Day 1
5 February 1998
Introduction to Complex Systems
Summary of this Day's Class
We began the class with an exploration, constructing Möbius strips and making predictions about how many sides the strip had and what exactly would happen if it was cut it in half, lengthwise down the center of the strip.
Möbius Strips have some very surprising properties and exactly what will happen when you cut them is difficult to predict.
Here are some Möbius strip links:
Moebius Strip by Alexander Bogomolney. He has a nice Escher picture, a good description, and some references.
Möbius Strip by Eric W. Weisstein. This site has a table listing properties of the strip when it is cut and twisted.
How to knit a Möbius Band from The Geomtery Center at the University of Minnesota in Minneapolis.
Still pictures of a Möbius Strip from The Geomtery Center.
The Möbius Strip is definitely complicated in some sense, but is it complex in the sense that we mean to discuss in this course? After some discussion it was agreed that Möbius strips were not complex in the same sense that an organism is complex. However, I should note that our discussion of Möbius Strips was not a useless one since they will enter into the picture under the guise of period doubling in dynamical systems.
Next we compiled a list of systems that we thought should be classified as complex.
Using this list as a guide we proceeded to make a list of qualities that we thought were characteristic of complex systems.
The quality adaptive sparked considerable discussion as it was difficult to agree on precisely what adaptive means. For further reading on this topic I refer the reader to Murray Gell-Mann's article listed below in the readings.
The last 15 minutes or so were spent ranking the complexity of various systems on a handout. We will discuss this next week when we consider measures of complexity.
Homework Assignment - Due 10 Feb 98
1. Take three complex systems and for each system make a list addressing the following questions or properties:
Reading Assignment - To be discussed 10 Feb 98
Holland, J.H. 1995. Hidden order. How adaptation builds complexity. Addison Wesley Publishing Company, Reading MA, Chapter 1, pp. 1-40.
Gell-Mann, M. 1995. Complex adaptive systems. In: Eds. H.J. Morowitz, J.L. Singer, The mind, the brain, and complex adaptive systems. Proceedings volume XXII in the Santa Fe Institute Studies in the Sciences of Complexity. Addison-Wesley, Reading MA, pp. 11-23.
Gopnik, A. 1984. Conceptual and semantic change in scientists and children: why there are no semantic universals. In: Eds. B. Butterworth, B. Comrie, Ö. Dahl, Explanations for language universals. Mouton, Berlin, pp. 163-179.
Rank the Following Systems According to their Complexity
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