Why is it called the Science of Complexity?

2018-03-03 Note: I plan to expand this as I read more and find those books that I hope will have what I am looking for to better understand and explain complexity. Consider this as ver 0.1, only a beginning. I have a lot of work ahead of me to get this into half decent shape which means a coherent narrative which it currently is not.

The story of the science of complexity is closely entwined with the story of the Santa Fe Institute. To understand the one you also need to understand the other.

The answer is fairly straightforward. In the book "Complexity" Mitchell Waldrop writes that after the first workshops in Santa Fe in 1984 it became apparent that everyone was dealing in some way with a "system composed of many, many "agents." ... the agents were constantly organizing and reorganizing themselves into larger structures through the clash of mutual accommodation and mutual rivalry. ... Complexity, in other words, was really a science of emergence." (Waldrop, p. 88) And on the following page we learn that George Cowan had decided to call this new science the science of complexity. "It seemed a much better canopy for everything we were doing than any other phrase we were using, including 'emerging syntheses'..." (Waldrop, p.89) This is how Waldrop understood it and in Cowan's memoir we are given the same story from Cowan's perspective.

The theme of the first meeting about the direction of the new institute that Cowan wanted to create was "Emerging Syntheses in Science" described as an exploration of the "territory at the interfaces between the conventional disciplines" (Cowan, p. 143). What name should be given to this new scientific frontier? "We struggled to find a term that would embrace their commonalities and settled on 'Complexity.' Later our mantra became "Complex Adaptive Systems (CAS)." (Cowan, p.144) Cowan then goes on in his memoir to discuss a paper by Warren Weaver (see attachment) that examined the relationship between science and complexity in the evolution of science, and the idea of organized complexity that Weaver proposed made quite an impression on him so it seemed that the word 'complexity' could serve as a big tent for his project because it was a word that all of the scientists at this first meeting had used, although with different meanings, but one that they could all agree on.

"In the most general dynamical terms, systems are complex when the differential equations that define their states at any given moment in time cannot be analytically solved. Simulated behaviors can be described by models that involve numerical computations, usually on computers, but precise predictions are not possible. Existing models don't simulate emergence, a term that means the whole is more than the sum of its parts." (Cowan, p. 144)

Complexity does not require a vast number of agents to be complex because the three-body problem ( ) defied solution and drove mathematicians and scientists to despair. Non-linear behavior is one very important part of complexity. Nonlinear phenomena have always been difficult mathematically and it was only with the advent of the computer that it became easier to explore them and their behavior, particularly their global behavior, using the ability of computers to create visualizations.

Complexity is about:

"COMPLEXITY This term means different things in different disciplines, and is not rigorously defined outside of a specific context. In general, the complexity of a system emerges from the interactions of its interrelated elements as opposed to the characteristics of those elements in and of themselves. Complexity science is the study of such emergent system behavior, and seeks to understand how the complex behavior of a whole system arises from its interacting parts. Complex behavior generally cannot be reduced to, or derived from, the sum of the behavior of the system's components." (Glossary entry at

What complexity science studies is complexity which is a term that is hard to define, as would be the case when using the second definition of complex. It is often described as something found on the border between chaos and order, having both form and structure enough to allow for the possibility of emergence, patterns that emerge from interactions where the sum of the whole is greater than the sum of the parts. Emergence runs counter to reductionism because reductionism cannot explain emergent phenomena by reaching deeper down into the constituent elements. The explanatory arrow does not always point down. And another thing about this phenomena is that there is no central intelligence or director coordinating the emergent activities but it is a decentralized system, a massively parallel computation using simple rules that produces the effect that could be flocking behavior or the behavior of economic markets described by Adam Smith's Invisible Hand.

