KEY NOTIONS AND CONCEPTS IN THE PARADIGM OF COMPLEXITY

Vlad Dimitrov

1. Key notions

COMPLEXITY

The interaction of many agents, giving rise to holistic properties which are not found in any of the individual agents. The origin of the word complexity comes from the Latin word "complexus" which means totality. The paradigm of complexity tries to grasp totality of the existential dynamics.

WHAT IS AN ENTITY?

An entity is a holistic web of interconnected (interrelated, interdependent) interacting agents functioning as a whole and distinguishable from its surrounding by recognizable and permeable boundaries.

There are many varieties of entities in respect to dynamic interactions of the envolved agents: on the one hand the interactions between the agents may be fixed (e.g. an engine), at the other extreme, the interactions may be unconstrained (e.g. a gas). The function depends upon the nature and arrangement of the agents and usually changes if agents are added, removed or rearranged. The entity has properties that are emergent, if they are not intrinsically found within any of the agents, and therefore exist only at some higher level of description.

COMPLEX ENTITIES

Entity that cannot be described by a single rule is complex; its structure exists on many scales whose characteristics are not reducible to only one level of description. Complex entities exhibit unexpected features, that is, features which are not contained within entities’ specifications.

DYNAMICS

The behaviour of an entity in time defines its dynamics. Changes with time are at the essence of complexity studies; a static entity is merely a snapshot within an evolutionary continuum, however interesting it may be in its own right.

NONLINEAR ENTITY

Entity that behaves in an apparently ‘irrational’ way, not changing proportionally to a change in its input is called nonlinear. Sometimes such entity tends to go down when one expects it to go up, doing nothing instead, or changing drastically when only minor changes occur at its input.

PERTURBATION

Perturbation is a forced change to an entity. This can result in sudden shift to a new state, an immediate return to the old state or a long transient resulting in one or the other.

FEEDBACK

Feedback represents a linking of the output of an entity back to the input. Traditionally this can be negative, tending to return the entity to a wanted state, or positive tending to diverge from that state. Life seems to employ both methods.

PHASE (STATE) SPACE

The phase (state) space includes all the possibilities available to an entity in theory, that is, the sum total of possible states the entity can occupy. In general only a very small proportion of such states are found - the entity is said to occupy only a minute proportion of state or phase space.

CHAOTIC ENTITY

An entity whose long-term behaviour is extremely sensitive to small perturbations and, therefore, unpredictable: tiny changes in the accuracy of the starting value rapidly diverge to anywhere in its phase (state) space is considered chaotic. There can be however a finite number of available states, so rough prediction can still be used.

BUTTERFLY EFFECT

This term has been introduced by Edward Lorenz to denote possibility that a large change can occur from a minor shift in the initial dynamics of the entity. "Butterfly flapping its wings in the Amazon may lead to changes in the location of a typhoon somewhere else". Another name of the butterfly effect is "extreme sensitivity to initial conditions".

EMERGENCE

Emergence is appearance of a property or feature not previously observed as a functional characteristic of the entity. Generally, higher-level properties are regarded as emergent. Teams and communities are emergent properties of individuals, cultures - emergent properties of individual values (beliefs, dispositions, customs, traditions) and behaviours, mind - an emergent property of brain cells, economy - an emergent property of individuals and corporations, ecology - an emergent property of species and environment.

WHAT ARE DISSIPATIVE ENTITIES?

Entities that use energy flow to maintain their form and function are called dissipative. These would include atmospheric vortices, living entities and similar. The term can also be used more generally for entities that consume energy to keep going, e.g. engines or stars. Such entities are generally open to their environment.

ORGANIZATION

Organization represents an arrangement of selected constituents (agents, processes) so as to promote a specific function. This restricts the behaviour of the entity in such a way as to confine it to a smaller volume of its phase space. Energy considerations are often regarded as an explanation of organization existence; it is said that the drive towards minimal energy causes an organization, although there are often alternative arrangements that require the same energy.

WHAT IS SELF-ORGANIZATION?

The evolution of an entity into an organized form in the absence of external constraints is called self-organization. Self-organization expresses an ability to create structure without any external pressures; in this sense, self-organization is an emergent property of the entity, which persists leads to changes in a certain direction. Self-organization is also a move from a large region of phase space to a persistent smaller one, under the control of the entity itself. This smaller region of phase space is called an attractor.

WHAT IS AN ATTRACTOR?

