This link has been bookmarked by 12 people . It was first bookmarked on 03 Aug 2006, by Bill H.
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08 Feb 14
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23 Oct 12
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Abhay BothraAnnotated link http://www.diigo.com/bookmark/http://pespmc1.vub.ac.be/COMPLEXI.html
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Edmonds (1996)
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complexity necessarily depends on the language that is used to model the system
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two or more components, which are joined in such a way that it is difficult to separate them
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duality between parts which are at the same time distinct and connected
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The aspects of distinction and connection determine two dimensions characterizing complexity
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Distinction corresponds to variety, to heterogeneity, to the fact that different parts of the complex behave differently
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Connection corresponds to constraint, to redundancy, to the fact that different parts are not independent, but that the knowledge of one part allows the determination of features of the other parts
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fashionable expression, "on the edge of chaos".
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Complexity can then be characterized by lack of symmetry or
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, by the fact that no part or aspect of a complex entitity can provide sufficient information to actually or statistically predict the properties of the others parts.
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symmetry breaking
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. A fractal or self-similar shape, on the other hand, has infinite scale extension: however deeply we zoom in, we will always find the same recurrent structure. A fractal is invariant under a discrete group of scale transformations, and is as such orderly or symmetric on the scale dimension
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The fractal is somewhat more complex than the triangle, in the same sense that a crystal is more complex than a single molecule: both consist of a multiplicity of parts or levels, but these parts are completely similar.
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complexity increases when the variety (distinction), and dependency (connection) of parts or aspects increase, and this in several dimensions
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time or dynamics
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spatial scale
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temporal or dynamical scale
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In order to show that complexity has increased overall, it suffices to show, that - all other things being equal - variety and/or connection have increased in at least one dimension.
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The process of increase of variety may be called differentiation, the process of increase in the number or strength of connections may be called integration
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That degree of independence will be determined by the "objective" complexity of the system
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02 Jan 10
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15 Dec 09
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28 May 07
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03 Aug 06
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The aspects of distinction and connection determine two dimensions characterizing complexity. Distinction corresponds to variety, to heterogeneity, to the fact that different parts of the complex behave differently. Connection corresponds to constraint, to redundancy, to the fact that different parts are not independent, but that the knowledge of one part allows the determination of features of the other parts. Distinction leads in the limit to disorder, chaos or entropy, like in a gas, where the position of any gas molecule is completely independent of the position of the other molecules. Connection leads to order or negentropy, like in a perfect crystal, where the position of a molecule is completely determined by the positions of the neighbouring molecules to which it is bound. Complexity can only exist if both aspects are present: neither perfect disorder (which can be described statistically through the law of large numbers), nor perfect order (which can be described by traditional deterministic methods) are complex. It thus can be said to be situated in between order and disorder, or, using a recently fashionable expression, "on the edge of chaos".
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We may conclude that complexity increases when the variety (distinction), and dependency (connection) of parts or aspects increase, and this in several dimensions. These include at least the ordinary 3 dimensions of spatial, geometrical structure, the dimension of spatial scale, the dimension of time or dynamics, and the dimension of temporal or dynamical scale. In order to show that complexity has increased overall, it suffices to show, that - all other things being equal - variety and/or connection have increased in at least one dimension.
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The process of increase of variety may be called differentiation, the process of increase in the number or strength of connections may be called integration. We will now show that evolution automatically produces differentiation and integration, and this at least along the dimensions of space, spatial scale, time and temporal scale.
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17 Oct 05
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23 Apr 05
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