"The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations among things; outside these relations there is no reality knowable."Henri Poincaré, Science and Hypothesis, 1905
"I salute the light within your eyes where the whole universe dwells; for when you are at that center within you, and I am at that place within me, we shall be One"Crazy Horse, Native American Lakota Tribe
Before we introduce the detailed concepts behind complexity research it will be useful to position this quest in the wider context of our lives, relating it to science in general, to humanity in our social structures and to nature in the ecological interactions between species and environment. Complexity science relates to the formal study of complex systems, but it is not another specialist subject (in the sense that we can regard geology, genetics and anthropology say). Instead our subject matter is any form of system that comprises many components interacting with each other. This means that it is what is called an interdisciplinary science, and is pursued (often in different ways) by researchers from all sorts of backgrounds and specialisms. It has also captured the interest of many non-academic people and is widely enjoyed by artists, children, businessmen and alternative thinkers (in the forms of fractals , artificial life , Complex Adaptive Systems and chaos respectively).
Most forms of study taught in our schools relate to objects, facts are compartmentalised and learnt as discrete things, collections of separate concepts, to be remembered in isolation from any connection with our everyday lives. This bias is seen in the layout of encyclopaedias, in the structure of memory-related activities like 'Trivial Pursuit' or 'University Challenge' and in our academic examination processes. This is a filing cabinet form of knowledge.
Complexity studies however relate to a very different form of knowledge, which comprises
the connections between things and not the things themselves, in other words what is important is the patterns that the relationships form overall. It is the study of what
happens when things are connected, when information can flow around the system and
change the system properties. Thus it is the study of change rather than stability, of dynamics
rather than statics, and is as such especially applicable to our modern highly dynamic world.
Because connectivity is such a general concept (a road connects towns, wiring connects computer chips, water connects plant cells, talking connects people), these studies potentially can
apply in all areas, it is the interaction structures that are important not which objects are
interacting (a somewhat 'black-box' approach to science, often modelled using cellular automata).
To illustrate this, consider the way in which we interact with our world as human beings (this also applies to a lesser degree to all animals and even plants). We first perceive our environment, this is a form of incoming interaction. Suppose we detect food. We then have various options or choices, we can eat or not, give it to someone else or not, store it or not. We need to plan what we wish to do, considering our goals or instincts, this is an internal form of interaction. Once we have decided, we then act, an external form of (outgoing) interaction. At no point here have we specified any 'thing' that was performing these processes. The actual object could be a man, a cat, a computer or an alien - even a virtual reality game character ! We can investigate the system entirely in terms of abstract or logical flows of activations over interaction pathways, with no reference to how exactly the parts work (which is the usual objective of traditional reductionist science).
Another important aspect of our human interactions is that we learn by them. Our mental world is not a fixed object but an ever changing set of memories, abilities and desires. Studying how these changes take place in mankind is the province of cognitive science and trying to duplicate them involves the field of artificial intelligence (AI), both of these disciplines contribute to complexity studies. But other systems change with time also, they do not need to be conscious. Rivers develop whirlpools, ecosystems evolve. These structures are not imposed from outside, they are created by the internal interactions within the system. This we call self-organisation and it is a feature studied extensively in complexity science. Such studies take into account how animals and plants develop, how brains learn, how societies and organizations structure themselves and look to identifying the conditions under which such processes occur. This relates to the border between stability and chaos, a position which allows the system to change without destroying itself and is a common feature (called edge of chaos) found in all these self-stabilising cybernetic systems.
Systems in general occur in many forms, those of interest to us here are those with sufficient complexity to produce interesting properties. Whilst we often think of our brain as the only intelligent part about us, this is not in general true. Other systems (for example the immune system) have their own embedded knowledge and the capacity to make decisions. Each of our cells is such a system, and the combinations of organisms in an
ecosystem is another. A general model of these systems formalises the perceiving, planning, action process we saw earlier, so we have a system with inputs, a process of options and outputs. What is common to all forms of complex system is that they can exist in many different states, and can move between these alternative modes (which we call attractors) dependent upon the environmental situation in which they
find themselves.
This model, familiar in the form of a computer program (which operates using statements like IF A=1 AND B=0 AND C=0 THEN DO D ), need not operate on symbols (as do the computer languages used in AI) but can operate directly as a dynamic system (with direct non-linguistic cause and effect). This mode (widely used in mechanics) assumes a system continuously in motion through time, so that it plots out a path or trajectory through the space of possible dispositions, often illustrated graphically. But this set of states needn't be fixed, we can assume that new states can come into being and old ones can be replaced. In this way we can model creativity or innovation, the formation of new attractors with time. These alternative states are widely studied in the complexity sciences, both in terms of what attractors exist, and in how systems move between them and learn new ones over time (as in the brain), and this study also includes the genetic search for better possibilities underlying evolution.
