David Pines (Minesh Bacrania Photography)

By David Pines, Co-Founder in Residence, Santa Fe Institute

When electrons or atoms or individuals or societies interact with one another or their environment, the collective behavior of the whole is different from that of its parts. We call this resulting behavior emergent. Emergence thus refers to collective phenomena or behaviors in complex adaptive systems that are not present in their individual parts.

Examples of emergent behavior are everywhere around us, from birds flocking, fireflies synchronizing, ants colonizing, fish schooling, individuals self-organizing into neighborhoods in cities – all with no leaders or central control – to the Big Bang, the formation of galaxies and stars and planets, the evolution of life on earth from its origins until now, the folding of proteins, the assembly of cells, the crystallization of atoms in a liquid, the superconductivity of electrons in some metals, the changing global climate, or the development of consciousness in an infant.

Indeed, we live in an emergent universe in which it is difficult, if not impossible, to identify any existing interesting scientific problem or study any social or economic behavior that is not emergent.

From complex interactions of matter and energy arise the emergent properties of our universe, including the formation of stars such as this cosmic nebula with a neutron star. (Dreamstime.com)

From emergence to complexity to emergence

The Santa Fe Institute began exploring emergent behavior in science and society at its 1984 founding workshops, “Emerging Syntheses in Science,” during which every speaker dealt with an aspect of emergent behavior as well as the search for the organizing principles that bring about that behavior [1]. However, in the early days of SFI, SFI’s scientists often focused on defining and understanding the ways these systems were complex, rather than focusing on the organizing principles responsible for the emergent behavior these systems exhibited. Indeed, some members of the Institute’s growing scientific community dreamed of creating a unified science of complexity through which complexity itself could be defined and quantified – and thus classify complex systems in some kind of grand hierarchical schema.

In 1993 SFI held a major workshop to define complex adaptive systems and assess the status of its initial quest for a science of complexity. As the title of the resulting proceedings – “Complexity: Metaphors, Models, and Reality” – suggests, in the course of that workshop the dream of a unified theory of complexity was abandoned [2]. As it turns out, we might have heeded our friend, the great mathematician Stanislaw Ulam, who, prior to his death in 1984 just as the Institute was forming, had dismissed the predecessor of complexity science, nonlinear science, as “the study of non-elephants” – by which he meant that nonlinear is not a useful descriptor because everything is nonlinear (a.k.a. complex). By the end of the workshop the participants agreed that while complexity is difficult to define, and that there can be no unified science of complexity, it is highly useful to devise models of a wide variety of systems and ask to what extent the ideas behind a model that describes complex behavior in one system might be applicable to understanding another system.

In arriving at this realization, we were endorsing the pursuit of emergence as a unifying theme for science at SFI – but without using the language of emergence. To paraphrase the character M. Jourdain in Molière’s Le Bourgeois Gentilhomme (1670) – who remarks, “Good heavens! For more than forty years I have been speaking prose without knowing it” – we were studying emergent behavior in complex adaptive systems without being explicit about doing so.

Flocking, the collective motion of many birds in flight, is an emergent behavior arising from individuals following simple rules without central coordination or leadership.

But our lexicon began to change within a few years. In what was perhaps the first general-audience book to focus on emergent behavior, Emergence: From Chaos to Order (Helix Books, 1998), John Holland, one of SFI’s early intellectual leaders, wrote about systems (e.g. games, simple molecules, etc.) in which the organizing principles responsible for emergent behavior are a set of comparatively simple rules. His book was soon followed by The Emergence of Everything: How the World Became Complex (Oxford University Press, 2002), in which another early SFI intellectual leader, Harold Morowitz, addressed emergent behavior from the perspective of a theoretical biologist. He considered systems for which the rules are not yet known, and wrote about emergence in nature, from the Big Bang to the emergence of humans on earth and the development of agriculture.

