Complexity Theory for Design & Process

"Complexity Theory for Design & Process," turned out to be another good course in my pursuit of a Doctor of Philosophy degree in Engineering.  The course was broken down into 5 distinct components:

• Defining and Measuring Complexity
• Modeling Complexity
• Managing Complexity
• Reducing Complexity
• Application (Examples of applying to different disciplines)

Of the five components, we spent a considerable amount of time up front on defining and measuring complexity -  due to lack of a generally excepted definition for the term "complexity".  Of course, this inability to settle on a consensus around the term, reminded me of the literature review of The Structure of Scientific Revolution, by Thomas Kuhn.

In my blog on Structure, as the book is affectionately called by Kuhn, I postulated about how the notion of scientific development can be reduced to three distinct phases: pre-paradigm, normal science, and revolutionary science.  In this instance, complexity and the science around it, fits Kuhn's model of the pre-paradigm phase.  In other words, complexity is marked by deep debates over legitimate methods, problems, and standard of solutions.  At any rate, since we didn't settle on a specific definition for the term, we used a set of characteristics to describe whether or not something was complex.  What follows are a few of the characteristics we settled on to describe complexity:

• Interactions: A large number of components with different relationships; Systems consisting of large networks of individual components, each typically following simple rules with no central control or leader; collective action of vast numbers of components that give rise to the complex, hard-to-predict and changing patterns of behavior
• Emergence: A New Kind of Science - Stephen Wolfram; Randomness = Complexity; The notion of "computational equivalence" and "computational irreducibility"; There is a pretty cool youtube video on  Wolfram's notion of complexity.  http://www.youtube.com/watch?v=_eC14GonZnU.  It is pretty long, but exciting to watch.
• Adaptation: Systems that tend to change over time (maybe because of some stimulus) - also described as "Complex adaptive systems"; "Self Organizing"; and "Resilience"; Systems adapt—that is, change their behavior to improve their chances of survival or success—through learning or evolutionary processes
• Signaling and Information Processing: Systems produce and use information and signals from both internal and external environments

As you can see there is a lot of puzzles to solve with respect to complexity and the science of complexity seems to be in its infancy.  Over the many weeks to come, I will deposit more on this most interesting topic as it evolves.  Look out for more from Melanie Mitchell and Nam P. Suh.  And, of course,  the Santa Fe Institute 

In the meantime, how would YOU describe complexity?  Drop me a comment and let me know what you think.





A few good references on complexity:

• "Complexity: Theory and Applications," Nam P. Suh
• "Complexity: A Guided Tour," Melanie Mitchell
• "Measures of Complexity: A Nonexhaustive List," Seth Llyod

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