The History of Complexity Sciences
(Creative Commons license—https://en.wikipedia.org/wiki/Complex_systems)
The Philosophy of CAS - Paul Cilliers [
The notion “complexity” has up to now been used in a somewhat general way, as if we know what the word means. According to conventional academic practise it would now be appropriate to provide a definition of “complexity”. I will nevertheless resist this convention. There is something inherently reductionist in the process of definition. This process tries to capture the precise meaning of a concept in terms of its essential properties. It would be self-defeating to start an investigation into the nature of complexity by using exactly those methods we are trying to criticise! On the other hand, we cannot leave the notion of “complexity” merely dangling in the air; we have to give it some content. This will be done by making a number of distinctions which will constrain the meaning of the notionFootnote 6 without pinning it down in a final way. The characterisation developed in this way is thus not final—in specific contexts there may be more characteristics one could add, and some of those presented here may not always be applicable—but it helps us to make substantial claims about the nature of complexity, claims that may shift our understanding in radical ways.
In the first place one should recognise that complexity is a characteristic of a system. Complex behaviour arises because of the interaction between the components of a system. One can, therefore, not focus on individual components, but on their relationships. The properties of the system emerge as a result of these interactions; they are not contained within individual components.
A second important issue is to recognise that a complex system generates new structure internally. It is not reliant on an external designer. This process is called self-organisation. In reaction to the conditions in the environment, the system has to adjust some of its internal structure. In order to survive, or even flourish, the tempo at which these changes take place is vital (see Cilliers, 2007 for detail in this regard). A comprehensive discussion of self-organisation is beyond the scope of this chapter (see Chap. 6 in Cilliers, 1998 for such a discussion), but some aspects of self-organisation will become clear as we proceed.
An important distinction can be made between “complex” and “complicated” systems. Certain systems may be quite intricate, say something like a jumbo jet. Nevertheless, one can take it apart and put it together again. Even if such a system cannot be understood by a single person, it is understandable in principle. Complex systems, on the other hand, come to be in the interaction of the components. If one takes it apart, the emergent properties are destroyed. If one wishes to study such systems, examples of which are the brain, living systems, social systems, ecological systems, and social-ecological systems, one has to investigate the system as such. It is exactly at this point that reductionist methods fail.
One could argue, however, that emergence is a name for those properties we do not fully understand yet. Then complexity is merely a function of our present understanding of the system, not of the system itself. Thus one could distinguish between epistemological complexity—complexity as a function of our description of the system—and ontological complexity—complexity as an inherent characteristic of the system itself. Perhaps, the argument might go, all complexity is merely epistemological, that finally all complex systems are actually just complicated and that we will eventually be able to understand them perfectly.
If one follows an open research strategy—a strategy which is open to new insights as well as to its own limitations—one cannot dismiss the argument above in any final way. Nevertheless, until such time as the emergent properties of a system are fully understood, it is foolish to treat them as if we understand them already. Given the finitude of human understanding, some aspects of a complex system may always be beyond our grasp. This is no reason to give up on our efforts to understand as clearly as possible. It is the role of scientific enquiry to be as exact as possible. However, there are good reasons why we have to be extremely careful about the reach of the scientific claims we make. In order to examine these reasons in more detail, a more systematic discussion of the nature of complex systems is required. The following characteristics will help us to do thisFootnote 7:
Complex systems are open systems.
They operate under conditions not at equilibrium.
Complex systems consist of many components. The components themselves are often simple (or can be treated as such).
The output of components is a function of their inputs. At least some of these functions must be nonlinear.
The state of the system is determined by the values of the inputs and outputs.
Interactions are defined by actual input–output relationships and these are dynamic (the strength of the interactions changes over time).
Components, on average, interact with many others. There are often multiple routes possible between components, mediated in different ways.
Many sequences of interaction will provide feedback routes, whether long or short.
Complex systems display behaviour that results from the interaction between components and not from characteristics inherent to the components themselves. This is sometimes called emergence.
Asymmetrical structure (temporal, spatial, and functional organisation) is developed, maintained, and adapted in complex systems through internal dynamic processes. Structure is maintained even though the components themselves are exchanged or renewed.
Complex systems display behaviour over a divergent range of timescales. This is necessary in order for the system to cope with its environment. It must adapt to changes in the environment quickly, but it can only sustain itself if at least part of the system changes at a slower rate than changes in the environment. This part can be seen as the “memory” of the system.
More than one legitimate description of a complex system is possible. Different descriptions will decompose the system in different ways and are not reducible to one another. Different descriptions may also have different degrees of complexity.
