Complexity_ A Guided Tour - Melanie Mitchell [161]
“a new hypothesized mechanism that resulted in power law distributions”: For surveys of some such mechanisms, see Mitzenmacher, M., A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2), 2003, pp. 226–251; and Newman, M. E. J., Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46, 2005, pp. 323–351.
“The reported cause of the shutdown”: The cascading failure and its causes are described in detail in the U.S.-Canada Power System Outage Task Force’s Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations [https://reports.energy.gov/].
“The computer system of the US Customs and Border protection agency”: see Schlossberg, D. “LAX Computer Crash Strands International Passengers.” ConsumerAffairs.com, August 13, 2007, [http://www.consumeraffairs.com/news04/
2007/08/lax_computers.html]; and Schwartz, J., “Who Needs Hackers?” New York Times, September 12, 2007.
“Long-Term Capital Management”: see, e.g., Government Accounting Office, Long-Term Capital Management: Regulators Need to Focus Greater Attention on Systemic Risk. Report to Congressional Request, 1999, [http://www.gao.gov/cgi-bin/getrpt?GGD-00-3]; and Coy, P., Woolley, S., Spiro, L. N., and Glasgall, W., Failed wizards of Wall Street. Business Week, September 21, 1998.
“The threat is complexity itself”: Andreas Antonopoulos, quoted in Schwartz, J., “Who Needs Hackers?” New York Times, September 12, 2007.
“Self-Organized Criticality”: for an introduction to SOC, see Bak, P., How Nature Works: The Science of Self-Organized Criticality. New York: Springer, 1996.
“Highly Optimized Tolerance”: For an introduction to HOT, see Carlson, J. M. and Doyle, J., Complexity and robustness. Proceedings of the National Academy of Science, USA 99, 2002, pp. 2538–2545.
“Next to the mysteries of dynamics on a network”: Watts, D. J., Six Degrees: The Science of a Connected Age. New York: W. W. Norton, 2003, p. 161.
Chapter 17
“the surface area scales as the volume raised to the two-thirds power”: Let V denote volume, S denote surface area, and r denote radius. V is proportional to r3, so cube-root (V) is proportional to the radius. Surface area is proportional to radius2, and thus to cube-root(V)2, which is .
“If you plot a power law on a double logarithmic plot, it will look like a straight line, and the slope of that line will be equal to the power law’s exponent”: In the example here, the power law is
metabolic rate α body mass3/4.
Taking the logarithm of both sides, we get
log (metabolic rate) α 3/4 log (body mass).
This is the equation of a straight line with slope 3/4, if we plot log (metabolic rate) against log (body mass), which is actually what is plotted in figure 16.2
“Enquist later described the group’s math results as ‘pyrotechnics’”: Grant, B., The powers that be. The Scientist, 21 (3), 2007.
“You really have to think in terms of two separate scales”: G. B. West, quoted in Mackenzie, D., Biophysics: New clues to why size equals destiny. Science, 284 (5420), 1999, pp. 1607–1609.
“The mathematical details of the model”: A technical, but not too difficult to understand, description of the Metabolic Scaling model is given in West, G. B. and Brown, J. H., Life’s universal scaling laws. Physics Today, 57 (9), 2004, pp. 36–43.
“Although living things occupy a three-dimensional space”: West, G. B., Brown, J. H., and Enquist, B. J., The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 284, pp. 1677–1679.
“the potential to unify all of biology”: Grant, B., The powers that be. The Scientist, 21 (3), 2007.
“as potentially important to biology as Newton’s contributions are to physics”: Niklas, K. J., Size matters! Trends in Ecology and Evolution 16 (8), 2001, p. 468.
“We see the prospects for the emergence of a general theory of metabolism”: West, G. B. and Brown, J. H., The origin of allometric scaling laws in biology from genomes to ecosystems: Towards a quantitative unifying theory of biological