The game of chess can be described using fewer than a dozen rules. Yet we’ve been playing it for centuries and have yet to exhaust all the possible sequences of moves those few rules permit.

That, in a nutshell, describes what psychologist and computer scientist John Holland is now studying — how a few relatively simple building blocks can combine to produce systems of enormous complexity.

Holland, the recipient of the School of Engineering and Applied Science’s 1999 Harold Pender Award, calls this phenomenon “emergence,” and in his Pender Award lecture on Oct. 27, he explained why it is important for the future of scientific research.

The University of Michigan professor and board member of the Santa Fe Institute for Research began his remarks by noting that “by any measure, we’ve had a flood of innovations in the last half of the 20th century. But these innovations are based on an understanding of addition” — a process which, he maintained, will soon prove useless as a basis for further innovation.

This, he said, is because addition is a linear function, while the phenomena we need to explore are nonlinear in nature. As another example, he cited what he called “a problem we don’t even know exists” — that of keeping Philadelphia’s grocery shelves stocked with food.

“Most grocery stores keep only about two or three weeks’ worth of food on their shelves,Ó he said, yet at any given time, there’s always plenty available. “But there’s no ‘planning commission’ that is responsible for food delivery,” he continued. “Economists would attribute this to the ‘invisible hand,’ but ask them, What are the mechanisms [that make this system work]? and you would get no answer.”

The food-distribution system is one example of what Holland called “complex adaptive systems” — systems that seem to spontaneously organize simple building blocks to perform a variety of constantly changing tasks.

In a pre-lecture interview, he described the human body as another such system.

Holland is known as the father of the “genetic algorithm” — the explanation of how the DNA building blocks combine to produce specialized cells and organs or express particular traits in an animal or plant. And it was his interest in finding a similar explanation for similar systems elsewhere in the world that led to his current research in the field of complexity.

Holland said in the interview that a successful theory of complexity could explain many social and natural phenomena.

But one major obstacle is that our mathematics cannot yet explain nonlinear functions.

“[The 19th-century scientist] James Charles Maxwell used the metaphor of gears floating in a fluid to explain electrical currents and electromagnetism,” he said, showing that metaphor worked where mathematics didn’t, especially when it comes to explaining new and little-understood phenomena. So, he said in the lecture, we must rely on other tools, such as metaphor, to explain many phenomena for now.