The Principles of Complexity

This project, supported by the John Templeton Foundation, addresses fundamental questions concerning the nature of hidden regularities in complex systems across the biological and social realms. The larger goal of the project is to initiate and promote a fundamentally new research program in complexity with the potential to generate new quantitative frameworks with broad application, concepts of general scientific and social value, and educational programs that will exist at the intersection of the disciplines.

The three large-scale organized research projects that constitute the core of this project are the examination of: (1) the evolution of complexity and intelligence on earth (more); (2) the scaling laws that pervade complex biological and social phenomena with specific reference to urban life (more); and (3) universal patterns in the emergence of complex societies (more). All of our activities seek to reveal hidden principles of organization that could potentially unify many complex phenomena from brains to societies. The recent revolution in data collection and computational power, when combined with strong mathematical foundations, is allowing us to probe complex phenomena in radically new ways.

Each of these core projects is seeking to answer fundamental questions. All three projects actively engage with problems associated with scaling -- how does increasing complexity relate to increasing densities of genes, individuals and societies. All projects seek to understand the interconnectedness between competition, cooperation and increasingly efficient and robust means of acquiring and communicating information about these resources. And all projects consider the crucial role of multiple temporal and spatial scales in complex systems, why hierarchical and modular structure is ubiquitous, how mechanisms have evolved to exploit rapid changes in their surroundings, and how adaptive systems have found a way of overcoming and exploiting the rapid turnaround and loss of their most elementary components.

The integration of classical physical concepts of energy and matter with the concepts of information, emergence, and complexity has long been sought, but for want of empirical richness has remained limited in its progress. This situation is rapidly changing, and this project seeks to address three areas of research where the Santa Fe Institute has a proven track record of excellence and where new research and analyses are likely to make a real difference.

The outcomes of this project span potential tectonic shifts in the way we organize knowledge, questioning the current preference for grouping together ideas based on the area of their application (biology, physics, economics, etc.), and replacing this with grouping together ideas based on common hidden mechanisms and dynamics, such as common principles of scaling, network structures and modularity, and mechanisms of information acquisition and transfer. This is already happening in the universities (physicists in biology, biologists in economics, etc.), but slowly and without a strong mechanism of support. With the support of the John Templeton Foundation, the Santa Fe Institute is playing a pivotal role in stimulating this process of change, significantly broadening the approach to complex phenomena from simple interdisciplinary strategies to a visionary transdisciplinary approach with new insights into heretofore hidden regularities in complex processes at various scales.

This project includes a substantially revised curriculum at the undergraduate level in complex systems. SFI is amassing a significant database of complex systems curricula with a view to creating what we are calling the Complexity Explorer (more), which a) offers online tools to provide educators with a platform that can generate curricula in real time based on their individual weights and preferences; b) supplies a core set of ideas and references; c) and generates from a large database relevant material from our archive of digital education media. The Complexity Explorer will be made available to schools and colleges and to the general public.

The outputs of this project will have impact well beyond the scientific and education communities. SFI has works with many forward looking, entrepreneurial companies including Boeing, Cisco Systems, Google, eBay, Inc, Intel, Steelcase and Fidelity, who have formed partnerships with the Institute to explore the application of complex systems science to applied research projects, the reorganization of companies, and the future of markets. SFI makes available its most relevant findings to these communities, who then actively apply or extend the ideas and tools provided by the SFI community. Some recent SFI insights of great interest to the business community have included new approaches to the calculation of systemic risk and design and control of large-scale, distributed software systems.

These projects also will generate bridges to the humanities, by emphasizing a nonreductive approach to emergent phenomena, through the use of new ideas and computational models, that could catalyze a rapprochement between the two cultures. These projects have the promise of illuminating many undiscovered regularities in our world and addressing several big questions facing the world of complexity science. They will help the general public and decision-makers alike better appreciate the systemic contexts of the very difficult problems that confront them as they attempt to navigate through what seem to be incredibly unstable social situations. Such theoretical advances could provide new ways of thinking about long-term planning for seemingly intractable and unpredictable quandaries such as rapid growth, the interface between people and machines, and how to live in a super-connected world across the globe in the 21st century.

The Project

The dominant approach to understanding the physical world has been to seek to discover the fundamental constituents of matter through a process of reductionism. The Nobel laureate Steven Weinberg describes it thus: “[A]ll of nature is the way it is…because of simple universal laws, to which all other scientific laws may in some sense be reduced…” The biological and social sciences have been developing along different lines however. These sciences have proceeded by cataloguing and describing the multitude of events, cases, and species on our own planet. Rather than contemplate ensembles -- those common features shared by many organisms -- these sciences have regularly collected and focused on details.