Many people are rather uneasy with science, it seems to them complex and obscure, riddled with equations and jargon. And so it is ! But behind all the hype and mathematics lies a very simple idea. That is that we test our ideas before we use them. Rather than being a newish idea originating with Francis Bacon in 1620 (only his formalism was new) this methodology goes back to the beginning of life on Earth. As we grow whilst children we must learn how to behave, and we do so largely by trial and error. We try a behaviour or speak a word and if it works we repeat it, if it doesn't we discard it and try another option. Thus we learn by what are actually scientific principles, we hypothesize subconsciously as to how the world works and develop ways of behaving or 'laws' that give us success in what we wish to do, testing the effectiveness of our implicit theories by their results. The same methodology operates at all levels of life, and forms the principle behind the idea of natural selection. Science is just a formal way of doing this by social agreement, rather than relying on just individual knowledge, and relates to comparing alternative ways of behaving (theories) and evaluating by experiment which is the most successful or fit, rather than assuming the truth of an unevaluated idea and applying it regardless of consequences - a mode that frequently proves fatal to animals (e.g. lemmings) and can prove so also for humans, as in religious intolerance and similar unexamined prejudices or beliefs.
The formalism of science can best be presented in five steps. Science is about finding explanations, so first we must have something to explain. This first step is the "Problem Statement", e.g. why is it always raining now ? Such a statement can be about any aspect of life, not just the subject matter of conventional specialisms. The second step is "Collection of Facts", i.e. what evidence is there that it is always raining ? What else always happens at the same time ? This is the data on which science is based, but note that what we choose to collect is biased by our previous world view, our experience of what we think is 'relevant'. The third step is "Formulating an Hypothesis", this is a tentative way of linking up the facts we have obtained into a causal flow, a possible explanation, e.g "aircraft disturb clouds and thus it rains more now because there are more aircraft today". The fourth step is "Making Further Inferences", this means we should determine what our explanation would predict, e.g. it never rains unless an aircraft flies through a cloud, and always does if it happens. The final step is "Verifying the Inferences", this is the 'experimental stage' where we collect data on new events, e.g. we check aircraft movements and see if they correlate (match) with rainfalls around our area or around the world. If they do then the hypothesis is supported (contrary to popular belief it can never be 'proved' beyond doubt !), if the results don't correlate then the hypothesis is 'falsified' and should not be believed - we must then start from step 2 onwards again with better data (possibly based upon a wider world view or additional expertise).
Most forms of science adopt a type of analysis of systems that breaks them down into parts, the 'system' is then said to comprise only those parts. This is the mode of study called reductionism (in our example above the parts were 'clouds' and 'aircraft') . For complexity studies this will not suffice, since that form of analysis discards the interactions that we study, i.e. those relationship patterns within the whole system (not just part of it, in our example we must add air temperature, height, cloud type, etc.), and it is these in total that cause the system to have properties of its own (e.g. an automobile is not just a heap of parts - its functionality requires a specific organization or interconnection, along with a context in which the function applies, e.g. the road transport system). Instead we use a mode of study called synthesis, we combine parts to form larger systems and look at the overall properties that then become evident. Looking at the whole is an holistic viewpoint, but because we also include the parts then we can study how the properties of the whole emerges from the parts and not just treat the system properties as mystical entities, incapable of being understood. This concept helps bridge the two incompatible worlds of conventional science and the humanities (including religion).
It is often convenient for us to concentrate on one property of a system, for example if we are buying a particular food we may at present consider only the relative price between stores. Complex systems however have many simultaneous properties and we can only gain a full picture of the system if we take all of these into account. As well as the number of properties (often called variables in science) we must also consider how they affect each other or coevolve and in complex systems this usually happens nonlinearly. Since we consider in complexity science the interactions between parts, we also must consider the interactions between the emergent system properties, the higher level features. Thus our studies, if they are to be complete, must include multiple nested levels of detail (e.g. molecules, cells, organisms, societies, ecosystems), multiple variables within a level (e.g. hunger, thirst, reproduction, safety) and all the interdependencies between them (e.g. should we start eating or flee a possible predator ?). This overall viewpoint is rather different than that usually taken in science, and involves many different philosophical assumptions or axioms, which instead treat our world as one interconnected whole whose apparent divisions (those 'boxes' we create) are simply human simplifications and prove to be largely arbitrary.
We have seen some of the issues that must be addressed if we are to fully understand complex systems. This quest however is still a young science and we must feel our way carefully. Most research into complex systems concentrates (by computational necessity) on scenarios that are quantitatively rather simple by comparison with real ecologies, brains and societies. The techniques we outline in the following introductions are all ways of studying complex systems of various types. Many of these techniques are equivalent to each other, and form alternative models or mappings of the basic complexity techniques to the area of interest to particular researchers.
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to read our first Introduction.