The missing links in risk analysis practices by overlooking the evolution of evolution

By Dr Rahman Khatibi, Consultant Mathematical Modeller, Swindon, UK; May 2010

There are missing links in existing risk analysis practices. Risk analysis, an integration of risk assessment, risk management and risk communication, emerged in the late 1960s and the early 1970s. It is a formal procedure but broad brush as any factor not fitting its procedure is overlooked. Risk analysis involves value-laden judgements and seeks dialogue between technical experts and affected citizens without conceptualising our value systems. The outcome is that the science of risk analysis overlooks hierarchy in risk assessment and naturally, it is unable to assess its own risks. As it is now, our models of risk may just be doing what we have fixated them for. So can we reference our risk models to non-fixated models?

Risk analysis is an outcome of evolving human interests and forms a business sector throughout diverse fields of modern life. These practices may seem to be growing organically, forming one area of complexity associated with floods, food industry, finance/banking, pharmaceutical industry, waste disposal industry and health and safety, to name but a few. The various areas of risk may be imagined as a branch of the enterprise of complexity, with others of made up by management, planning, design, communication and so on. Each branch of complexity is jumbled up seemingly growing organically but in reality, they all can have a “fractal” structure, in which a hidden simple structure is replicated.

Risk analysis is a formal procedure that is neither concerned with uncovering a possible simple structure within risk complexity nor uncovering its own risks. Formidable human ingenuity is able to map a broad view of the universe throughout time but complexity (and risk complexity) is often seen as a jumble. It is not surprising that risk models did not predict the ongoing economic downturn in the late 2000s. A modeller, being a layperson with respect to the world of finance, immediately asks if we can rely on risk models that cannot assess their own risk. It is easy to ask questions but answers are more difficult.

It may be that science has reached a postmodernist outcome with plenty of questions but no answers and one should start contemplating postmodernist anecdotal areas of risk analysis. In this article, I want to suggest that anything is possible due to the way risk analysis is lurching around without referencing itself to a solid area of knowledge. It would not be surprising if even postmodernism would retard risk analysis. I am hopeful that we do not have to despair, as there is a way out by integrating evolutionary thinking with systemic thinking. I refer to the integrated outcome as evolutionary systemic modelling to be outlined below.

The crunch of the matter may be articulated in three steps:

Step 1: I claim that evolutionary processes themselves evolve – the evolution of evolution

Step 2: That we can understand the evolution of evolution through feedback loops customary in systems science or cybernetics

Step 3: What is more, the evolution of evolution is the language of complexity.

The evolution of evolution comprises four stages:

Stage 1: This is the process of formation of an area of complexity, e.g. flood risk. I call it the zero+ feedback loop reflecting on basic instinct in a period of evolution dominated by singular acts such as hazards or hazard avoidance. This is a very slow and long process, during which new possibilities may spontaneously be primed leading to the next stage.

Stage 2: The new possibilities referred to above are new entities, made up of the combination or recombination of elementary building blocks with an emergent property acting as a selective advantage. Selective advantage is just a potential and nothing more. The act of selection brings the new entity to life and without the acts of selection, the new entity is doomed.

Positive feedback loops are at the centre of survival of life through evolution and its engine is mindless proliferation (positive feedback) but this also depends on the ability to diversify and adapt. These abilities are opposed spontaneously by entropy or disorder, continually reducing the efficacy of the evolving entity to the point of destruction. Positive feedback is a mindset for collective featuring of mindless proliferation, diversification, adaptation and entropy.

In the process of positive feedback loops, the hazards are not avoided but defence strategies are worked out for an economical gain through the causative mindset, i.e. by judging things in terms of pure causes-and-effects without assessing the long term impacts. For instance, lands at-risk of flooding are developed for economical gain by flood defence measures and residual impacts are dealt with by further defences (positive feedback). One response to entropy is a natural regulation through cycles of booms-and-busts but better approaches are through the provision of regulatory systems superimposed on the systems on its positive feedback growth stage.

Stage 3: Entropy kicks in a selective advantage for the priming of regulatory mechanisms, which is a subsystem composed of at least four components of (i) transmitters measuring the state of the main system; (ii) a fact engine deciding on the amount of change to maintain the main system within the prescribed set-points; (iii) actuators to modulate the changes at the interface; and (iv) a flexible system that can accommodate changes.

Negative feedback loops perform as a system of active responses to maintain the broader system within a safe range of operations. It is highly improbable that a primed system driven by positive feedback loops will have sophisticated negative feedback loops. Negative feedback superimposes control over entropy but its components themselves proliferate under positive feedback.

Negative feedback is a mindset for acting with an insight into the complexity and for seeking intelligent solutions. Flood risk management is a classical example.

Stage 4: Negative feedback alone can act as trap by preserving the fact engine and not allowing changes when the environment itself is subject to change. Other symptoms include goal displacement and goal fixation. Feedforward loops remove such traps through anticipation and foresight.

