Effective Complexity: In Which Sense is It Informative?
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Effective Complexity: In Which Sense is It Informative? Esteban Céspedes1,2 · Miguel Fuentes3,4,5
© Springer Nature B.V. 2020
Abstract This work responds to a criticism of effective complexity made by James McAllister, according to which such a notion is not an appropriate measure for information content. Roughly, effective complexity is focused on the regularities of the data rather than on the whole data, as opposed to algorithmic complexity. McAllister’s argument shows that, because the set of relevant regularities for a given object is not unique, one cannot assign unique values of effective complexity to considered expressions and, therefore, that algorithmic complexity better serves as a measure of information than effective complexity. We accept that problem regarding uniqueness as McAllister presents it, but would not deny that if contexts could be defined appropriately, one could in principle find unique values of effective complexity. Considering this, effective complexity is informative not only regarding the entity being investigated but also regarding the context of investigation itself. Furthermore, we argue that effective complexity is an interesting epistemological concept that may be applied to better understand crucial issues related to context dependence such as theory choice and emergence. These applications are not available merely on the basis of algorithmic complexity. Keywords Effective complexity · Algorithmic complexity · Epistemic context · Emergence · Physical theory
1 Effective Complexity How is it possible to obtain information from very complex things? It seems harder, for example, to know what occurs in cities that are very complex than in small towns. But information hides not only in the complex. We can also ask: how is it possible to * Esteban Céspedes [email protected] Miguel Fuentes [email protected] 1
Instituto de Sistemas Complejos de Valparaíso, Artillería 470, 2360448 Valparaíso, Chile
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Instituto de Filosofía, Universidad de Valparaíso, Serrano 546, 2362415 Valparaíso, Chile
3
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
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Instituto de Investigaciones Filosóficas, Bulnes 642, 1176 Buenos Aires, Argentina
5
Facultad de Ingeniería y Tecnología, Universidad San Sebastián, Lota 2465, 7510157 Santiago, Chile
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E. Céspedes, M. Fuentes
obtain information from very simple things? It can also be hard to know what someone means if that person employs a few simple symbols to communicate. Considering this, it is crucial for epistemology in general and for any theory of information to analyze the relations between information and complexity. According to the notion of algorithmic complexity (also called Kolmogorov Complexity), the complexity of a string of digits or of an expression is equal to the length of the shortest algorithm that may generate it on the basis of a universal computer (Kolmogorov 1965; Chaitin 1969; Li and Vitányi 1997). The information content of such a string will be its algorithmic complexity.
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