Still another SFI perspective on emergence, that of the theoretical physicist, can be found in two articles addressed to a general scientific audience. In a remarkably prescient article, “More Is Different” [3], written more than a decade before SFI’s founding, Philip Anderson (who spoke at our 1984 founding workshops and later co-chaired, with fellow Nobel laureate Ken Arrow, the Institute’s initial foray into economics) questioned the way fundamental research was characterized by many leading scientists. He also discussed the role of hierarchies and symmetry in complex systems from what we would today describe as an emergent perspective. A companion piece, “The Theory of Everything” [4], was written 28 years later by Stanford physicist R.B. Laughlin and myself. Both perspectives emphasized the limitations of a reductionist approach to complex systems in which one seeks to explain them by studying their components in ever-finer detail [5].

Laughlin and I pointed out that the dream of some 20th century reductionists – discovering a “Theory of Everything” whose equations would enable one to derive all properties of matter – is hollow, and that such ambitions should be replaced by a focus on emergent behavior. Richard Feynman famously said “Life is nothing but the wiggling and jiggling of atoms.” We argued that this perspective does not tell us how atoms gave rise to LUCA, the last universal ancestor that is the progenitor of living matter, to say nothing of the subsequent 3.5 billion years of evolution.

Although we know the simple equations that govern our immediate world, we find that these formulas are almost useless in telling us about the emergent behavior we encounter, whether we are working on a problem at the frontiers of science or seeking to understand and change familial or societal behavior. In concluding our article, we wrote:

“The central task of theoretical physics in our time is no longer to write down the ultimate equations, but rather to catalogue and understand emergent behavior in its many guises, including potentially life itself. We call this physics of the next [21st] century the study of complex adaptive matter. For better or worse, we are now witnessing a transition from the science of the past, so intimately linked to reductionism, to the study of complex adaptive matter, firmly based in experiment, with its hope for providing a jumping-off point for new discoveries, new concepts, and new wisdom.”

Emergence as a unifying paradigm

What replaces the reductionist path to understanding emergent behavior in the physical, biological, and social sciences? The short answer is a new starting point: recognizing that understanding emergent behavior requires a focus on the emergent collective properties that characterize the system as a whole and a search for their origin. It means identifying emergent collective patterns and regularities through experiment or observation, and then devising models that embody candidate collective organizing concepts and principles that might explain them. These patterns, principles, and models are the gateways to emergent behavior observed in the system under study. Only through studying these gateways can we hope to grasp emergent behaviors on a grand, unifying scale.

Nanowires, like these grown by depositing atoms on a silicon crystal, are among new manmade materials with emergent properties. (U.S. National Institute of Standards and Technology)

For the physicist or chemist studying emergent electronic behavior in quantum matter or turbulence in fluids, the gateways might include growing and studying new materials and developing new probes to measure fluctuations that might disclose universal scaling behavior or new coherent and possibly competing ordered states. The candidate organizing concepts that accompany these gateways often include introducing effective fields to describe emergent interactions, and can include the possibility of protected behavior that is independent of detail and governed by higher organizing principles.

For the biologist, biological physicist, or ecologist studying living systems, the collective components begin with proteins, neurons, or species and go on to cells, brains, and ecological dysfunction. The candidate organizing concepts include self-organization, energy landscapes, chemical motors that supply energy, and above all, evolution and replication – as biological systems are often far from equilibrium. Their study is made even more difficult because evolution has fine tuned earlier organizing principles. Thus, what we can observe is often the remnants of many interacting evolutionary processes.

The scientist studying human and animal behavior or social and economic systems searches for patterns in human development, societal behavior, and in economic and urban data. Candidate organizing concepts include self-organization into groups/communities/societies and the role played by environment – be it climate change, new technology, or societal regulations – in bringing about emergent behavior. The tools for that study often include an approach pioneered at SFI, agent-based and group-based modeling.

The scientific strategies employed by the physicist, biologist, ecologist, cognitive scientist, and archeologist are thus quite similar:

· Use experiment or observation to identify emergent patterns of behavior in the system as a whole.

· Decide what might be the most important connections or interactions between objects, individuals, or groups.

· Construct and solve a simple model that incorporates these connections into organizing concepts that might explain the observed emergent behavior. (In so doing, it is often helpful to consider organizing concepts used in models that have previously been shown to explain emergent behavior in other systems or fields.)

· Compare your results and predictions with experiment or observation.