying seeming chaos within complex systems are explained (Concept 7).

Concept 5 – Sensitivity to initial conditions

Outline of the concept

The behaviours of complex systems are sensitive to their initial conditions. Simply, this means that two complex systems that are initially very close together in terms of their various elements and dimensions can end up in distinctly different places. This comes from nonlinearity of relationships – where changes are not proportional, small changes in any one of the elements can result in large changes regarding the phenomenon of interest.

Detailed explanation

Imagine a small ball dropped onto the edge of a razor blade, as shown in the first image in Figure 1 below. The ball can strike the blade in such a way that it can go off to the left (centre image) or to the right (right-hand image). The condition that will determine whether the ball goes to the left or right is minute. If the ball were initially held centred over the blade (as in the first image), a prediction of which direction the ball would bounce would be impossible to make with certainty. A very slight change in the initial conditions of the ball can result in falling to the right or left of the blade.

Sensitivity to initial conditions – ball striking razor blade
Figure 1. Sensitivity to initial conditions – ball striking razor blade1.
The concept of phase space (Concept 6) allows a more precise understanding of initial conditions. Phase space allows for the analysis of the evolution of systems by considering the evolution process as a sequence of states in time2. A state is the position of the system in its phase space at a given time. At any time, the system’s state can be seen as the initial conditions for whatever processes follow. The sensitive dependence on initial conditions, in phase space terms, means that the position of a system in its phase space at a particular moment will have an influence on its future evolution. The interactions that are taking place at any moment in time have evolved from a previous moment in time, that is, all interactions are contingent on an historical process. Put simply, history matters in complex systems.

The infamous butterfly effect was a metaphor developed to illustrate this idea in the context of the weather. Edward Lorenz3, a meteorologist, used the metaphor of a flapping wing of a butterfly to explain how a minute difference in the initial condition of a weather system leads to a chain of events producing large-scale differences in weather patterns, such as the occurrence of a tornado where there was none before. As more recent thinkers have put it, in relation to complex systems in general, an initial uncertainty in measurement of the state of a system:

… however small, inevitably grow[s] so large that long-range prediction becomes impossible … even the most gentle, unaccounted-for perturbation can produce, in short order, abject failure of prediction4

A large proportion of complex systems are prone to exhibiting the butterfly effect, so much so that some have defined complex behaviour as occurring where the butterfly effect is present5. As no two situations will be exactly alike, the phenomenon will inevitably occur in many settings. As with nonlinearity, many have not used formal models to demonstrate the butterfly effect, but instead have tried to develop a qualitative understanding of the likely quantitative nature of real life situations.

Sensitivity to initial conditions also means that ‘the generalisation of good practice [between contexts] begins to look fragile’ 6 because initial conditions are never exactly the same, and because the complexity and nonlinearity of behaviour make it extremely difficult to separate the contributions to overall behaviour that individual factors have. Any notion of ‘good practice’ requires a detailed local knowledge to understand why the practice in question was good.

This concept highlights the importance of understanding what can be forecast in complex systems to what level of certainty, as well as what is comparable across complex systems. It reinforces the point that both of these areas are necessarily restricted by the perspective of the observer. Sensitive dependence on initial conditions suggests that no single perspective can capture all there is to know about a system, that it may be wise to look in detail at how appropriate our solution to a problem is, and that it may be better to work with inevitable uncertainty rather than plan based on flimsy or hopeful predictions.

This may mean, to take the example of predictability, that the success of a nation may be best explained not by its population’s virtues, its natural resources and its government’s skills, but rather simply by the position it took in the past, with small historical advantages leading to much bigger advantages later. Another example is how socioeconomic policy can result in a separation of neighbourhoods, driving a large gap between the rich and the poor so that, in short order, a gulf in wealth can result between two families who once had similar wealth7.

This is closely related to the notion of ‘path dependence’, which is the idea that many alternatives are possible at some stages of a system’s development, but once one of these alternatives gains the upper hand, it becomes ‘locked in’ and it is not possible to go to any of the previous available alternatives. For example,

… many cities developed where and how they did not because of the “natural advantages” we are so quick to detect after the fact, but because their establishment set off self-reinforcing expectations and behaviours8

In economic development, the term ‘path dependence’ is used to describe how standards which are first-to-market can become entrenched ’lock ins’ – such as the QWERTY layout in typewriters still used in computer keyboards9. In certain situations, positive feedbacks leading from a small change can lead to such irreversible path dependence10. Urry11 gives the example of irreversibility across an entire industry or sector, whereby through sensitive dependence on initial conditions, feedback can set in motion institutional patterns that are hard or impossible to reverse. He cites the example of the domination of steel and petroleum-based fuel models, developed in the late 19th century, which have come to dominate over other fuel alternatives, especially steam and electric, which were at the time preferable.