"Chaos and complexity are chasing each other around in a circle trying to find out if they are the same or different." "Totally ordered over here.... Totally random over here." ... "Complexity happens somewhere in between." "The science of Complexity has to do with structure and order." (Lewin, Complexity, p. 10)

"You can only understand complex systems using computers, because they are highly nonlinear and are beyond stardard mathematical analysis. And, he (Chris Langton) said, so far few biologists are aware of complexity as it is understood at the Santa Fe Institute. 'If they were they'd probably think we're nuts." (Lewin,Complexity, p.11)

Melanie Mitchell maintains that complex systems share the following properties:

  1. Complex collective behavior
  2. Signalling and information processing
  3. Adaptation

And goes on to offer the following definition: A Complex System is a "system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution." (Mitchell, Complexity: A Guided Tour, pp.12-13)

Lorenz used a Royal McBee LGP-30 computer. Here is a YouTube vid of one warming up LGP-30 warm up
John Holland liked to use a Commodore that he programmed in hex, that is, he programmed in Assembler but did not use a compiler because he knew the opcodes so well from his earlier work at IBM. (??)
Mitchell Feigenbaum used an HP hand calculator
Benoist Mandelbrot and the IBM mainframes with punch cards and tractor feed printouts

To learn more about the Science of Complexity and also about the Santa Fe Institute I encourage you to visit their websites, the Sante Fe Institute where I find the working papers particularly interesting and the Complexity Explorer where free courses and tutorials are offered but they also welcome any and all contributions. It offers the opportunity to learn more about the science of complexity to anyone interested in learning regardless of background or education level although high school algebra and an open mind are recommended. The description of the various offerings will give you an idea of what you need to know to get the most out of them.

Another book that I am enjoy is "Think Complexity: Complexity Science and Computational Modeling 2nd Ed." by Allen Downey because it has examples of Python code for many of the models found in the Science of Complexity. It is one thing to read about complexity and another to be able to work with programs to explore it. The use of computers to explore nonlinear systems is an important part of the science of complexity and part of what made it possible. It is a good complement to the courses offered by Complexity Explorer.


Arthur, W. Brian. Increasing Returns and Path Dependence In the Economy. Univ. of Michigan Press, 1994.

Arthur, W. Brian. The Nature of Technology: What It is and How It Evolves. Free Press, 2009.

Arthur, W. Brian. Complexity and the Economy. Oxford Univ. Press, 2014.

Bak, Per. How Nature Works: The Science of Self-Organized Criticality. Copernicus, 1996.

Barabasi, Albert-Lazlo. Linked: The New Science of Networks. Perseus Publ., 2002.

Beinhocker, Eric D. The Origin of Wealth: Evolution, Complexity, and the Radical Remaking of Economics. Harvard Business School Press, 2006.

Bonabeau, Eric, Marco Dorigo and Guy Theraulaz. Swarm Intelligence: From Natural to Artificial Systems. Oxford Univ. Press, 1999.

Bruner, Robert F. and Carr, Sean D. The Panic of 1907 John Wiley & Sons, Inc, 2007.

So why is an economic history here? Banks fails all the time but this is the story of how a bank failed and set off a cascade of events that culminated in the Bank Panic of 1907 which threatened to bring the economy of the USA to a halt if not for the intervention of J. P. Morgan. What sets this bank failure apart from the others is that it started a chain of events that touched all the banks in the national network. Think of an earth tremor, they happen all the time and most go without much notice but there are some that stand apart from the rest because of their power. It is an example of a power law where a small event has the potential to trigger a major outcome. You can look at the Panic of 1907 as an example of Self-organized Criticality or the Edge of Chaos. One small change can affect the entire system. This is what the Science of Complexity hopes to explain. It cannot predict the future in anything more than general terms , but it can be used to predict the past to produce an explanation in the form of an historical narrative of events that helps us to understand this major financial earthquake. No equations here because it is a particular instance of a complex system in action. It is a narrative that embraces all that makes this event both unique, idiographic and an expected but rare outcome of a complex financial network.

Buchanan, Mark. NEXUS: Small Worlds and the Groundbreaking Science of Networks. W. W. Norton & Co, 2002.

1177 B.C.: The Year Civilization Collapsed Princeton Univ. Press, 2014.

Cowan, George A. Manhattan Project to the Santa Fe Institute: The Memoirs of George A. Cowan. Univ. of New Mexico Press, 2010.

Gleick, James. Chaos: Making a New Science. Penguin Books, 1987.

Holland, John H. Emergence: From Chaos to Order. Addison Wesley, 1998.

Holland, John H. Complexity: A Very Short Introduction. Oxford Univ. Press, 2014.