Attractor is a preferred position for the entity, such that if the entity is started from another state it will evolve until it arrives at the attractor, and will then stay there in the absence of other factors. An attractor can be a point (e.g. the centre of a bowl containing a ball), a regular path (e.g. a planetary orbit), a complex series of states (e.g. the metabolism of a cell) or an infinite sequence (called a strange attractor). All specify a restricted volume of phase space. The larger area of state space that leads to an attractor is called its basin of attraction. The ratio of the volume of the basin to the volume of the attractor could be used as a measure of the entity’s degree of self-organization.

HOW DO ATTRACTORS AND SELF-ORGANIZATION RELATE?

Any entity that moves to a (dynamically) stable structure is seen as being drawn to an attractor. A complex entity can have many attractors and these can alter with changes to the entity’s parameters. Studying self-organization is equivalent to investigating the attractors of the entity, their form and dynamics, as well as entity’s potential for change, evolution and transformation.

FRACTALS

Fractals are similar structures which repeat at different levels of organization of a complex dynamic entity. Mandelbrot is the "father" of fractals .

CRITICALITY

Point of criticality is a point at which the properties of the entity change suddenly. Entity dynamics become vortical (percolated). Properties arise that connect the opposite sides of the entity's structure. Criticality assumes presence of high degree of dynamical interconnectivity (wholeness).

WHAT IS SELF-ORGANIZED CRITICALITY?

Self-organized criticality is ability of an entity to evolve in such a way as to approach a critical point and then maintain itself at that point.

Theorem (Back, 1991): Any large dynamical system (with many degrees of freedom) driven by constantly supply of energy, that eventually dissipates somewhere in the entity) is unavoidably pulled towards the critical state where avalanches of changes occur.

WHAT IS 'EDGE OF CHAOS '?

This is the name given to the critical point of the entity, where small changes can either push the entity into a totally random behaviour ('deep chaos') or lock the entity into a fixed behaviour. It is at this point where all the really interesting behaviour occurs in a complex entity, and it is where entities tend to gravitate, give them the chance to do so. Transient perturbations (disturbances) can last for very long times (infinitely in the limit) and/or cover the entire entity, yet more frequently effects will be local or short lived - the entity is dynamically unstable to some perturbation, yet stable to other.

2. Revolutionary ideas of complexity science

2.1 The dynamics of entities are independent of the physical manifestation of their agents and depend only on the nature of agents’ interactions. In this way the findings of complexity studies can be shown to be equally applicable to all forms of entity - inorganic, organic, biological, social, psychological. In each case the emergent features will show equivalent properties relevant to that level of description.

2.1.1 Complex entities have a universal property called Sensitive Dependence to Initial Conditions: no matter how accurate our measurements of the initial state of a complex entity (and we never can reach an absolute accuracy), our predictions based on these measurements can never exceed a certain point in the future of the entity, where the accuracy of our prediction is doomed to break down.

2.1.2 Local interactions and decisions of agents in complex entities bring forth phenomena that emerge at global level. The features of these phenomena, that is, the emergent properties, cannot be described within the vocabulary applicable to the agents.

2.2 The emergent properties can themselves interact with each other (e.g. interacting molecules produce emergent cells, these interact to form organisms, which interact to form societies). There are number of nested levels of detail ("fractals"), each has properties different from those levels that comprise it, and so needs a new type of 'label' to be applied. Despite these different labels the properties found at the different levels are considered similar, each being due to the same form of connectivity applied within the specific space and time framework applicable to that type of structure. By studying the lower level connectivity of each entity we can "sense" possible emergent features, and conversely by relating the features to those of entities whose connectivity is known, we may be able to infer their internal connectivity.

Note: More about the new revolutionary concepts of complexity science and their social interpretations can be found in Vlad's papers at :

http://vlad-home-page.fcpages.com/internet-papers/think.html (Understanding and Working with Complexity )

http://vlad-home-page.fcpages.com/internet-papers/human-dynamics.html (Complex Nature of Human Dynamics)

http://vlad-home-page.fcpages.com/internet-papers/emergence1.html (Paradigm of Complexity )

http://vlad-home-page.fcpages.com/internet-papers/laws.html (The Laws of Complexity )

http://vlad-home-page.fcpages.com/internet-papers/life-dynamics.html (Complexity of Human Life )

http://vlad-home-page.fcpages.com/internet-papers/power.html (The Power of Complexity )

http://www.zulenet.com/VladimirDimitrov/pages/SAM.html (Strange Attractors of Meaning )

http://www.zulenet.com/VladimirDimitrov/pages/complexthink.html (Complexity, Chaos and Creativity)

http://vlad-home-page.fcpages.com/internet-papers/manifesto.html (Manifesto of Emergence)

http://vlad-home-page.fcpages.com/internet-papers/fractal.html (Fractals of Human Life )

http://www.zulenet.com/VladimirDimitrov/pages/creativity.html (Self-organization and Creativity)