Complexity in the context of Computational intelligence

Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 BC), though analysis as a formal concept is a relatively recent development.

The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.

Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant for decision-making. Uncertainty arises in partially observable or stochastic or complex or dynamic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, entrepreneurship, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

Sociocultural evolution, sociocultural evolutionism or social evolution are theories of sociobiology and cultural evolution that describe how societies and culture change over time. Whereas sociocultural development traces processes that tend to increase the complexity of a society or culture, sociocultural evolution also considers process that can lead to decreases in complexity (degeneration) or that can produce variation or proliferation without any seemingly significant changes in complexity (cladogenesis). Sociocultural evolution is "the process by which structural reorganization is affected through time, eventually producing a form or structure that is qualitatively different from the ancestral form".

Most of the 19th-century and some 20th-century approaches to socioculture aimed to provide models for the evolution of humankind as a whole, arguing that different societies have reached different stages of social development. The most comprehensive attempt to develop a general theory of social evolution centering on the development of sociocultural systems, the work of Talcott Parsons (1902–1979), operated on a scale which included a theory of world history. Another attempt, on a less systematic scale, originated from the 1970s with the world-systems approach of Immanuel Wallerstein (1930–2019) and his followers.

A complex system is a system composed of many components that interact with one another. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.

The behavior of a complex system is intrinsically difficult to model due to the dependencies, competitions, relationships, and other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links represent their interactions.

In sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in systems theory, wherein the phenomenon being studied has many parts and many possible arrangements of the parts; simultaneously, what is complex and what is simple are relative and change in time.

Contemporary usage of the term complexity specifically refers to sociologic theories of society as a complex adaptive system, however, social complexity and its emergent properties are recurring subjects throughout the historical development of social philosophy and the study of social change.

Ecosystem diversity deals with the variations in ecosystems within a geographical location and its overall impact on human existence and the environment.

Ecosystem diversity addresses the combined characteristics of biotic properties which are living organisms (biodiversity) and abiotic properties such as nonliving things like water or soil (geodiversity). It is a variation in the ecosystems found in a region or the variation in ecosystems over the whole planet. Ecological diversity includes the variation in both terrestrial and aquatic ecosystems. Ecological diversity can also take into account the variation in the complexity of a biological community, including the number of different niches, the number of and other ecological processes. An example of ecological diversity on a global scale would be the variation in ecosystems, such as deserts, forests, grasslands, wetlands and oceans. Ecological diversity is the largest scale of biodiversity, and within each ecosystem, there is a great deal of both species and genetic diversity.

Konstantin Sergeevich Mereschkowski (Russian: Константи́н Серге́евич Мережко́вский, IPA: [mʲɪrʲɪˈʂkofskʲɪj]; 4 August 1855 [O.S. 23 July] – 9 January 1921) was a Russian biologist and botanist, active mainly around Kazan, whose research on lichens led him to propose the theory of symbiogenesis – that larger, more complex cells (of eukaryotes) evolved from the symbiotic relationship between less complex ones. He presented this theory in 1910, in his work, The Theory of Two Plasms as the Basis of Symbiogenesis, a New Study of the Origins of Organisms, although the fundamentals of the idea had already appeared in his earlier 1905 work, The nature and origins of chromatophores in the plant kingdom.
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In cybernetics, the term variety denotes the total number of distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity. Variety is used in cybernetics as an information theory that is easily related to deterministic finite automata, and less formally as a conceptual tool for thinking about organization, regulation, and stability. It is an early theory of complexity in automata, complex systems, and operations research.

Systems novel is a literary genre named by Tom LeClair in his 1987 book In the Loop: Don DeLillo and the Systems Novel, and explored further in LeClair's 1989 book, The Art of Excess: Mastery in Contemporary American Fiction. LeClair used systems theory to critique novels by authors including Thomas Pynchon, William Gaddis and Ursula K. Le Guin. Citing Fritjof Capra's description of systems theory as a "new vision of reality", LeClair invoked ideas from thinkers such as James Lovelock, Gregory Bateson and Douglas Hofstadter to analyse how the novels in question depicted processes and relationships within social, cultural, economic and political systems. LeClair's systems novels were all "long, large and dense" and all in some way striving for "mastery", showing similarity to Moby-Dick and Absalom, Absalom! in "range of reference, artistic sophistication, and desire for profound effect."

Subsequent critics widened the geographical range but mostly adhered to the notion that systems novels were typically large and dense, making the concept overlap with other critical terms such as encyclopedic novel and maximalism. This weakened its usefulness as a genre definition, but with the rise of the internet, the systems novel has come to be seen as reflecting the conditions of network culture. The term is now used in at least two different ways, stemming from LeClair's thesis though with different emphases. One highlights bulk, broadness of scope, range of content and greatness of ambition. The other highlights engagement with scientific and technological concepts such as information theory, complexity and emergence. Some systems novels fit both categories, though not all.

Douglas R. White (1942 – 22 August 2021) was an American complexity researcher, social anthropologist, sociologist, and social network researcher at the University of California, Irvine.

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern and tells how a fractal scales differently, in a fractal (non-integer) dimension.

The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions. In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used (see Fig. 1). In terms of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick. There are several formal mathematical definitions of fractal dimension that build on this basic concept of change in detail with change in scale, see § Examples below.

Simplicity is the state or quality of being simple. Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we choose to describe it. In some uses, the label "simplicity" can imply beauty, purity, or clarity. In other cases, the term may suggest a lack of nuance or complexity relative to what is required.

The concept of simplicity is related to the field of epistemology and philosophy of science (e.g., in Occam's razor). Religions also reflect on simplicity with concepts such as divine simplicity. In human lifestyles, simplicity can denote freedom from excessive possessions or distractions, such as having a simple living style. In some cases, the term may have negative connotations, as when referring to someone as a simpleton.

Assemblage (from everyday French: agencement, – arrangement, layout, "a collection of things which have been gathered together or assembled") is a philosophical concept developed by Gilles Deleuze and Félix Guattari and subsequently taken up by other theorists, such as Bruno Latour and Michel Callon who developed Actor-network theory, Manuel DeLanda in his work on assemblage theory, and Jane Bennett who combines Latour with Deleuze and Guattari forming her own assemblage theory. Bennett’s assemblage thinking has influenced: Environmental philosophy (e.g., Timothy Morton’s Hyperobjects), Political theory (e.g., William Connolly’s work on complexity and politics), and New materialism (e.g., Rosi Braidotti, Karen Barad).

Assemblage is a philosophical concept used when studying ontological diversity of agency, which means redistributing the capacity to act from an individual to a socio-material network of people, things, and narratives. Also known as assemblage theory or assemblage thinking, this philosophical approach frames social complexity through fluidity, exchangeability, and their connectivity. The central thesis is that people do not act predominantly according to personal agency; rather, human action requires material interdependencies and networks of discursive devices distributed across legal, geographical, cultural, or economic infrastructures.