What is complex systems science?

It has been the great triumph of the sciences to find consistent means of studying phenomena hidden by both space and time, overcoming the limits of cognition and material culture. To hide in space means that phenomena lie beyond the scope of our everyday senses because they are either too small or too distant to be detected without amplification. Things can be hidden in time by being too fast for us to perceive or too slow for a single lifetime to encompass.

The scientific method is the portmanteau of instruments, formalisms, and experimental practices that succeed in discovering basic mechanisms despite the limitations of individual intelligence.

There are, however, on this planet, phenomena that are hidden in plain sight. These are the phenomena that we study as complex systems: the convoluted exhibitions of the adaptive world — from cells to societies. Examples of these complex systems include cities, economies, civilizations, the nervous system, the Internet, and ecosystems.

Paradoxically, the complex world is one that we can, in many senses, perceive and measure directly. Unlike distant stars or nearby minerals that require a significant increase in optical capability to arrive at insights into their elementary properties, behavior — both individual and collective — seems to present itself in ways that can be investigated rather modestly through observation or experiment.

But the way in which complex phenomena are hidden, beyond masking by space and time, is through nonlinearity, randomness, collective dynamics, hierarchy, and emergence — a deck of attributes that have proved ill-suited to our intuitive and augmented abilities to grasp and to comprehend.

Over the course of thirty-five years, the Santa Fe Institute has been looking into this proximal, near-invisible reality, working in highly diverse, nondisciplinary teams to invent new concepts to render up complex reality to science; searching for order in the complexity of evolving worlds.

—David Krakauer, President
 Santa Fe Institute

Adapted from Worlds Hidden in Plain Sight (SFI Press, 2019)

Books

Less technical

Complexity: The Emerging Science at the Edge of Order and Chaos
M. Mitchell Waldrop (1993)

The classic popular science book that introduced SFI and the sciences of complexity to the general public. Still a highly enjoyable read, it profiles the people behind the science.

 

Chaos: Making a New Science
J. Gleick (Penguin, 1988)

The highly acclaimed popular science book that introduced complexity's "cousins," chaos and nonlinear dynamical systems, to the general public. It also features several scientists currently or formerly associated with SFI.

 

Complexity: A Guided Tour
M. Mitchell (Oxford University Press, 2009)

A wonderful introduction to complexity research by SFI Davis Professor Melanie Mitchell, suitable for both scientists and educated non-experts. A very readable book that also became the first online course in complexity, for SFI's online courses on Complexity Explorer.

 

Complexity: A Very Short Introduction
J. H. Holland (Oxford University Press, 2014)

Key attributes, elements, examples, and frameworks of complexity, as described by one of the giants of the field.

 

A Crude Look at the Whole: The Science of Complex Systems in Business, Life, and Society
J.H. Miller (Basic Books, 2016)

A popular description of classic complex systems phenomena by SFI External Professor and Science Board member John Miller, with a focus on how insights from complexity science could be applied in social systems and economics.

 

Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies
G. West (Penguin, 2017)

About the universal scaling laws in biology and in man-made living systems such as cities and companies. A unique and acclaimed popular science book by SFI Distinguished Shannan Professor Geoffrey West.

 

Worlds Hidden in Plain Sight
D. Krakauer (SFI Press, 2017)

A collection of first-person essays on complex systems, authored by the scientists who have been pioneering new methods to understand them. Edited by David Krakauer, SFI President and William H. Miller Professor of Complex Systems.

 

More technical

Exploring Complexity: An Introduction
G. Nicolis and I. Prigogine (W.H. Freeman, 1989)

One of the first textbooks on complexity science, co-authored by Nobel Laureate Ilya Prigogine. Mostly written from a physics point of view (non-equilibrium and non-linear systems theory), but with clear explanations of all topics and terminology.

 

Complexity: Metaphors, Models, and Reality
G. A. Cowan, D. Pines and D. Meltzer (Avalon, 1994)

Proceedings from the first 10 years of complexity research. A rich collection of review and research papers by many of the scientists associated with SFI in the early days.

 

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
S. H. Strogatz (Avalon, 2000)

An introductory textbook on two central topics in complexity science, by former SFI External Professor Steven Strogatz (one of the best teachers on the topics).

Networks
M. Newman (Oxford University Press, 2010)

The standard textbook on everything related to networks, by SFI External Professor Mark Newman. Network science is a pillar for studying complex systems, and an offshoot of complex systems science.