There is one notable exception: the Darwinian revolution represents the clearest and perhaps unique example of an attempt at a unified theory for adaptive phenomena -- from biology through to culture, but one that is not grounded in physical and chemical theory. Building on the deep homologies that exist among all living species, Darwin sought to explain adaptive forms of order in terms of the principle of natural selection. The most notable and significant missing ingredient in the theory of selection is some means of explaining why and how the biotic and cultural domains have evolved into such a range of complex forms. Why the earth is in possession of birds and not just bacteria. From the perspective of selection these are all similar, and all fulfill the essential requirements of the Darwinian theory posed in terms of a diversity of locally adapted replicators. There has been a search to find new and complementary ideas that make the question of complexity more tractable: to take us beyond a theory of diversity, to theories that connect the abiotic and biotic domains (Davies 1999)(Rees 2002, 2010) and might help explain why it is that one species, Homo Sapiens, was able to construct a theory of evolution in the first place.

The Complexity Revolution

Subsequent to Darwin, we have witnessed the creation of entirely new theoretical frameworks for macroscopic systems (Aubin and Saari 1994), including the theory of computation, thermodynamics and nonlinear statistical mechanics, learning theory, and information theory. We have more recently compiled rich databases spanning observations in the biological and social sciences (genomic, proteomic, gene expression and protein structure databases in biology, and demographic, textual and economic databases in the social sciences). Through these we have begun to uncover hidden regularities that span biology and culture, including ubiquitous quarter-power scaling laws, characteristic network structures including short average geodesics, power laws of connectivity, and overrepresented motifs. In adaptive systems we have found common mechanisms of information coding and transmission, including common block codes (e.g. genetic code), and widespread mechanisms of computation and cognition (in operons and nervous systems), including approximate Bayesian inference, compressed sensing, and information maximization.

These patterns exist at multiple scales of time and space (Levin 2006), and in their generality are comparable to universal mechanisms discovered in the physical sciences at only the lowest levels of organization. Unlike physical phenomena, these complex phenomena cannot be explained purely in terms of our existing physical theories of, for example, quantum mechanics, electromagnetism, and condensed matter. This insight was made by Schroedinger when he wrote: “[L]iving matter, while not eluding the 'laws of physics'…is likely to involve 'other laws…,' hitherto unknown, which…will form just as integral a part of [its] science.” And later more forcibly by SFI faculty member and Nobel laureate Phil Anderson: “…the ability to reduce everything to simple fundamental laws…implies the ability to start from those laws and reconstruct the universe. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. [T]he whole becomes…very different from the sum of its parts.”

Complex phenomena require a new approach to unification based on emergent principles of organization (Weaver 1948, Simon 1999). Complex systems are all characterized by adaptive behavior emerging from the coordinated, collective dynamics of large populations of agents (Levin 2005, May 1986). Agents can be molecules in cells, cells in bodies, individuals in societies and computers in networks. All complex systems form natural hierarchies consisting of modular structures capable of achieving high degrees of functional differentiation and specialization. A range of characteristic time and space scales allows us to classify these hierarchies. The insights of the renormalization group are important for this problem as they help to explain patterns such as scale invariance when we consider successively inclusive levels of organization. Measures of complexity seek to reveal either dynamical or structural characteristics of hierarchical systems and afford us with some means of comparison. For example, the concept of multi-information arises as a natural measure of complexity when considering stochastic interdependence on a product space. Theories for the evolution of complex systems seek to explain why and how systems characterized by these properties come into existence, and how they are able to persist in the face of great uncertainty and noise (Simon 1962). Mechanisms of robustness such as redundancy, neutrality, and non-linear feedback all play an important role in ensuring the persistence of complex systems, and minimizing the odds of them becoming chaotic and uncontrollable. (Strogatz 1994, 2003)

This ambitious project explores the principles of complex systems spanning biological and cultural phenomena. Building on successful on-going research projects, we are conducting this project under three study foci, all of which utilize large bodies of data and make use of ideas from thermodynamics, evolutionary dynamics, and information theory, complementing these with new ideas from non-linear statistical mechanics, discrete mathematics, and computer science.

Each project seeks to discover new principles that can generate, in the language of Poincaré, a “harmony of the diverse parts.” In other words, we seek new theories and tools for complex systems and in so doing address some of the Big Questions facing the world today. The three projects were chosen to most effectively span the space of complexity science: from the origin of biological complexity, the fundamental effective laws for complex systems, and the emergence of complexity in human societies. All three projects have at their core the relationship between complexity and scaling, efficient resource allocation and distribution across networks, and mechanisms of information transfer (communication) and information processing (computation). These common themes shall provide ongoing links that connect the projects and promote common methodological foundations.

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