Complexity

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Complexity

• Bruce Kogut
• October 2006

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We are entering the epoch of the digitalization
of knowledge past, present, and future

• Sciences bring to this new epoch
• More powerful statistical methods (some which
  date back 50 years in physics)
• Tools to manage and mine large datasets.
• Methods, such as imaging, to make inferences from
  damaged and missing data.
• Visualization technologies that make our standard
  powerpoint slides look very sad

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What Complexity Seems to Mean In Practice

• Interdisciplinary sharing of knowledge and
  creation of a larger community of scholarship.
• Appreciation of the non-linear view of the
  world where critical events and self-organization
  matter.
• Analyzing the statistical properties of large
  datasets (100,000)
• Understanding local interactions by micro-rules
  whose effects depend on topology (structure)
• Identification of common patterns by re-scaling
  and normalization (e.g. power laws) to seek more
  general explanations.

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Example from Venture Capital deals

• Over 200,000 transactions over 40 years in the US
  alone.
• Several thousand VC investors, targets
• Lets start by posing a simple question
• Can we find rules by which VC companies do deals?
• Do these deals explain aggregate patterns?

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Examples of Rule-based Formation

• We choose 18 firms that are connected from the
  actual data. Actual links are green lines.
• We simulate for 60 iterations, with each click
  representing implementation of the stochastic
  rule. Rules are analyzed one at a time.
• Red lines show outcome.
• We collect network statistics at the end.

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Simulations with Four Rules
Random
Preferential
Transitivity
Propensity
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Simulation Strategy Estimate from Data,Simulate
Forward to the Future
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The common hypothesis is that Venture Capital
Deals Favor the Big Players Rich get Richer
(sometimes called preferential attachment)
Inference by adduction the dog did not bark, the
graph does not show linear slopes, there are no
power laws in degree, hence the culprit of rich
get richer is innocent and released. So much for
complexity, big science, and robust patterns.
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Power Laws in Complex Weighted Graphs Incumbents
like to rely upon trusted partners

• Most Deals are Incumbent to Incumbent
• Hence we find power laws in repeated ties.
• Trusted expertise based on experience,

These modest results can be shown to refute the
leading hypothesis on venture capital VC
partnerships are not clustered by regions, they
span regions even in the early history of the
industry.
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Complexity is Already Percolating, and We Need to
Take Notice

• Organizational studies claims of self-organizing
  teams and innovations.
• Finance clustered volatility, whereby there is
  memory and hence inefficiency in markets.
• Marketing Data mining is the principal example.
• Economics Re-scaling shows remarkable
  commonalities in size and growth distributions.
• Macro-sociology Dynamics result in scale-free
  networks.
• Statistics Search for new methods applicable to
  big networks can sort out whether you smoke
  because you are born that way, or because you
  hang out with the (wrong/right?) friends.
• Operations Research once again, we can do math.

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Todays Panel

• Nigel Gilbert sociologist and founding editor of
  the Journal of Artificial Societies and
  Simulation, shows how ideas from complexity have
  implications for how we do social science and
  management research.
• Roberto Serra Physicist, former manager,
  academic, now engaged in promoting complexity
  education.
• Ralph Dum Physicist, EU Commission, Catalyst for
  Complexity Research, Wants to See a European
  Santa Fe Institute built.
• Jeff Johnson, Researcher in Design,Believer that
  Complexity requires math and math can be learned
  even by Ph.D. graduates.