 

Introduction to the Theory of Complex Systems
S. Thurner, R. Hanel and P. Klimek (Oxford University Press, 2018)

The most up-to-date textbook on complex systems, co-authored by SFI External Professor Stephan Thurner. It presents many foundational topics such as networks, scaling laws, evolution, and information theory, along with a complexity theory based on a universal statistical mechanism.

 

Foundational Papers in Complexity Science
Santa Fe Institute (SFI Press, Forthcoming)

A forthcoming collection of research papers that set the course for the science of complex systems. Follow the link above to view the table of contents.

 

Papers

More is Different
P. W. Anderson
Science 177:393-396, 1972

A very early paper about complexity by Nobel laureate and SFI co-founder Phil Anderson. It describes broken symmetry, emergence, and the hierarchical structure of science. It set a new course for complex systems science as a departure from reductionism.

 

What is Complexity?
M. Gell-Mann
Complexity 1:16-19, 1995

Remarks on simplicity and complexity by Nobel laureate and SFI co-founder Murray Gell-Mann, in the very first issue of the Complexity journal.

 

The Architecture of Complexity
H. A. Simon
Proceedings of the American Philosophical Society 106:467-482, 1962

Another very early paper about complexity and its hierarchical structure by Nobel laureate Herbert Simon.

Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets
S. A. Kauffman
Journal of Theoretical Biology 22:437-467, 1969

The introduction of random boolean networks by former SFI Professor Stuart Kauffman, which helped launch network-based complexity science.

The Evolution of Cooperation
R. Axelrod and W. D. Hamilton
Science 211:1390-1396, 1981

A groundbreaking paper introducing computer simulations based on game theory in evolutionary biology. It provides an explanation for the evolution of cooperation among selfish individuals.

The Evolution of Emergent Computation
J. P. Crutchfield and M. Mitchell
PNAS 92:10742-10746, 1995

An overview of the evolution of emergent computation in cellular automata, by SFI External Professor Jim Crutchfield and SFI Davis Professor Melanie Mitchell.

Studying Artificial Life with Cellular Automata
C. G. Langton
Physica D 22:120-149, 1986

Former SFI faculty member Chris Langton's early work on cellular automata, which led to a new field of research in artificial life (ALife).

Chaos
J. P. Crutchfield, J. D. Farmer, N. H. Packard and R. S. Shaw
Scientific American 254:46-57, 1986

"There is order in chaos," posits this overview article by some of the pioneers of chaos theory, including SFI external faculty members Jim Crutchfield, Doyne Farmer, and Norman Packard.

Punctuated Equilibrium and Criticality in a Simple Model of Evolution
P. Bak and K. Sneppen
Physical Review Letters 71:4083-4086, 1993

The introduction of a simple model for studying self-organized criticality, which formed the basis of many later models and studies, by Per Bak and Kim Sneppen.

Positive Feedbacks in the Economy
W. B. Arthur
Scientific American, February 1990, 92-99

A complex systems view of the economy by SFI External Professor Brian Arthur.

A General Model for the Origin of Allometric Scaling Laws in Biology
G. B. West, J. H. Brown and B. J. Enquist
Science 276:122-126, 1997

The groundbreaking paper by SFI's Geoffrey West, James Brown, and Brian Enquist which explains universal scaling laws (aka power laws) in biology.

Collective Dynamics of 'Small-World’ Networks
D. J. Watts and S. H. Strogatz
Nature 393:440–442, 1998

Another groundbreaking paper introducing a model for the well-known "six degrees of separation" phenomenon in social networks, by SFI associates Duncan Watts and Steven Strogatz.

Emergence of Scaling in Random Networks
A.L. Barabasi and R. Albert
Science 286:509-512, 1999

A nice overview paper on scaling in random networks, by some of the experts on the topic.

Emergent Computation: Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks
S. Forrest
Physica D 42:1-11, 1990

An introduction to the topic of emergent computation by SFI External Professor Stephanie Forrest.

Resource Letter CS-1: Complex Systems
M. Newman
American Journal of Physics 79:800, 2011

A working definition of complex systems that catalogs quantitative progress in understanding them, by SFI External Professor Mark Newman.

Universality and complexity in cellular phenomena
S. Wolfram 
Physica D 10:1-35, 1984

A landmark paper on cellular automata, which are in-silico models for biological evolution.