5. Co-evolution: Each of the above loops is a mindset and can act on its own or the newly emerging mindset can create a pluralistic culture with the older mindsets. This is the strength of evolutionary systemic modelling, which emulates the reality, where there is the pluralism of these mindsets associated with individuals, communities and institutions. Each mindset can act as an attractor or repellent in the sense of chaos and/or catastrophe theories and therefore in principle it is possible to study the dynamics of complexity.

The picture of the evolutionary systemic modelling capability that I sketched above is in its infancy but it is possible to see that each branch and area of complexity has a simple fractal structure composed of hierarchies and each hierarchy composed of interconnected building blocks, whose interaction can be analysed by the potential four loops of: zero+, positive and negative feedback and feedforward. As it is now, it is a qualitative model but I am presently working on its mathematisation by developing a completely new calculus for a whole family of number sequences based on natural numbers. Admittedly, it is counterintuitive to apply a calculus of number sequence to explain interconnectivity in each hierarchy.

This new calculus can shed light into interconnectivity at each hierarchy of an area of complexity. The counterintuitive aspect of this claim can be mitigated for the first reader by stating that this new calculus also explains the mathematics of object selection (with and without replacement and with and without order). Therefore, if one regards a building block at a hierarchical level as objects, mathematical doors can be opened to the science of complexity; and as there are countless number sequences based on natural numbers, it is a thought-provoking idea that these sequences can be matched with building blocks in the natural and manmade complexity.

For mathematically minded readers, further explanations are presented at the end of this article for the persuasion that each hierarchy can be studied by the four feedback loops and their interconnectivity can be studied by the new calculus. The hierarchies associated with each areas of complexity can be studied by taking science as a model organised hierarchically from subatomic physics, to physics until anthropology. This is just a glimpse but sufficient to state that there is a potentially untapped rigour round the corner waiting to boost the science of complexity including risk analysis practices.

In this short article, I am pointing to the science of complexity, not of the established academic type but of a practical/academic future science. The particular focus is on risk analysis practices but the overall vision is that:

The rise of science in the 17th century has given rise to a formidable capability to understand complexity of natural and social systems, in which evolutionary thinking and systemic thinking stand out, each for its importance, but still both need to be integrated with each other.

Science at the same has instigated countless new streams of complexity or enterprises with complexity as their by-products but oblivious of the structure in these by-products. Failing to see the structure of complexity has already started acting as entropy infecting science.

In a planet on which the global population is increasing by one billion individuals every dozen years, this really means that research and science have failed to understand the basics of our future. The obvious evidence for this includes booms-and-busts in the economy and also in philosophy, as well as the persistent need for rethinking in the various professional activities. For instance, decision-making in and performance of various systems are infested by too many singular acts and causative mindsets (without negative feedback loops) that science simply turns a blind eye to. It should be mentioned that dualistic philosophies have retarded moralistic philosophies and not surprisingly, man is finding ways of tampering with Nature and playing dangerous games without even understanding complexity.

Prediction in science and modelling studies are often carried out by formulating scenarios but these scenarios neither account explicitly for the above mindsets nor for the role of individuals, communities and institutions. As complexity is pluralistic, the science of complexity must also have pluralistic capabilities, which are intrinsic to evolutionary systemic modelling.

A vision is outlined in this article for the science of complexity based on evolutionary systemic modelling, which can emulate both the whole complexity or focus on its individual areas through feedback loops. This is a bottom-up model and studies the routemap of evolution as it evolves, without pontificating how it should be, as in traditional philosophical doctrines. This capability offers a way to uncover interconnectivity with each area of complexity and identify inherent hierarchies and value systems. It is also possible to study the dynamics of evolutionary processes and reference one type of complexity against another, which can serve as a way of trapping self-induced risks inherent in the models.

Dr Rahman Khatibi has a track record on industry and research but has now devoted his time to his personal research. He is the author of some 70 articles and journal papers and has been engaged for the last 16 years on personal research on (i) integrating evolution with systems science, for which you may refer to ( and (ii) developing an analytical capability for the sequences of natural complexity, the first paper for which is currently under review. This article is a preview of a journal paper that he is drafting on the science of complexity.

Further explanations on new calculus:

The new calculus was under the nose of mathematicians for the last three hundred years waiting to be discovered but this did not materialise because of a failing to factorise sequences. For instance, the sequence of is known to be equal to but I rework and factorise it as: . This enables the following:

  • The operator: is generic and the complexity of the sequences is defined by n = 3, above which the sequence just adds layers upon layers without adding to complexity.

  • The sequence: 3!= {1 4 1} is the specific signature of the cubic sequence of natural numbers. For power 4, the sequence becomes: 4!={1 11 11 1}, where these sequences are interconnected through a systematic rule and therefore it is possible to derive an equivalent of the Periodic Table and the tree of life to the world of natural number sequences.
  • Each element in a sequence is not what it seems to be. For instance, are in fact can hint to bonding of building blocks. To illustrate this, their expansion is given below without any explanation. However, mathematically-astute readers can easily spot their logic and this logic is general and is the tip of the iceberg.

Added 18-09-11 11:50 PM

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