Arguments for or against a trend in the evolution of complexity are weakened by the lack of an unambiguous definition of complexity. Such definitions abound for both dynamical systems and biological organisms, but have drawbacks of either a conceptual or a practical nature. Physical complexity, a measure based on automata theory and information theory, is a simple and intuitive measure of the amount of information that an organism stores, in its genome, about the environment in which it evolves. It is (...) argued that physical complexity must increase in molecular evolution of asexual organisms in a single niche if the environment does not change, due to natural selection. It is possible that complexity decreases in co‐evolving systems as well as at high mutation rates, in sexual populations, and in time‐dependent landscapes. However, it is reasoned that these factors usually help, rather than hinder, the evolution of complexity, and that a theory of physical complexity for co‐evolving species will reveal an overall trend towards higher complexity in biological evolution. BioEssays 24:1085–1094, 2002. © 2002 Wiley‐Periodicals, Inc. (shrink)

This article analyses 2001 in terms of what I term paleofuturism. Fusing deep future and deep past, this cyclical figure reconciles rational machinic intelligence with diverse repressed temporal layers: archaic cultures, the embryonic state of individuals, and bygone biological and geological eras. In 2001, paleofuturism is nourished by Nietzsche’s Übermensch of the future, reborn as a child, and by Jungian ideas of individuation, the reconciliation with the shadow of the collective unconscious that leads to the black cosmos itself. Further paleofuturist (...) contexts for 2001 are explored in the so-called “ancient astronaut thesis” of science fiction, speculative science, and pseudo-science. Finally, in minimalism and earth art of the late 1960s we meet a structural parallel to 2001’s bypassing of the organic human body, one that bridges the inorganic entropic realities of deep future and deep past. (shrink)

Complex systems research is becoming ever more important in both the natural and social sciences. It is commonly implied that there is such a thing as a complex system, different examples of which are studied across many disciplines. However, there is no concise definition of a complex system, let alone a definition on which all scientists agree. We review various attempts to characterize a complex system, and consider a core set of features that are widely associated with complex systems in (...) the literature and by those in the field. We argue that some of these features are neither necessary nor sufficient for complexity, and that some of them are too vague or confused to be of any analytical use. In order to bring mathematical rigour to the issue we then review some standard measures of complexity from the scientific literature, and offer a taxonomy for them, before arguing that the one that best captures the qualitative notion of the order produced by complex systems is that of the Statistical Complexity. Finally, we offer our own list of necessary conditions as a characterization of complexity. These conditions are qualitative and may not be jointly sufficient for complexity. We close with some suggestions for future work. (shrink)

Einstein’s razor, a corollary of Ockham’s razor, is often paraphrased as follows: make everything as simple as possible, but not simpler. This rule of thumb describes the challenge that designers of a legal system face—to craft simple laws that produce desired ends, but not to pursue simplicity so far as to undermine those ends. Complexity, simplicity’s inverse, taxes cognition and increases the likelihood of suboptimal decisions. In addition, unnecessary legal complexity can drive a misallocation of human capital toward comprehending and (...) complying with legal rules and away from other productive ends. While many scholars have offered descriptive accounts or theoretical models of legal complexity, most empirical research to date has been limited to simple measures of size, such as the number of pages in a bill. No extant research rigorously applies a meaningful model to real data. As a consequence, we have no reliable means to determine whether a new bill, regulation, order, or precedent substantially effects legal complexity. In this paper, we begin to address this need by developing a proposed empirical framework for measuring relative legal complexity. This framework is based on “knowledge acquisition”, an approach at the intersection of psychology and computer science, which can take into account the structure, language, and interdependence of law. We then demonstrate the descriptive value of this framework by applying it to the U.S. Code’s Titles, scoring and ranking them by their relative complexity. We measure various features of a title including its structural size, the net flow of its intra-title citations and its linguistic entropy. Our framework is flexible, intuitive, and transparent, and we offer this approach as a first step in developing a practical methodology for assessing legal complexity. (shrink)

The intriguing recent suggestion of Tegmark that the universe—contrary to all our experiences and expectations—contains only a small amount of information due to an extremely high degree of internal symmetry is critically examined. It is shown that there are several physical processes, notably Hawking evaporation of black holes and non-zero decoherence time effects described by Plaga, as well as thought experiments of Deutsch and Tegmark himself, which can be construed as arguments against the low-information universe hypothesis. Some ramifications for both (...) quantum mechanics and cosmology are briefly discussed. (shrink)

Even though complexity is a concept that is ubiquitously used by biologists and philosophers of biology, it is rarely made precise. I argue that a clarification of the concept is neither trivial nor unachievable, and I propose a unifying framework based on the technical notion of “effective complexity” that allows me to do justice to conflicting intuitions about biological complexity, while taking into account several distinctions in the usage of the concept that are often overlooked. In particular, I propose a (...) distinction between two kinds of complexity, “mechanical” and “emergent”, which can be understood as different ways of relating the effective complexity of mechanisms and of behaviors in biological explanations. I illustrate the adequacy of this framework by discussing different attempts to understand intracellular organization in terms of pathways and networks. My framework provides a different way of thinking about recent philosophical debates, for example, on the difference between mechanistic and topological explanations and about the concept of emergence. Moreover, it can contribute to a proper assessment of metascientific arguments that invoke biological complexity. (shrink)

A short review of complexity research from the perspective of history and philosophy of biology is presented. Complexity and its emergence has scientific and metaphysical meanings. From its beginning, biology was a science of complex systems, but with the advent of electronic computing and the possibility of simulating mathematical models of complicated systems, new intuitions of complexity emerged, together with attempts to devise quantitative measures of complexity. But can we quantify the complex?

1.1 - Background - page 17 1.2 - The Style of Approach - page 18 1.3 - Motivation - page 19 1.4 - Style of Presentation - page 20 1.5 - Outline of the Thesis - page 21..

Complexity is heterogenous, involving nonlinearity, self-organisation, diversity, adaptive behaviour, among other things. It is therefore obviously worth asking whether purported measures of complexity measure aggregate phenomena, or individual aspects of complexity and if so which. This paper uses a recently developed rigorous framework for understanding complexity to answer this question about measurement. The approach is two-fold: find measures of individual aspects of complexity on the one hand, and explain measures of complexity on the other. We illustrate the conceptual framework of (...) complexity science and how it links the foundations to the practised science with examples from different scientific fields and of various aspects of complexity. Furthermore, we analyse a selection of purported measures of complexity that have found wide application and explain why and how they measure aspects of complexity. This work gives the reader a tool to take any existing measure of complexity and analyse it, and to take any feature of complexity and find the right measure for it. (shrink)