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Nelson Fernández edited Measures.tex
almost 11 years ago
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\section{Measures}
The measures apply in this
paper, paper have recently
proposed developed and compared with other previously
find proposed in
the literature (Fernández et al., 2012; Gershenson and Fernández, 2012);
More more refined
measures measures, based on
axioms axioms, have been presented in Fernández et al., (2013).
In general, Emergence refers to properties of a phenomenon that are present now and were not before. If we suppose these properties as non-trivial, we could say it is harder now than before to reproduce the
phenomenon. In other words, there is emergence in a phenomenon
when this phenomenon is producing information and, if we recall, Shannon proposed a quantity which measures how much information was “produced” by a process.Therefore, we can say that the emergence is the same as the Shannon’s information {\it I}. Thus {\it \E=I}
As we have mentioned, complexity comes from {\it Latin} plexus, which means interwoven. Thus, something complex is difficult to separate. This means that its components are interdependent, Self-organization has been correlated with an increase in order, i.e.
their future a reduction of entropy (Gershenson and Heylighen, 2003). If emergence implies an increase of information, which is
partly determined by their interactions. Thus, studying the components in isolation—as reductionistic approaches attempt—is not sufficient analogous to
describe entropy and disorder, self-organization should be anti-correlated with emergence. We propose as the
dynamics of complex systems. measure {\it S = 1 − I = 1 − E}.
As measure we can define complexity C as the balance between change (chaos) and stability (order). We have just defined such measures: emergence and self-organization. Hence we propose:
{\it C = 4 · E ·
S. S.}. Where the constant 4 is added to normalize the measure to [0, 1]