The concept of path dependence has received some criticism from exponents of complexity science, because it has imported into economics the view that minor initial perturbations are important while grafting this onto an underlying theory that still assumes that there are a finite number of stable and alternative end-states, one of which will arise based on the particular initial conditions. As will be explained in Concept 7 on attractors and chaos, this is not always the case in complex systems12.

Example: Sensitive dependence on initial conditions and economic growth

Economists have generally identified sensitive dependence on initial conditions as one of the important features of the growth process – that is, what eventually happens to an economy depends greatly on the point of departure. There is mounting evidence that large qualitative differences in outcomes can arise from small (and perhaps accidental) differences in initial conditions or events13. In other words, the scope for and the direction and magnitude of change that a society can undertake depend critically on its prevailing objective conditions and the constellation of sociopolitical and institutional factors that have shaped these conditions.

For specific economies, the initial conditions affecting economic growth include levels of per capita income; the development of human capital; the natural resource base; the levels and structure of production; the degree of the economy’s openness and its form of integration into the world system; the development of physical infrastructure; and institutional variables such as governance, land tenure and property rights. One might add here the nature of colonial rule and the institutional arrangements it bequeathed the former colonies, the decolonisation process, and the economic interests and policies of the erstwhile colonial masters.

Wrongly specifying these initial conditions can undermine policy initiatives. Government polices are not simply a matter of choice made without historical or socioeconomic preconditions. Further, a sensitive appreciation of the differences and similarities in the initial conditions is important if one is to avoid some of the invidious comparisons one runs into today and the naive voluntarism that policymakers exhibit when they declare that their particular country is about to become the ‘new tiger’ of Africa. Such comparisons and self-description actually make the process of learning from others more costly because they start the planning process off on a wrong foot14.

Implication: Rethink the scope of learning and the purpose of planning in an uncertain world

Sensitivity to initial conditions suggests that there are inevitably degrees of non-comparability across, and unpredictability within, complex systems. Some have argued that this implies that:

… the map to the future cannot be drawn in advance. We cannot know enough to set forth a meaningful vision or plan productively15

The general implications for development theory and practice have been highlighted by a previous ODI working paper on participatory approaches, which suggests that this implies the notion of development as planned change is paradoxical. To quote directly,

… perfect planning would imply perfect knowledge of the future, which in turn would imply a totally deterministic universe in which planning would not make a difference16

Sellamna goes on:

For this reason, development planning should abandon prescriptive, goal-oriented decision making and prediction about future states and focus instead on understanding the dynamics of change and promoting a collective learning framework through which concerned stakeholders can constantly, through dialogue, express their respective interests and reach consensus17

With regards to learning, this poses profound issues for the transferability of ‘best practice’, a concept that has taken on increasing meaning within the development sector since the rise of knowledge management and organisational learning strategies18. While it is possible that, for example, an understanding of the interplay of factors driving urban change in the Philippines may be relevant for analysis of urban change in Guatemala, this is not necessarily the case. The sensitivity to initial conditions gives us a strong reason to suppose that, even if we have a generally useful perspective on urban environments, this may entirely fail to capture the key features of the next situation we look at. This means that the search for ‘best practices’ may need to be replaced by the search for ‘good principles’. Some have suggested that the most appropriate way to bring the principles of effective approaches from one context to another is for

… development workers to become facilitators … enabling representatives of other communities … to see first hand what in the successful project they would wish to replicate19

Moving onto planning, to say that prediction of any kind is impossible may be overstating the case. Complexity does suggest that, in certain kinds of systems, future events cannot be forecasted to a useful level of probability and that, from certain perspectives, it is not possible to offer any firm prediction of the way the future will pan out on certain timescales. However, in other systems, future events can be foreseen in a helpful manner. For example, Geyer20 suggests that, with political dynamics, it is fairly safe to predict the short-term dynamics of basic power resources and political structures and that, therefore, there is decent scope for forecasting voting and decision outcomes of policy. On the other hand, examining party and institutional dynamics becomes more difficult, and grasping the potential shifts in contested political and social debates is even harder, while the longterm development of political dynamics is effectively characterised by disorder, as far as our ability to predict is concerned.

