research:
REALWORLDS
Analysis of Organic Internetworks
As Complex Adaptive Systems
 

ABSTRACT

The function of this paper is to report on current research of the Internet and World Wide Web (WWW) from the perspective of nonlinear, dynamic and emergent systems. It is the goal of this research to develop a new understanding and new methodologies for better understanding quality of service issues and provide a new means for virus simulation and threat assessment to the Internet community. The approach of this research is to study the Internet and subordinate web of electronic information in four dimensions through the application of chaotic systems (Lorenz, Yorke, Feiganbaum, Mandelbrot) analysis with consideration given to bandwidth, error correcting technologies, preferential attachment and movement in real-time.

Since virtually all complex systems inherit the properties of graphs (Green 2000) and can be abstractly modeled accordingly, this research begins with some existing and well known models of exponential random graph networks (Erdös-Rényi, 1959) that display the small world effect (Milgram, 1967). Also pertinent to this work are the studies of systematically rewired random graphs with small world properties (Watts-Stogratz, 1999) and randomly rewired (Newman-Watts, 1999) small world random graph networks. The unique approach of this research is the combination of these models with more applied scale-free networks whose connectivity decay as a power law (Albert-Barabási, 1999) to create a hybrid, and subsequently more "realworld", model of networks. Finally, significance is given to realworld clustering influences (Adamic, 1999), which when considered together can produced a new and more pragmatic network model from which to work.

INTRODUCTION TO DISTRIBUTED COMPUTING

One of the earliest paradigms in computing was that of a powerful centrally located processor performing many tasks for many people. In this model, control over the computing landscape was at its greatest. But mainframe computing was expensive and began to lag in the area of processing power. The idea of distributed computing, spread over a multitude of smaller and less expensive processors, sprang to life from the creation of APRAnet in the late 1960s (Segaller, 1998) and the proliferation of personal computers in the early 1980s (Freiberger-Swaine, 1994). The mainframe processing of the 1960s gave way to networked file servers and then client/server architectures where personal computers accessed data and applications from smaller servers using much of their own processing power for computations.

The problem that this new paradigm created was one of decentralized control. Suddenly, over the period of less than a decade, the computing world had small mainframe-like systems appearing rapidly in businesses and at home. Operating systems, application software and telecommunications bowed to the ever growing populous of computer users. No longer did anyone need an account on a large system to perform Herculean tasks; they could buy a small personal computer for a few thousand dollars, plug a phone cord into a modem and begin computing and sharing almost immediately. From that moment, distributed computing began to emerge and has since been locked into a role which is leaving a dramatic imprint on many aspects of our society.

Distributed computing systems have grown and matured into highly specialized and heterogeneous systems like the Internet, local area networks, wide are networks, ARPAnet, SIPRnet, NIPRnet, intranets, extranets, and virtual private networks. These are all complex and ever-changing networks made up of a myriad of personal computers, specialized hardware, operating systems, processors, applications, drivers, standards, virtual machines, protocols, application programming interfaces and user interfaces.

What we have found to be true is that these distributed systems are notoriously complex and prone to all types of failure making them difficult and expensive to manage on a large scale. These systems seem to uphold the second law of thermodynamics perfectly as they slide toward decay and disorder. But they also display the opposite, a tendency toward emergence and self organization, which hint at an underlying deterministic quality that few have explored with any focused research (Albert-Barabási, 1999). As we propel ourselves into the next phase of an instant-knowledge information-dependent society we become more and more reliant on these distributed networks. Yet in the three decades that they have existed we have never taken a more elegant approach than brute force to understanding and managing them.

WHY CHAOS IS APPLICABLE

The first glimmer of an opportunity seems to lie in the readily observed behaviors of the typical distributed computing system. As mentioned previously these systems tend to be entropic. But they also tend toward emergence; they are inclined to be self-healing to a degree and they tend to generate something that equates to more than the simple sum of its parts. Bartering, online weddings, cyber-sex and cyber-terrorism are not part of the programming in any piece of a network yet they emerge in large distributed computing systems nonetheless. Large distributed networks also tend to exhibit a self symmetry with a richness, a robustness of information, at the network edge.

Chaos theory has been defined as the “qualitative study of unstable, aperiodic behavior in deterministic, nonlinear dynamic systems”. In part this implies that chaotic systems are not disorderly yet they are so complex that their order is not readily apparent. Chaotic systems are ordered and they are deterministic and with an understanding of that order comes the ability to better understand, model, predict, manage, secure and defend that system. The difficult task is to find the hidden order, the determinism, built into the system’s observed behavior. This research asks what set of data points mapped in phase space will unleash the universality buried in the system.