Jacobs, Jane. The Death and Life of Great American Cities. Vintage Books, 1992.

Originally published in 1961, this book explains why a city is more that just a group of buildings serving as an inspiration to many who study complexity. The final chapter, The Kind of a Problem a City Is, features a discussion of the Warren Weaver essay on the course of the development of science and how it might apply to the study of cities. She saw cities as examples of organized complexity not understandable using the methods of either simplicity or disorganized complexity roundly criticizing the urban planners of her time as disconnected from reality.

Johnson, Neil. Simply Complexity: A Clear Guide to Complexity Theory. Oneworld Publ., 2007.

Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. Touchstone, 2002.

Kauffman, Stuart. The Origins of Order. Oxford Univ. Press, ????.

Kauffman, Stuart. At Home in the Universe. Oxford Univ. Press, 1995.

An introduction to catalytic closure, random boolean networks, using NK networks to explore the transition zone between order and chaos, supracritical and subcritical reactions, NK Networks and fitness landscapes, and other ideas about evolution co-evolution and complex adaptive systems. He also has a rather novel approach to understanding the economy and economic growth.

Kauffman, Stuart. Reinventing the Sacred. Basic Books, 2008.

Kauffman, Stuart. Humanity in a Creative Universe. Oxford Univ. Press, 2016.

Krakauer, David C., John Lewis Gaddis and Kenneth Pomeranz. History, Big History, & Metahistory. SFI Press, 2017.

Lewin, Roger. Complexity: Life at the Edge of Chaos. McMillan Publ., New York, 1992.

Mitchell, Melanie. Complexity: A Guided Tour. Oxford Univ. Press, 2009.

Pagels, Heinz. The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity. Simon and Schuster, 1988.

Pines, David ed. Emerging Syntheses in Science. Addison-Wesley, 1988.

Prigogine, Ilya. The End of Certainty: Time, Chaos and the New Laws of Nature. Free Press, 1996.

Strogaatz, Steven. SYNC: The Emerging Science of Spontaneous Order. Theia, 2003.

Ulanowitz, Robert E. A Third Window: Natural Life Beyond Newton and Darwin. Templeton Foundation Press, 2009.

Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos. Simon & Schuster, 1992.

Watts, Duncan. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton Univ. Press, 1999.

Weaver, Warren, ed. The Scientists Speak. Boni & Gaer, 1947.

A collection of 79 essays commissioned by U.S. Rubber Co. to be read during the intermissions of nationwide radio broadcasts of Sunday afternoon concerts by the New York Philharmonic-Symphony during the years of 1943-1946. When the end of the war was in sight a decision was made to change the topic to look at what the future might bring and the role that science would play in that future. Dr. Warren Weaver, director of the natural sciences of the Rockefeller Foundation, served as the chairman of the Advisory Committee for the Intermission Science Series. He contributed an essay on Science and Complexity, an earlier version of the essay that Jane Jacobs discusses in her book and one that many in the Science of Complexity also refer to. I was very lucky to find this volume on Amazon.

Reviewed by George Sarton, "The Scientists Speak. Warren Weaver," Isis 39, no.3 (Aug., 1948): 191-192.

Reviewed by Bentley Glass, "The Scientists Speak. Warren Weaver," The Quarterly Review of Biology 23, no. 1 (Mar., 1948): 42-43.

Weaver, Warren. The Rockefeller Foundation Annual Report, 1958. Rockefeller Foundation.

Another iteration of Warren Weaver's summary of scientific progress and its future course, the one referenced by Jane Jacobs in her "The Death and Life of Great American Cities".

West, Geoffrey. Scale: The Universal Laws of Growth, Innovation, Sustainabilit, and the Pace of Life in Organisms, Cities, Economies, and Companies. Pengiun Press, 2017.

Wolfram, Stephen. A New Kind of Science. , .

Bettancourt, Lobo, Helbing, Kuhnert, and West. Growth, Innovation, Scaling and the Pace of Life in Cities. PNAS 2007 April, 104(17) 7301-7306.

Marion, Russ. The Edge of Organization: Chaos and Complexity Theories of Formal Social Systems. Sage Publ 1999.