Abstract
This talk will examine two features common in complex systems: power laws and hierarchical organization. Using sandpiles it will be demonstrated that complex systems often tend to self-organize to what are called critical states where the behavior of the system is similar across scales. This similarity across scales is called power law behavior and we will see how it occurs in systems similar to sandpiles like avalanches and earthquakes, and also in apparently dissimilar systems such as brain activity and music. Hierarchical structure in complex systems will also be examined using a monetary system model where we will find scaling properties similar to power law behavior. In this new context, we will examine the hierarchical structure of language. Finally, we will pose the question as to whether power law behavior and hierarchical organization are related phenomena.

Several people have expressed an interest in obtaining copies of the transparencies used in this talk. Please email me and I will send you copies.
email: kknuth@balrog.aecom.yu.edu

References of material presented in the talk

Bak, P. 1996. How Nature Works. The Science of Self-Organized Criticality. Springer-Verlag, NY.

Caianiello, E.R., Scarpetta, G., and Simoncelli, G. 1982. A systemic study of monetary systems. Int. J. General Systems, 8:81-92.

Nagel, K. and Paczuski, M. 1995. Emergent Traffic Jams. Physical Review E 51:2909.

Negro, A., Tagliaferri, R., and Tagliaferri, S. 1987. Hierarchy and modularity in natural languages. In: Topics in the General Theory of Structures, Eds. E.R. Caianiello and M.A. Aizerman, pp.59-68.

Pattee, H.H. 1970. The problem of biological hierarchy. In: Towards a Theoretical Biology: Volume 3 Ed. C.H. Waddington. International Union of Biological Sciences and Edinburgh University Press, Edinburgh. pp.117-136.

Voss, R.F. and Clarke, J. 1975. '1/f noise' in music and speech. Nature, 258:317-318.

Zipf, G.K. 1949. Human Behavior and the Principle of Least Effort Addison-Wesley, Cambridge MA.

For Further Information
1/f Noise Bibliography composed by Wentian Li of Rockefeller University