I t is a common observation that complex systems have a nested or hierarchical structure: They consist of subsystems, which themselves consist of subsystems, and so on, until the simplest components we know, elementary particles. It is also generally accepted that the simpler, smaller components appeared before the more complex, composite systems. Thus, evolution tends to produce more complex systems, gradually adding more levels to the hierarchy. For example, elementary particles evolved subsequently into atoms, molecules, cells, multicellular organisms, and societies of organisms. These discrete steps, characterized by the emergence of a higher level of complexity, may be called “evolutionary transitions.” The logic behind this sequential complexification appears obvious: You can only build a higher order system from simpler systems after these building blocks have evolved themselves. The issue becomes more complicated when you start looking for the precise mechanisms behind these evolutionary transitions and try to understand which levels have appeared at what moment and why. In recent years, several authors have tried to tackle this issue. As we will see, their approaches are diverse, and their results are concomitantly different. Part of the reason for this incoherence is that these researchers have worked mostly in isolation: They come from different traditions, and their works hardly make reference to each other. This is understandable because the emergence of hierarchical levels is a preeminently multidisciplinary issue, involving at least physics, chemistry, biology, and sociology. Another reason for the lack of coherent results is that the problem is intrinsically difficult, involving a host of phenomena (e.g., the origin of life) about which we know very little, spanning an enormous range of scales and domains, and being in essence ill-defined (e.g., most authors cannot even agree about which levels to include in their hierarchy). In spite of these difficulties, some of the results are truly impressive, and there is enough similarity in the different conceptual frameworks to express the hope that cross-fertilization may lead to an integrated theory in a nottoo-far-away future. Given the diversity of approaches, it is worth trying to classify them. One basic classification distinguishes quantitative from qualitative approaches, whereas another one distinguishes “structural” approaches, which focus on subsystems embedded in supersystems, from “functional” approaches, which focus on levels of information processing or control (cf. Ref. [1]). The quantitative approaches are basically inductive: They gather numerical data about the different levels of complexity, such as the typical size, mass, or information content of a system at a given level and the time of its emergence; they then try to find regularities or “laws” that govern the relations between these parameters. A typical example of this approach is proposed by Max Pettersson in his book Complexity and Evolution [2]. In spite of this apparently scientific procedure, the limitations of the quantitative approach should be obvious. First, as Pettersson [2] notes about his results, such “laws” can only be descriptive, not predictive, because you cannot create a new level at will or even wait until one emerges. Second, the data from which these laws are induced are extremely limited: Most authors distinguish about nine levels, and it is very difficult to meaningfully state a “law” that applies to only nine COMPLEXITY AND EVOLUTION By Max Pettersson, Published by Cambridge University Press, Cambridge, UK, 1996 Reviews book & software
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