It is important to clarify that certain levels of uncertainty are unavoidable when looking into the future. Complexity science suggests that it is important to identify and analyse these levels of unpredictability as part of the nature of the systems with which we work, and not treat uncertainty as in some way ‘unscientific’ or embarrassing. Rather than rejecting planning outright, there is a need to rethink the purpose and principles of planning. This has two key strands.

First, it is necessary to incorporate an acceptance of the inherent levels of uncertainty into planning. The requirement for a certain level of detail in understanding future events should be balanced with the understanding that both simple and intricate processes carry uncertainty of prediction. While improving one’s models of change and analyses of facets of a situation may be worthwhile, it is just as important and often more practical to work with a realistic understanding of this uncertainty and build a level of flexibility and adaptability into projects, allowing for greater resilience.

It has been argued that development projects have ‘fallen under the enchantment of [delivering] clear, specific, measurable outcomes’ 21. In many cases, this could be unrealistic, ineffective or even counterproductive; it is uncertain whether valuable social outcomes could be planned in terms of a specific series of outputs, and it is unclear why it is more productive to be able to hold agencies strictly accountable to promises at the expense of their promises delivering real results. This resonates with critiques of the log frame approach cited earlier, which argue that the adoption of the log frame as a central tool in effect and impact evaluations assumes higher powers of foresight than in fact is the case22.

What is needed is higher levels of flexibility in the funding of international aid work, involving less stringent ‘targets’ and requirements from donors. The role of M&E would be shifted to value learning from unexpected outcomes. This is at the heart of the participatory approach to M&E developed by IDRC called outcome mapping.

Second, the way organisations look into the future should be adjusted by taking a more systematic and realistic view of what the future can hold:

A single vision to serve as an intended organisational future … is a thoroughly bad idea … not that the long term is dismissed as an effective irrelevance, [instead we need a] refocusing: rather than establish a future target and work back to what we do now to achieve it, the sequence is reversed. We should concentrate on the significant issues which need to be handled in the short term, and ensure that the debate about their long-term consequences is lively and engaged23

What is needed is a ‘pragmatic balance between present concerns and future potentialities’ 24; this means that ongoing systematic thinking about the future is an important task for any organisation working in development or humanitarian aid. Foresight is ‘the ability to create and maintain viable forward views and to use these in organisationally useful ways’ 25, and futures techniques, such as driver analysis or scenario planning, are suitable for this task. Scenario planning constructs a number of possible futures, in order to produce decisions and policies that are robust under a variety of feasible circumstances. This encourages a move away from looking for ‘optimal’ policies or strategies: ‘any strategy can only be optimum under certain conditions’ and ‘when those conditions change, the strategy may no longer be optimal’ 26, so it may be preferable to produce strategies that are robust and insensitive to future variability rather than optimal for one possible future scenario.

Path dependence and ’lock ins’ are also important to consider in the context of the practices of international aid agencies. The widespread use of the logical framework approach, despite the often serious critiques, is a clear example of path dependence at play. In fact, it could be argued that linearity has a ’lock in’ when it comes to the thought processes and approaches of international agencies. How ‘lock ins’ may be addressed in specific agency contexts is touched upon in Concept 7 on attractors and chaos.

Next part (part 15): Concept 6 – Phase space and attractors.

Article source: Ramalingam, B., Jones, H., Reba, T., & Young, J. (2008). Exploring the science of complexity: Ideas and implications for development and humanitarian efforts (Vol. 285). London: ODI. (https://www.odi.org/publications/583-exploring-science-complexity-ideas-and-implications-development-and-humanitarian-efforts). Republished under CC BY-NC-ND 4.0 in accordance with the Terms and conditions of the ODI website.

Header image source: qimono on Pixabay, Public Domain.


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Ben Ramalingam and Harry Jones with Toussaint Reba and John Young

Authors of the Overseas Development Institute (ODI) Working Paper "Exploring the science of complexity: Ideas and implications for development and humanitarian efforts".

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