Abstract
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or mutual disagreement. Two are the main objectives of the present work: (i) to review some of the main approaches to complexity; and (ii) to suggest a cost-based approach that, to a great extent, can be understood as an integration of the several facets of complexity while keeping its meaning for humans in mind. More specifically, it is poised that complexity, an inherently relative and subjective concept, can be summarized as the cost of developing a model, plus the cost of its respective operation. As a consequence, complexity can vary along time and space. The proposal is illustrated respectively to several applications examples, including a real-data base situation.
Highlights
One of the most often mentioned terms in science currently is complexity
It should be kept in mind that, though we limited our discussion to just three possibilities, there is a virtually infinite number of alternatives, which contributes to making complexity even more complex
In the remainder of the present work, we aim at describing an approach to complexity that circumvents the problem that several of the other existing approaches of not being general enough, in the sense that counterexamples can often be found
Summary
One of the most often mentioned terms in science currently is complexity. Though we have an intuitive understanding of this concept, to the point of often being able to readily recognize if something is complex or not, it turns out that it is difficult to objectively define complexity (e.g. [1,2,3]). The alternative of proposing a definition and characterization of complexity purely from mathematical and physical considerations has proven to be rather difficult to be accommodated generally into the human common sense, as our simple discussion above has already illustrated These mathematical approaches are welcomed and fine in themselves, as they provide additional insights into more specific aspects of complexity. The approach to complexity developed in this work is aimed at trying to summarize as best, objective and quantitatively as possible its human connotation This has been achieved at the expense of obtaining a strict, fully accurate and objective mathematical definition. The suggested approach to complexity aims at achieving as much compatibility with its human connotation at the expense of a more strict mathematical definition which would probably incur in being too specific and not able to accommodate the fact that complexity as understood by humans can vary along time and space. Four case examples are discussed in order to better illustrate the proposed approach
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