Where is the Architect?
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Where is the Architect? |
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Book Review Nexus: Small
Worlds and the Groundbreaking Science of Networks Reviewed By: Rick Presley* Mark Buchanan holds a doctorate in physics and is a science writer living in France. He has been an editor at Nature and New Scientist. His latest book is a summary of the strides being made in an emerging branch of mathematics, networks, which is an offshoot of complexity theory. In Nexus, Buchanan attempts to link the discoveries of leading theorists in mathematics with a wide range of phenomena in both the natural and social sciences. He attempt to demonstrate that the mathematical architecture of networks underlies society, the internet, the world wide web, economics, ecology, phase transitions of chemicals, neural arrangement and activity, the electrical grid in the United States and the spread of disease. Whether he succeeds in this endeavor is open to question and further research but the implications for proponents of Intelligent Design are profound. Oddly, while Buchanan identifies this near-universal underlying mathematical architecture as a fundamental component of nearly every aspect of the world, he fails to hint at the existence of an Architect. Introduction to Networks Buchanan’s book opens with the curious notion that there may be a mathematical architecture that underlies human behavior. He traces the publication of the article “Collective Dynamics of ‘Small-World’ Networks” in Nature by Steve Strogatz and Duncan Watts. This paper was inspired in part by the work of Stanly Milgram who pioneered the idea that everyone in the world is connected by “six degrees of separation.” Milgram claimed to have produced evidence that, through our network of social contacts, we can connect any two people in the world through an average of just six people. Watts and Strogatz developed a mathematical model that they dubbed “Small-World Networks” to explain Milgram’s surprising finding. They found that by adding a small number of random links to a clustered network, the degree of separation between any two links drops dramatically. In fact they found that the bigger the network, the relative number of random links required to reduce the degree of separation between any two points decreases significantly. While Watts and Strogatz do not prove Milgram’s “six degrees of separation,” they do provide a mathematical architecture to explain how such a close network composed of so many parts is possible. It is this structure that interested the editors at Nature enough to publish their findings. Since then, many more applications of their Small Worlds model continue to turn up. Buchanan’s book lists a wide array of incidents where this same structure turns up, some of which are obvious and others that are more surprising. Human Networks In the area of social connections, Small Worlds architecture is being applied to an understanding of the structure of the Internet and the World Wide Web. These networks form a specialized architecture called an aristocratic network. In this type of structure some members of the network have many links while others have comparatively few links. It is intriguing that this structure follows a “power law” formula in which each time the number of links doubles, the number of nodes with the same number of links decreases by about five times. This means, for example, that the Internet, which seems to have grown in a random and haphazard sort of way, has an underlying order that isn’t immediately apparent. Just as importantly, the essential connectedness of this Small World architecture is largely unaffected by the variation in structure. In other words, even with the wide disparity in the number of links any one Web site may have, it takes very few steps to navigate from one site on the Web to any other site. Is this connectedness an artifact of human construction or is it a deeper underlying principle of nature? Buchanan’s book explores this question in a wide-ranging overview. It turns out, this power law rule holds true for a wide range of networks that at first glance appear totally random. Networks in Nature Buchanan documents a number of places in the biological world where the Small World architecture is applied. Examples include the neural net of the flatworm Caenorhabditis elegans, the synchronized blinking of fireflies in New Guinea, cellular chemistry, genomics, ecological communities and their food webs, epidemiology and disease outbreaks can all be explained in terms of the Small Worlds model. Since the same mathematical model can explain such widely separated phenomena, he insists that there must be a fundamental structure at work in the biological world. It also appears to be the same architecture at work in man-made networks. Even more startling than Small World network architecture found in the biological world is the same structure appearing in the inanimate world. The principles that explain the pattern of the worlds major river systems, thermodynamics of heated liquids, chemical phase changes, and the formation of diffusion-limited aggregates can all be accounted for using the Small World model. Buchanan hints that there is a deeper architecture at work in the universe that explains the fundamental structure of everything from basic chemistry to economic principles. While he never hints at an Intelligent Design behind this near-universal architecture, the book provides a very good case for it. The Architect If Buchanan’s assertion is correct, that Small World architecture is a fundamental structure found throughout nature and society, then where is the Architect? The concept of Small World networks is only about four years old and its widespread implications are only now being explored. Judith Kleinfeld, a psychologist at the University of Alaska in Fairbanks, is following up on Milgram’s original research with some disturbing findings for “Six Degrees of Separation” fans. (Discover June 2002) Christians have the opportunity to be in the forefront of this new branch of science and to explore its implications for Intelligent Design. A universal fundamental structure to the universe certainly implies a Designer. Buchanan’s book gives Christians a first glimpse at what may prove to be a groundbreaking area of mathematics with far-reaching implications. If nothing else, it is a thought-provoking introduction to a simple mechanism for explaining a wide variety of complex phenomena. Whether one agrees with Buchanan’s conclusions or not, the potential for proponents of Intelligent Design to add more ammunition to their apologetic arsenal makes this worth investigating. Even though the book begins with a mathematical proposition, there are no complex or arcane formulas to prevent the reader from enjoying the work. Buchanan includes a number of illustrations and graphs to bring the concepts clearly to life and encourages the reader to speculate on the wider implications of this work. Hopefully, even the most recalcitrant can see that such an elegant and universal architecture demands an Architect. *Rick Pressley Writes: I’m glad you were able to use my book review. I hope it spurs some discussion there among your readership. I think there are some points worth discussing among a Creationist audience that Buchanan misses. I graduated from Indiana University in 1987 with a Bachelor of Science in Education with a major in biology. I taught biology, advanced biology, life science and physical science in a Christian School in Columbus, Ohio for five years. After the birth of my third child, I left the teaching field and worked as a lab technician and technical service representative in the chemical industry for over seven years. In 2000, I left the chemical industry to put both my biology and education backgrounds to work for the American Red Cross, Biomedical Services as an Education Coordinator. During most of that time I was involved in a bi-vocational church-planting effort. In addition to helping my wife of 22 years raise our five children, I still manage to squeeze in a little time for reading about some of the latest scientific breakthroughs in a variety of fields. Nexus: Small Worlds and the Groundbreaking Science of Networks, (W. W. Norton & Company, 2002; ISBN 0-393-04153-0) by Mark Buchanan, 235 pages, $25.95. |
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