Complexity: Worlds hidden in plain sight

On August 14, 2003, 50 million people across the American Northeast lost electrical power. Around 70,000 megawatts went AWOL, which for reference is on the order of 100 coal plants spontaneously disappearing from energy production.

The initial cause was thought to be a fault in a 345 kilovolt line in Northern Ohio. In less than an hour, this fault lead to further lines being lost due to excessive load propagating through the power grid. This negative-electrical epidemic spread across a considerable part of the nation and led to a regional blackout.

Further investigation pointed to additional “causes.” A parallel and compounding problem was a software failure in a control center. Another was that trees that had been supporting electrical cables had grown too tall, promoting short circuits. Another was that the utility companies managing parts of the grid did not have as effective or efficient a communication strategy as is needed under pressure.

The blackout inflicted an economic cost of around $10 billion.

To summarize, a software network interacted with a physical cable network supported by a forest ecological network overseen by a stressed human social network. The failure was not “disciplinary” or “departmental”; it was complex. A full understanding of one critical infrastructure, the power grid, requires an understanding of a multitude of overlapping networks.

Complexity science is an effort to discern and theorize common patterns in complex systems from multiple scientific perspectives. Many scientific disciplines are already associated with powerful models and theories: in biology, for example, there is the theory of evolution, in economics there is utility maximization and game theory, and in engineering mathematics there is Alan Turing’s theory of computation.

Complexity science seeks to connect these theories, to find explanatory and predictive frameworks that allow us to, for example, describe biological mechanisms in computational terms or social structures in energetic terms.

For the last few decades we have been steadily surveying the landscape of complex phenomena, and it is gratifying that along the way we find that complex systems nominally unrelated bear strong family resemblances. These similarities include how the mathematical structure of evolutionary adaptation looks a lot like the mathematics of learning, that the distribution of energy within a body made of tissues and fluids follows rules similar to those governing the distribution of energy in a society, that networks within cells adhere to the geometric principles we find on the internet, and that the rise and fall of ancient civilizations follow a sequence similar to the extraordinary growth and contraction of urban centers we see in our own millennium.

It comes as something of a surprise, though, that many of the systems we scientists understand the best are those that we shall never touch (the sun), never see (the quark), and never feel (the Higgs field). My Santa Fe Institute colleague and Nobel laureate in physics Murray Gell-Mann captured the essence of this achievement in his Nobel Prize banquet speech in 1969:

“How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the Waka, can predict universal regularities of Nature.”

Compare this to the world in which we live, the biological, psychological, social, and cultural domains with which we enjoy direct sensory experience. This complex world continues to elude the compressive eloquence of the formulae of physics and chemistry, with their uncanny resemblance to the elegant artistic properties of the Japanese verse form, the Waka.

What is it that makes observable complex systems such as the economy, sustainable urbanization, or human conflict so challenging?

This paradox of comprehension was articulated explicitly by a great physicist of an earlier age:

“Sir Isaac Newton, when asked what he thought of the infatuations of the people, answered that he could calculate the motions of erratic bodies, but not the madness of a multitude.”

(Quoted from “The Church of England Quarterly Review,” 1850.)

It seems that from the perspective of mathematical science, there exist two natural domains. The first is the physical domain of particles, fields, and universal laws, with an associated search for elegant theories that apply everywhere in the known universe. Here, science has made great strides.

The second domain is that of complex phenomena. These are adaptive, interacting, many-body systems that include populations of cells, societies, economies, cities, human cultures, and technological networks — all phenomena with long histories and adaptive components, and they have a tendency to change as soon as we have come to understand them. Complexity theories extend to life — a remarkable state hitherto found only upon the crust of our third planet from the sun.

As with physical theory (such as the theory of gravity, which we need to understand if we are to make any progress with ballistics, aviation, and space flight), some form of complexity theory is required if we are to understand many of the intimate, and patently uncertain, interactions found in modern society. And the natural complement to the search for fundamental theory is the direct and ancillary discovery of tools to predict and control the complex, highly interconnected world in which we live.

Many of our most pressing challenges and failures in the 21st century derive from an underestimation of complexity. Society has a tendency to treat challenges as if they emerged from a single factor in a rather straightforward way. Hence we blame war on a single aggressor, starvation on the scarcity of a single food product, or poverty on the concentration of wealth.

The temptation to avoid complexity is rather firmly rooted in the abiotic, physical domain, where certainty reigns. And if this were not bad enough, our educational system tends to perpetuate this misunderstanding with departments and schools that treat the interconnected world around us as if it was simple and disconnected.

In this series of invited articles for the Christian Science Monitor, my colleagues at the Santa Fe Institute shall review the recent progress in complexity science. We shall examine the most fundamental, brain tickling mathematical and computational theories and methods coming out of this endeavor.

The falsehood that intellectual scholarship is incompatible with practical reality is one of the most pernicious modern myths propagated by the data-phobic and the political ideologues. We shall challenge this perspective.

Complexity science provides beautiful examples of hard technical problems engaging in a productive exchange with some of our thorniest societal dilemmas. The future prosperity of life on earth, and, at some point in the human trajectory, beyond the earth, require that we engage to the maximum extent possible with our precious faculty of reason to better understand the workings of complexity and, one day, Newton’s “madness of the multitudes.”

David Krakauer is the president of the Santa Fe Institute, a network of scientists from many fields and institutions pioneering the science of complexity.