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Complexity_ A Guided Tour - Melanie Mitchell [46]

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that would no doubt have pleased Turing, had he lived to see it explained.

The processes sketched above were understood in their basic form by the mid-1960s in a heroic effort by geneticists to make sense of this incredibly complex system. The effort also brought about a new understanding of evolution at the molecular level.

In 1962, Crick, Watson, and biologist Maurice Wilkins jointly received the Nobel prize in medicine for their discoveries about the structure of DNA. In 1968, Har Gobind Korana, Robert Holley, and Marshall Nirenberg received the same prize for their work on cracking the genetic code. By this time, it finally seemed that the major mysteries of evolution and inheritance had been mostly worked out. However, as we see in chapter 18, it is turning out to be a lot more complicated than anyone ever thought.

CHAPTER 7

Defining and Measuring Complexity

THIS BOOK IS ABOUT COMPLEXITY, but so far I haven’t defined this term rigorously or given any clear way to answer questions such as these: Is a human brain more complex than an ant brain? Is the human genome more complex than the genome of yeast? Did complexity in biological organisms increase over the last four billion years of evolution? Intuitively, the answer to these questions would seem to be “of course.” However, it has been surprisingly difficult to come up with a universally accepted definition of complexity that can help answer these kinds of questions.

In 2004 I organized a panel discussion on complexity at the Santa Fe Institute’s annual Complex Systems Summer School. It was a special year: 2004 marked the twentieth anniversary of the founding of the institute. The panel consisted of some of the most prominent members of the SFI faculty, including Doyne Farmer, Jim Crutchfield, Stephanie Forrest, Eric Smith, John Miller, Alfred Hübler, and Bob Eisenstein—all well-known scientists in fields such as physics, computer science, biology, economics, and decision theory. The students at the school—young scientists at the graduate or postdoctoral level—were given the opportunity to ask any question of the panel. The first question was, “How do you define complexity?” Everyone on the panel laughed, because the question was at once so straightforward, so expected, and yet so difficult to answer. Each panel member then proceeded to give a different definition of the term. A few arguments even broke out between members of the faculty over their respective definitions. The students were a bit shocked and frustrated. If the faculty of the Santa Fe Institute—the most famous institution in the world devoted to research on complex systems—could not agree on what was meant by complexity, then how can there even begin to be a science of complexity?

The answer is that there is not yet a single science of complexity but rather several different sciences of complexity with different notions of what complexity means. Some of these notions are quite formal, and some are still very informal. If the sciences of complexity are to become a unified science of complexity, then people are going to have to figure out how these diverse notions—formal and informal—are related to one another, and how to most usefully refine the overly complex notion of complexity. This is work that largely remains to be done, perhaps by those shocked and frustrated students as they take over from the older generation of scientists.

I don’t think the students should have been shocked and frustrated. Any perusal of the history of science will show that the lack of a universally accepted definition of a central term is more common than not. Isaac Newton did not have a good definition of force, and in fact, was not happy about the concept since it seemed to require a kind of magical “action at a distance,” which was not allowed in mechanistic explanations of nature. While genetics is one of the largest and fastest growing fields of biology, geneticists still do not agree on precisely what the term gene refers to at the molecular level. Astronomers have discovered that about 95% of the universe

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