The human immune system provides an incredibly powerful and adaptable defense against disease, yet there is no single locus of control. Instead, approximately a trillion white blood cells circulate throughout the body at a time, chemically tag any suspect cells, divide to create more white blood cells in close proximity to the invader, and signal other white cells to join the fight.
Exactly how white blood cells signal their cohorts remains a mystery, but the cells’ emergent behavior usually results in effective action against disease. Ant colonies, genes, the internet, and many other systems exhibit the same self-organizing behaviors, but the exact mechanisms for coordinating meaningful action remain a mystery.
In Complexity: A Guided Tour, Dr. Melanie Mitchell reviews the state of inquiry into the field of complex systems science. She discusses a wide range of topics, including von Neumann’s universal computer, how genetic information is passed from one generation to the next, Godel’s proof that there exist formally undecidable propositions in Principia Mathematica, and how computer programmers can use genetic algorithms to evolve optimal strategies to solve problems. It’s a lot to cover, but Mitchell handles the job effectively.
What is Complexity?
In the field of natural language processing during the early 1990s, you could bring a meeting to a grinding halt by asking anyone to provide a formal definition for what a “proper noun” was. Scott Adams, the author of the Dilbert comic strip, made a similar joke recently when he had Asok the intern ask if the company’s applications were Web 2.0-compliant. At the moment there’s a similar issue surrounding a precise definition of the term “complexity.” Fortunately, Mitchell doesn’t shy away from the lack of a formal definition of complexity, how to tell if a system is complex or not, or how to judge relative degrees of complexity. Instead, she describes the most popular approaches, of which there are disturbingly many, and discusses her preference.
Complex systems science wraps its arms around quite a few subjects. Rather than list the fields of inquiry, I’ll focus on Mitchell’s coverage of genetic algorithms, a topic I personally find fascinating.
An algorithm is a set of steps, or recipe, a person or computer can follow to complete a task. A genetic algorithm is an algorithm derived by a computer over time by combining elements of the most successful algorithms from the previous generation. As an example, Mitchell describes a situation where a robot has to traverse a grid and pick up randomly-placed cans using the fewest possible moving and without running into walls.
The computer starts with a set of random algorithms, scores each algorithm’s performance at the end of the round, discards the bottom half of the field, and combines the most successful algorithms to create a new set of the same size as the previous generation. To create the next set of algorithms, the computer takes about half of an existing algorithm (the exact percentage is determined randomly), draws the remainder of the algorithm from another example, and allows for the possibility that one or more steps in the strategy can change randomly, or mutate.
As the computer tests and combines the advancing generations of algorithms, the strategies’ performance improves. Over the course of several hundred iterations, the process generates incredibly efficient strategies. Like the immune system, genetic algorithms demonstrate how it is possible for useful behaviors to emerge from a complex system without human guidance kick-starting the process. Mitchell describes similar behaviors in other fields, providing an intriguing look into the many facets of complexity.
Is Complexity a Science?
After discussing the wide range of inquiries that fall under the complexity umbrella, Mitchell addresses the major critiques of complexity as a science. The most cutting of these criticisms asks whether complexity is, in fact, a science. In June 1995, journalist John Horgan wrote an article with the provocative label “Is Complexity a Sham?”, later turning the article into a book named The End of Science.
Deborah Gordon, an ecologist, added her voice to the critique by saying that complexity “offer[s] only smoke and mirrors, functioning merely to provide names for what we can’t explain…” Other critics point out that a lot of complex systems analysis occurs within the memory of a computer, making it a science that lacks an underlying reality.
Mitchell agrees that complex systems science is a long way from establishing any general principles that can be applied in the same way that force, mass, energy, and gravity can be used in physics. She does argue that delving into the behavior of complex systems could help identify useful commonalities. In turn, those discoveries could lead to mathematical representations of emergent and complex systems that yield testable hypotheses and useful predictions about the physical world.
Although the study of complex systems is in its relative infancy, Mitchell successfully argues that this field of inquiry is worth pursuing. Even if researchers never discover significant commonalities among the myriad systems currently under the “complexity” umbrella, they will most probably develop analytical tools to apply to narrower problem sets. I’ve also found no evidence that proponents of complex systems science have systematically overclaimed the importance of their results. Advocates of any new endeavor will wax rhapsodic about their specialty’s potential benefits, but since when isn’t it OK to work on a problem because you think it’s exciting?
Curtis Frye (firstname.lastname@example.org) is a Microsoft Office Excel MVP, freelance writer, and corporate entertainer who lives in Portland, Oregon. He offers free online resources for Excel users at www.thatexcelguy.com and provides information about his work as a speaker and corporate entertainer on www.curtisfrye.com.