David Alderson (California Institute of Technology):
"Why the Internet Scales: Interpreting Structure in Complex Systems"
Wednesday, January 28, 2004 at 3:00pm EST
Bartos Theatre, MIT Media Lab (E15)
One feature of many naturally occurring and man-made complex systems is tremendous variability in distributions of important quantities related
to their structure and behavior. Accordingly, such quantities are often measured using power law (scaling) distributions or relationships. Underlying the study of these systems is a fundamental question regarding the nature and implication of these highly variable phenomena and associated scaling laws. One popular approach over the last decades has treated high variability as "exotic," in the sense that it is viewed as unexpected or surprising, and theories to explain them have similarly been "exotic," in the sense that they rely on mechanisms that are generic or universal and independent of system-specific details.
This paper presents an alternate approach, relying on mathematical, statistical, and data-analytic arguments, and suggesting that highly variable event sizes should be viewed as "normal": either as normal, or more normal than Gaussian-type phenomena. To this end, we put power law distributions in the broader and more rigorous context of em scaling distributions. In doing so, we demystify power laws and enable a modeling approach that is no longer dependent upon them. Instead, the focus is on engineering or evolution, and on system-specific objectives, constraints, and tradeoffs to explain system behavior, and high variability becomes a natural by-product of a rational design process or of evolution. Not surprisingly, these two approaches reach opposite conclusions about the causes and implications of scaling in complex systems. We consider the Internet as a case study for illustrating what these two approaches have to say about the nature of high variability in complex systems, and for validating the resulting disparate claims.
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