If one considers the implications of these characteristics carefully a number of insights and problems arise:
The structure of a complex system enables it to behave in complex ways. If there is too little structure (i.e. many degrees of freedom), the system can behave more randomly, but not more functionally. The mere “capacity” of the system (i.e. the total amount of degrees of freedom available if the system was not structured in any way) does not serve as a meaningful indicator of the complexity of the system. Complex behaviour is possible when the behaviour of the system is constrained. On the other hand, a fully constrained system has no capacity for complex behaviour either. This claim is not quite the same as saying that complexity exists somewhere on the edge between order and chaos. A wide range of structured systems display complex behaviour
Since different descriptions of a complex system decompose the system in different ways, the knowledge gained by any description is always relative to the perspective from which the description was made. This does not imply that any description is as good as any other. It is merely the result of the fact that only a limited number of characteristics of the system can be taken into account by any specific description. Although there is no a priori procedure for deciding which description is correct, some descriptions will deliver more interesting results than others
In describing the macro-behaviour (or emergent behaviour) of the system, not all the micro-features can be taken into account. The description on the macro-level is thus a reduction of complexity, and cannot be an exact description of what the system actually does. Moreover, the emergent properties on the macro-level can influence the micro-activities, a phenomenon sometimes referred to as “top-down causation”. Nevertheless, macro-behaviour is not the result of anything else but the micro-activities of the system, keeping in mind that these are not only influenced by their mutual interaction and by top-down effects, but also by the interaction of the system with its environment. When we do science, we usually work with descriptions which operate mainly on a macro-level. These descriptions will always be approximations of some kind
These insights have important implications for the knowledge-claims we make when dealing with complex systems. Since we do not have direct access to the complexity itself, our knowledge of such systems is in principle limited. The problematic status of our knowledge of complexity needs to be discussed in a little more detail. Before doing that, some attention will be paid to three problems: identifying the boundaries of complex systems, the role of hierarchical structure, and the difficulties involved in modelling complexity.
Why Do We Need the Science of Complexity to Tackle the Most Difficult Questions? - David Krakauer
One quite useful distinction that one can make is between the merely complicated and the complex. So the universe is complicated in many parts; the sun is complicated, but in fact I can represent in a few pages of formula how the sun works. We understand plasma physics; we understand nuclear fusion; we understand star formation.
Now, take an object that’s vastly smaller. A virus, Ebola virus. Got a few genes. What do we know about it? Nothing. So how can it be that an object that we’ll never get anywhere close to, that’s vast, that powers the Earth, that is responsible in some indirect way for the origin of life, is so well understood, but something tiny and inconsequential and relatively new, in terms of Earth years, is totally not understood? And it’s because it’s complex, not just complicated. And what does that mean?
So one way of thinking about complexity is adaptive, many body systems. The sun is not an adaptive system; the sun doesn’t really learn. These do; these are learning systems. And we’ve never really successfully had a theory for many body learning systems. So just to make that a little clearer, the brain would be an example. There are many neurons interacting adaptively to form a representation, for example, of a visual scene; in economy, there are many individual agents deciding on the price of a good, and so forth; a political system voting for the next president. All of these systems have individual entities that are heterogeneous and acquire information according to a unique history about the world in which they live. That is not a world that Newton could deal with. There’s a very famous quote where he says something like, I have been able to understand the motion of the planets, but I will never understand the madness of men. What Newton was saying is, I don’t understand complexity.
So complexity science essentially is the attempt to come up with a mathematical theory of the everyday, of the experiential, of the touchable, of the things that we see, smell, and touch, and that’s the goal. Over the last 10, 20 years, a series of mathematical frameworks—a little bit like the calculus or graph theory or combinatorics in mathematics that prove so important in physics—have been emerging for us to understand the complex system, network theory, agent-based modeling, scaling theory, the theory of neutral networks, non-equilibrium statistical mechanics, nonlinear dynamics. These are new, and relatively, I mean on the order of decades instead of centuries; and so we’re at a very exciting time where I think we’re starting to build up our inventory of ideas and principles and tools. We’re starting to see common principles of organisation that span things that appear to be very different—the economy, the brain, and so on. So complexity science ultimately seeks unification—what are the common principles shared—but also provides us with tools for understanding adaptive, many body systems. And intelligence for me is in some sense, the prototypical example of an adaptive, many body system.
Ingenious: David Krakauer. The systems theorist explains what’s wrong with standard models of intelligence.