With the onset of inexpensive personal computers steadily obeying Moore’s Law of rapidly increasing processing power, growing connectivity to the urban areas of information age nations, pop culture popularity of the Internet, advances in telecommunications hardware and bandwidth, more lightweight and intelligent client/server technology and the explosion of peer-to-peer file sharing, distributed computing has become ubiquitous in today’s technological societies. But ubiquitous and manageable are two very different beasts. Anyone who has been employed on the front lines of a Helpdesk can attest to the complex, unpredictable and sometimes chaotic nature of a distributed network.

INITIAL APPROACH OF THIS RESEARCH

It is not the intention of this research to differentiate complex systems from nonlinear dynamic systems from chaotic systems. For the purposes of this abstract, the properties of these systems are the important factor and, in the most superficial and generalized way with all fashionable nomenclature aside, it is the properties themselves that will help the most when applied to the behaviors of distributed computing systems.

So what are the applicable properties of chaotic systems and what are the appropriate questions that this research proposes?

• Chaotic systems are deterministic however unapparent and hidden the underlying structure may be. Dynamic systems tend to behave in a nonlinear and aperiodic way so can we ask what are the deterministic qualities, the attractors?
   

• They are hypersensitive to their preliminary conditions where small initial changes will create vastly different and unpredictable outcomes. These systems display intricacy at multiple levels creating a scalable complexity; a self similarity so can we ask what data points can be obtained to develop a phase space diagramming of these new systems?
   

• Complex systems are information rich and do not have a propensity toward equilibrium. These types of systems live robustly at the edge where randomness and order collide in the thinnest of membranes. If they were to reach equilibrium they would be dead so can we ask where is the edge and what robustness is to be found there?
   

• Emergent systems have agents that are the building blocks of the larger entity so can we ask what are the agents of these networks and what roles are they playing?
   

• Emergent complex systems also tend to reach critical mass points where they enter in to a phase of explosive growth so can we ask what is the next tier?
   

• And finally, these systems are self organizing and it is in this deterministic self organizing nature of chaotic systems the most benefit to society is likely to be found.

CHAOTIC SYSTEMS

PAPERS

ADAMIC, L. A. 1999 The small world web.  [ PDF, 150K ]

ALBERT, R., JEONG, H. AND BARABASI, A.-L. 1999 Diameter of the world-wide web. Nature. [ PDF, 111K ]

NEWMAN,M. E. J., 1999 Small worlds. [ PDF, 150K ]

ERDOS, P. AND RENYI, A. 1959 On random graphs. Publicationes Mathematicae.

KASTURIRANGAN, R. 1999 Multiple scales in small-world graphs.

KLEINBERG, J. 1999 The small-world phenomenon: An algorithmic perspective. Cornell University Computer Science Department Technical Report.

MILGRAM, S. 1967 The small world problem. Psychology Today.

NEWMAN,M. E. J. AND WATTS, D. J. 1999b Scaling and percolation in the small-world network model. Physical Review.

WATTS, D. J. 1999 Small Worlds. Princeton University Press (Princeton).

WATTS, D. J. AND STROGATZ, S. H. 1998 Collective dynamics of “small-world” networks. Nature.

LI, T. Y. AND YORKE, J.A. 1975 Period Three Implies Chaos. Amer. Math. Monthly.

BOOKS

ALLIGOOD, K., SAUER, T., YORKE, J. (1996). Chaos: An Introduction to Dynamical Systems. Springer.

OTT, E., (1993). Chaos in Dynamical Systems. Cambridge Univ. Press.

LORENZ, E. N., (1993). The Essence of Chaos. Univ. of Washington Press.

MANDELBROT, B. (1977). Fractal Geometry of Nature. W H Freeman & Co.

COHEN, J. (1994). The Collapse of Chaos. Penguin Books.

STEWART, I. (2nd edition 1990). Does God Play Dice?: The Mathematics of Chaos. Blackwell Pub.

GLEICK, J. (1987). Chaos: Making a New Science. Viking Press.

WALDROP, M. (1992). Complexity: the Emerging Science At the Edge of Order and Chaos. Simon & Schuster.

DISTRIBUTED NETWORKING

BOOKS

SEGALLER, S. (1998). Nerds 2.0.1: A Brief History of the Internet. New York: TV Books.

FREIBERGER, P., SWAINE, M. (2nd edition, 1994). Fire in the Valley. New York, NY: McGraw-Hill.

HAFNER, K., LYON, M. (1997). Where Wizards Stay Up Late: The Origins of the Internet. New York, NY: Simon & Schuster.

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