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emphasizes the relevance of adaptation , of the dynamic changes that these self-organizing systems go through , whereas Raup ( 1966 ) question the Modern Synthesis of gradualism in evolution , favoring punctuated equilibrium . Gould and Eldredge ( 1977 ) use computational simulation to study evolution . Later , Anderson ( 1972 ), Langton ( 1986 ), and von Neumann ( 1986 ) consolidate the importance of the notion of interaction among parts . They defend that the lack of understanding of the connections across different scales compromises the understanding of the phenomenon . Anderson ( 1972 ) goes further , builts on the original idea of Weaver ( 1948 ), and establishes the famous ‘ more is different ’. Simon ( 1973 ) confirms this view of intertwined scales of interaction as he reinforces the value of hierarchies . Gell-Mann and Lloyd ( 2004 ) reinforce the relevance of scales and the basic tradeoff that scientists face , i . e ., whether to gain in precision ( and abstract the whole ), or to generalize and understand relations at higher orders . Rosenblueth and Wiener ( 1945 ) state that one should describe the minimum necessary , the essence of the phenomenon , so that modeling can occur .
The central concepts of complexity ‘ emerge ’ within the context of research of each of the authors writing at different moments in time , and follow the typical jargon of each discipline . There is , therefore , superposition , addition and complementation at different levels of detail and specificity . Part of the contribution of this text is to provide the reader with direct access to the original ( and complex ) thinking of the original authors , which is available dispersedly , but not fully consolidated . Thus , the objective of this text is to review the classic authors who have contributed to the constituent elements of a ‘ science of complexity ’.
The proposed selection of authors and papers is by no means exhaustive in an area of study that is particularly broad and boundless by construction . However , a decision was made to include those authors that could be seen as the main concepts contributors .
This paper is organized as follows . This introduction defines the general concept and establishes an initial chronological and concept-based approach ; the next section ( 2 ) discusses the foundational basis of information theory and early measures of complexity and section 3 introduces cellular automata and its importance to computer science and artificial intelligence . Section 4 presents brief concepts on evolution . The following section focuses on the relevance of interactions , nonlinearities , and the resulting dynamics ( see Section 5 ). Finally , the paper concludes with the case for the need of modeling as a scientific tool ( see Section 6 ) and final considerations ( see Section 7 ).
I - Information Theory and Measures of Complexity
The information theory discussed in
this section brings original elements of early computational efforts and the principles posed by Claude Shannon ( 1948 ). Information in this context superimposes the notions of entropy and uncertainty . In fact , information may be considered a measure of complexity of a system .
An original concept put forward by Weaver ( 1948 ) is that of organized complexity . The concept is used to describe problems that were neither about two or three variables — thus , easily managed — nor about a huge number of variables — also , handled easily through statistical mechanics and probability theory . Organized complexity would contemplate those problems that have a high number of interacting variables that are not easily manageable , but that at the same time is not so large as to allow the
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