Introduction To Complexity (professor's notes)

These are my notes.

  1. Books to take to class: Computational Beauty of Nature, three books for class

Introductory stuff

  1. Who am I?
    1. Education
    2. Work history
    3. My research history
    4. My programming history
  2. Who are you?
    1. Name
    2. The professor with whom you're studying
    3. Programming experience
    4. What, if any, research that you've done
  3. My view of IS research
    1. I differ from many of the other faculty here and in other institutions.
    2. I think a valid way of doing IS research is to use computers to conduct research, through simulation, multi-agent modelling, evolutionary algorithms, into how business works and, even better, into how information affects how business works.
    3. “If you can't build a model of it, then you don't understand it. You're merely conjecturing.”
    4. Better models are easier to understand by more people. They are also easier to explain.
  4. Benefits of using a computational model for at least part of your research investigations
    1. You can do a nice “show-and-tell” during a talk.
    2. You can gain insight into a problem, your understanding of it, and your understanding of existing theories.
    3. You can compare the performance of different theories of rules of action within one framework (e.g., a descriptive versus a normative theory).
  5. Sajeev's talk
    1. Your reaction?
    2. My reaction:
  6. Goals for the end of the course
    1. You should be able to discuss and read about computationally-based business research.
    2. You should understand the value of and potential contributions of this type of research.
    3. You should be able to implement simple multi-agent-based models.
  7. Schedule
    • We'll meet for a total of 13 class sessions, through the end of this semester.
    • Each of you must read all of the articles; further, each of you will be in charge of summarizing the main points of the article and in being the class “expert” on the article.
    • Your paper (and the model) will be due at the end of the Winter semester (i.e., end of April). Your paper outline will be due in mid-February. We will go through one complete round of revisions after you turn in your paper at the end of April to give you a feel of what this process is like when you're trying to get published.

Readings

  1. “Complexity: The Bigger Picture” by Vicsek
    • Points out that complexity is about a world that operates on many different scales.
    • Operations of the whole depend on the operations of its subunits in a non-trivial way.
    • “[L]aws that describe [the entire system's] behavior are qualitatively different from those that govern its individual units.” (From the middle of the second column.)
    • “[R]andomness and determinism are both relevant to the system's overall behavior.” (A little farther down the second column.)
    • “The big question is whether there is a unified theory for the ways in which elements of a system organize themselves to produce a behavior that is typical of large classes of systems.” (Bottom of the second column.)
    • We are beginning to realize that “the laws of the whole cannot be deduced by digging deeper into the details.” (Top of the third column.)
    • “[A] computer is a tool that improves not our sight (as does the microscope or telescope), but rather our insight into mechanisms within complex systems.” (Bottom half of the third column.)
    • “The aim [of computer models] is to capture the principal laws behind the exciting variety of new phenomena that become apparent when the many units of a complex system interact.”
  2. “Why do things become more complex?” by Arthur (SA)
    • His answer (top of third column): “[C]omplexity tends to increase as functions and modifications are added to a system to break through limitations, handle exceptional circumstances or adapt to a world itself more complex.”
    • He says that there is hope to ever-increasing complications (in the middle of the third column): “Sooner or later a new simplifying conception is discovered that cuts at the root idea behind the old system and replaces it.” What does complexity theory say about this? (Sometimes there are just a few simple rules that lead to the observed complex behavior; sometimes it doesn't take a complex theory to explain complex behavior.)
    • He ends with “[W]hen we seek [complexity] as an end or allow it to go unchecked, it merely hampers. It is then that we need to discover the new modes, the bold strokes, that bring fresh simplicity to our organizations, our technology, our government, our lives.” And I would add “and our theories.” Instead of using very complex math in order to (ahem) explain something, use a simple simulation instead.
  3. “What is complexity?” by Gell-Mann
    • Who is Gell-Mann?
    • Let student lead the discussion.
    • Discusses computational complexity; do people know about this?
    • Discusses algorithmic information content.
    • Discusses difficulty of computation as a measure of complexity. Both logical depth and crypticity (bottom of page 5).
  4. “Adapting to complexity” by Ruthen
    • Let student lead the discussion.
    • Quote from George Cowan (on page 2): “As these various systems organize themselves and learn and remember, evolve and adapt, persist and eventually disintegrate and disappear, what common patterns and fundamental principles, if any, shape their remarkable behavior?”
    • In the third column (on page 3; 132): "Holland is intrigued at the way a group of independent companies somehow manage to supply food for the seven million people in New York City. … “From the point of view of physics, it is a miracle that happens without any control mechanism other than sheer capitalism," Holland exclaims.”
    • Right after that: "To analyze the behavior of such systems, researchers must rely heavily on computer simulation because the equations that describe the forces underlying complex processes prove too difficult to solve."
    • We'll study genetic algorithms, the prisoner's dilemma, the economy as a complex system.
    • Arthur's point (in the third column on page 4; 133): “Such activities as international trade, high-technology business and the emergence of new companies exhibit truly complex dynamics … because they involve both negative and positive feedback mechanisms.”
    • On the top of page 134: “Yet a mixture of positive and negative feedback presents two challenging problems for economists. First, it means that any given economic system can evolve down many possible paths. … Second, a firm that is choosing a product strategy must try to guess which strategies other firms might use, knowing that small changes in its own strategy might alter the direction of others.” This can all be summarized with the phrase /path dependence.
    • On the top of the third column on page 134: “Arthur hopes the study of complex adaptive systems will lead to a much better understanding of how economic agents form strategies.”
    • The discussion on pages 134-5 basically says that algorithmic complexity is impossible (or at least really difficult) to determine.
    • The discussion on page 135 gives us insights into the proper way of building simulations. Begin with a simple model and see what it tells us. Do experiments with that model and record the results. Add features one-by-one, do experiments, record the results, see what it tells us. Repeat.
    • Near the end of page 135 is another discussion that points out that complexity is somewhere in the middle between complete order and complete randomness.
  5. “Self-organized criticality” by Bak and Chen
    • Let student lead the discussion.
    • Middle of column 2 on page 46, the theory of self-organized criticality: “[M]any composite systems naturally evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. Although composite systems produce more minor events than catastrophes, chain reactions of all sizes are an integral part of the dynamics. According to the theory, the mechanism that leads to minor events is the same one that leads to major events. Furthermore, composite systems never reach equilibrium but instead evolve from one meta-stable state to the next.”
    • Top of column 3 on page 48: “The sandpile has two seemingly incongruous features: the system is unstable in many different locations; nevertheless, the critical state is absolutely robust.”
    • Page 52: weakly chaotic systems versus fully chaotic systems.
    • Third column on page 52: we'll study the game of life.
    • Bottom of the second column of page 53: an economics-related, supply-chain related model.
  6. Preface to the Computational Beauty of Nature
    • This book captures my feelings toward the course better than anything that I could have written.
    • The “world economy” example on the middle of the second page is quite illustrative, especially the “on the other hand” part.
    • The last paragraph on the second page is absolutely phenomenal.
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