Editing Complexity (section)

== Overview ==
Definitions of complexity often depend on the concept of a "[[system]]" – a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime. Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. However, what one sees as complex and what one sees as simple is relative and changes with time.

[[Warren Weaver]] posited in 1948 two forms of complexity: disorganized complexity, and organized complexity.<ref name=Weaver>{{Cite journal
  | last = Weaver
  | first = Warren
  | title = Science and Complexity
  | journal = American Scientist
  | volume = 36
  | pages = 536–44
  | year = 1948
  | url = http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L1/Material/WEAVER1947.pdf
  | pmid = 18882675
  |jstor = 27826254
  | issue = 4
  | access-date = 2007-11-21
  | archive-date = 2009-10-09
  | archive-url = https://web.archive.org/web/20091009171939/http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L1/Material/WEAVER1947.pdf
  | url-status = dead
  }}</ref>
[[Phenomenon|Phenomena]] of 'disorganized complexity' are treated using [[probability theory]] and [[statistical mechanics]], while 'organized complexity' deals with phenomena that escape such approaches and confront "dealing simultaneously with a sizable number of factors which are interrelated into an organic whole".<ref name=Weaver/> Weaver's 1948 paper has influenced subsequent thinking about complexity.<ref>{{cite book
  | last = Johnson
  | first = Steven
  | title = Emergence: the connected lives of ants, brains, cities, and software
  | publisher = Scribner
  | year = 2001
  | page = [https://archive.org/details/emergenceconnect00john/page/46 46]
  | location = New York
  | isbn = 978-0-684-86875-2
  | url = https://archive.org/details/emergenceconnect00john
  | url-access = registration
  }}
</ref>

The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined system.

Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein.