System’s attribute and complexity

The majority of definitions are ground on the principal idea that complexity is an inherent part of the complex systems such as: economies, social structures, climate, nervous systems and etc. Complexity theory and chaos theory both attempt to reconcile the unpredictability of non-linear dynamic of these systems with a sense of underlying order and structure (David 2000).

First of all we have to discuss what we understand by complex systems. In a naïve way, we may describe them as systems which are composed of many parts, or elements, or components which may be of the same or different kinds. The components or parts may be connected in a more or less complicated fashion. The various branches of science offer

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us numerous examples, some of which turn out to be rather simple whereas others may be called truly complex (Haken 2002).

A modern definition of complex systems is based on the concept of algebraic complexity. It means, that at least to some extent, systems can be described by a sequence of data, the fluctuating intensity of the light or a curve that represents data by the numbers. There, one might attempt to follow up the paths of the individual parties and their collisions and then derive the distribution function, known as the Boltzmann distribution, of the velocity of the individual parts.

In all cases, a macroscopic description allows an enormous compression of information so that we are no more concerned with the individual microscopic data, but rather with global properties. An important step in treating complex systems consists in establishing relations between various macroscopic quantities (Haken 2002).

The more science becomes divided into specialized disciplines, the more important it becomes to find unifying principles (Haken 2002). We may recount the give in literature cross-discipline ideas of view on the complexity in the complex systems. As matter of fact, these definitions cannot be limited in the way of top of twenty (Sussman 2002), because common point is that all of them use word-combinations such as: intricate ways, subtle, degree and nature of the relationships, behaviour of macroscopic collections. This type wording is not acceptable for strong definition, because all of them should be also pre-defined.

First of all let us mention that we share a critical view of some authors on complexity whose treats this paradigm as some kind of holism. They suggest that any attempt to cope with complexity using such traditional tools is doomed to failure. Their remedies vary from a complete abandonment to introduce new techniques and approaches. Of course, any constructive suggestions for dealing with complexity are welcome from whatever source. Thus, all given techniques of “the new sciences of complexity” are welcome for studying what have been considered complexity of the complex systems. As it is evenly noted by Sussman (Sussman 2000) many of these techniques, however have nothing to do with complexity per se. It is stated (Sussman 2000) that many papers with the word

"complexity" in the title refer merely to some techniques for dealing with rather difficult (complex) systems. Considering this point of view, complexity as a solid attribute of the systems might contain the following features:

A system is complex when it is composed of many parts that interconnect in intricate ways (Moses 2002) - this definition has to do with the number and nature of the

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interconnections. Metric for intricateness is amount of information contained in the system.

A system presents dynamic complexity when cause and effect are subtle, over time (Senge 2006) - different effects in, the short-run and the long-run; dramatically different effects can be observed locally and in other parts of the system. Obvious interventions produce non-obvious consequences.

A system is complex when it is composed of a group of related units (subsystems), for which the degree and nature of the relationships is imperfectly known (Sussman 2000) – the overall emergent behaviour is difficult to predict, even when subsystem behaviour is readily predictable, small changes in inputs or parameters may produce large changes in behaviour.

A complex system has a set of different elements so connected or related as to perform a unique function not performable by the elements alone (Maier and Rechtin 2000) - requires different problem-solving techniques at different levels of abstraction

A complexity relates to the behaviour of macroscopic collections of units endowed with the potential to evolve in time (Highfield 1996) - this definition differs from computational complexity which estimates a number of mathematical operations needed to solve a problem using Turing machine concept.

The features of the complexity of the complex systems are the following:

• Complex systems are non-fragmental: if it were, it would be a machine. Their reduction to parts destroys important system characteristics irreversibly.

• Complex systems comprise real components that are distinct from its parts: there are functional components defined by the system which definitional dependable on the context of the systems. Outside the system they have no meaning. If removed from the system it looses its original identity.

• Complex systems don’t have analytic or synthetic largest FS mode”: if there were a largest model, all other models could be derived from it.

• Causalities in the system are mixed when distributed over the parts.

• Attributes of the systems are beyond algorithmic definition or realization: here, we deal with posing a challenge to falsify. One of example is the famous Church's thesis (Church 1936) (“…All the models of computation yet developed, and all those that may be developed in the future, are equivalent in power… We will not ever find a more powerful model...”).

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These are not definitive indicators but a system that has many of these attributes hard to be analyzable using linear determinism or statistical methods (Lucas 2000).

Another important feature of complexity as an attribute of the complex systems that have to be mentioned here, especially, because of T-DTS concept of out thesis is a self-organizing. In the literature we find complexity as an imprescriptible attribute of the systems that allow them to self-organize. Naturally, we have to have before an answer on the question “What is the complexity of self-organizing systems?”

The one strong definition that is relevant to the complexity couldn’t be found. It could be arisen in bio-organisms (Hinegardner and Engelberg-Kulka 1983), where it has a direct relationship with the evolutionary selection process. A very weak definition of such as size of genome could be sufficient to explain an increase in the maximum complexity of all species under evolution process. Henceforth, related to mutation of the genome, is self-organizing complexity suggested by Wimsatt (Wimsatt 1974). Under complexity it is meant co-adaptation of an organism's mechanisms (or as sub-mechanisms of other mechanisms) as a source of the evolution, it is called in another words descriptive complexity. Kauffman (Kauffman 1993) suggests that the order manifest in organisms is a result of selection acting upon a system that is basically organizing and that this self-organizational ability depends critically on the complexity of conflicting constraints. Here, a complexity is linked with biology. These some sorts of criteria that may allow or not the system to achieve the benefits in innovation based on survival (fitting real-word constraints) and adaptability that we see for natural complex systems (Lucas 2000).

Therefore, one may see arising difficulty of the strong common for these systems definition of complexity as inherited part of the complex systems, because not the different origin, but mostly because of different phenomena and processes that took a place and which are twisted around word (not a term) complexity.

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