by Judith Curry
In many large ensembles, the property of the system as a whole cannot be understood from studying the individual entities alone. The past decade has seen important progress in our fundamental understanding of what such seemingly disparate ‘complex systems’ have in common; some of these advances are surveyed here.
Nature Physics – Insights has a special issue on Complexity (h/t David Hagen). The papers are publicly available until Jan 31. From the table of contents:
- Editorial: Complexity, by Andreas Trabesinger
- Commentary: The Network Takeover, by Albert Laszlo-Barabasi
- Between Order and Chaos, by James Crutchfield
- Communities, Modules, and Large-scale Structures in Networks, M.E.J. Newman
- Modeling Dynamical Processes in Complex Socio-Technical Systems, by Alessandro Vespignani
- Networks Formed From Independent Networks, by Jianxi Gao et al.
I’ve selected the [article complexity network takeover] by Albert Laszlo Barabasi to highlight here:
Reductionism, as a paradigm, is expired, and complexity, as a field, is tired. Data-based mathematical models of complex systems are offering a fresh perspective, rapidly developing into a new discipline: network science.
Reports of the death of reductionism are greatly exaggerated. It is so ingrained in our thinking that if one day some magical force should make us all forget it, we would promptly have to reinvent it. The real worry is not with reductionism, which, as a paradigm and tool, is rather useful. It is necessary, but no longer sufficient.
[A]n increasing number of the big questions of contemporary science are rooted in the same problem: we hit the limits of reductionism. No need to mount a defence of it. Instead, we need to tackle the real question in front of us: complexity.
[D]ecades of research on complexity were driven by big, sweeping theoretical ideas, inspired by toy models and differential equations that ultimately failed to deliver. Think synergetics and its slave modes; think chaos theory, ultimately telling us more about unpredictability than how to predict nonlinear systems; think self-organized criticality, a sweeping collection of scaling ideas squeezed into a sand pile; think fractals, hailed once as the source of all answers to the problems of pattern formation. We learned a lot, but achieved little: our tools failed to keep up with the shifting challenges that complex systems pose.
Yet something has changed in the past few years. The driving force behind this change can be condensed into a single word: data. As scientists sift through these mountains of data, we are witnessing an increasing awareness that if we are to tackle complexity, the tools to do so are being born right now, in front of our eyes. The field that benefited most from this data windfall is often called network theory, and it is fundamentally reshaping our approach to complexity.
Born at the twilight of the twentieth century, network theory aims to understand the origins and characteristics of networks that hold together the components in various complex systems. By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, it led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour.
With its deep empirical basis and its host of analytical and algorithmic tools, today network theory is indispensible in the study of complex systems. [Q]uestion by question and system by system, network science has hijacked complexity research. Reductionism deconstructed complex systems, bringing us a theory of individual nodes and links. Network theory is painstakingly reassembling them, helping us to see the whole again. One thing is increasingly clear: no theory of the cell, of social media or of the Internet can ignore the profound network effects that their interconnectedness cause. Therefore, if we are ever to have a theory of complexity, it will sit on the shoulders of network theory.
JC comment: On a previous post, I presented the complexity challenge facing climate science in the following way:
Complexity and a systems approach is becoming a necessary way of understanding natural systems. A complex system exhibits behavior not obvious from the properties of its individual components, whereby larger scales of organization influence smaller ones and structure at all scales is influenced by feedback loops among the structures. Complex systems are studied using information theory and computer simulation models. The epistemology of computer simulations of complex systems is a new and active area research among scientists, philosophers, and the artificial intelligence community. How to reason about the complex climate system and its computer simulations is not simple or obvious.
The tools we are currently using seem inadequate to understand the complex climate system. We have massive amounts of data (particularly global satellite data sets) that are being put to little use in understanding the climate system or in evaluating models. Ever increasing degrees of freedom in climate models has surpassed our ability to understand how to reason about and draw inferences from climate model output. New insights are needed, and network theory may be one such source of new insights.