Complex Systems Summer School 2014-Panel Responses

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Panel participants: Marcus Hamilton, Simon DeDeo, Sander Bais, W. Brian Arthur, Sid Redner, Anne Kandler

1. What is the next big scientific question in the complex systems research?

• Brian: hierarchy; higher levels constrained by lower, lower levels programmed by higher; how do they arise?
• Simon: certain models we can get answers to (like agent-based sim with finite choices); if we consider universal computing devices/models then we have incompleteness; look for things in between
• Marcus: how do energy and information networks co-evolve, particularly in social systems
• Sid: look for new questions that people shrug off and don't have good answers to
• Anne: matching data with models

2. What is the origin and the importance of stochasticity in complex systems?

• Sid: competition between elements of same magnitude
• Anne: if you look at system in deterministic and stochastic ways, you learn different things; in some sense stochastic models are more "complex" than deterministic ones
• Simon: randomness is ignorance about a system; forgetting can be useful - otherwise overload of info, storage space, computational time, over-fitting
• Brian: a century of Physics work that relies on it; more interesting than studying change is studying the propagation of change; distributions resulting from probabilistic dispersion give rise to power laws
• Sander: close interactions may be modeled reasonably by deterministic processes, but farther away model like fluid dynamics
• student comments:
  • Jose: stochasticity is necessary for evolution, molecular noise
  • Michael: it's more general than that

3. What do you believe, but can not (yet) prove?

• Sid: mechanistic description for higher life function, like consciousness
• Simon: there are laws of history
• Marcus: humans are less unique than anthropologists think, simple rules and constraints that explain our behavior
• Sander: symmetry between magnetic and electrical phenomena broken if you look at Maxwell eqns; is it possible to have particles with a pure magnetic charge?

4. What mathematical tools do we lack most?

• Anne: non-equilibrium models
• Brian: ditto; algorithmic mathematics proposed by Chaitin: "the computer isn't just an aid to mathematics, it is a new kind of mathematics"
• Simon: ditto; linguists and generative grammars, analogy to physical complex systems; note for us: there are journals that don't require mathematical theory and analytical results (e.g. Physics Review)
• Sid: tools to deal with multi-body correlation functions, outstanding problem in non-equilibrium statistical physics; advice for us: work harder on analytical techniques - think first, compute second
• Sander: important to get "the equations"; equations are simple, but it's difficult to probe the solution space; development of approximation techniques; look for old methodologies that have been forgotten

Flavia: Is fractional calculus useful for complex systems?

• Sid: powerful, but not so useful - doesn't give much that isn't already known

Cole: From what field will theory of non-equilibrium systems come? statistical physics -> thermodynamics again?

• Brian: exists in biology, ecology, economics of self, computer science; not different mathematics, just different way of looking at the world; non-equilibrium is huge, equivalent to non-elephants compared to elephants, will be lots of ways of approaching it

5. What role do models play in the analysis of complex systems (prediction? mechanistic insights? computer experiments?) and what does that depend on?

• Anne: when working with very sparse data, models are essential
• Marcus: model- and theory-building is understanding scale-dependence; theory to explain behavior at each scale/level, question is how do they integrate; he is interested purely in mechanistic models
• Simon: model is not mechanism, should allow models to surprise you, not be biased by your prior beliefs; ML is an extreme example
• Sander: every equation is a model in some sense; ask question, get answer, often surprised by implications - and sometimes can't handle them because they shatter known beliefs (many examples in history, e.g. anti-matter, black holes)

6. How do we model the creation of novelty?

• Brian: evolution/novelty in technology is not like evolution of species (incremental change); it's more about finding a new combination of existing ideas
• Sander: remember Andreas Wagner's discussion of neutral theory
• Marcus: Darwin's ideas borrowed for cultural evolution, but don't necessary apply to systems besides bio/genetic ones
• Simon: novelty is when somebody does something that defies expectations

Matt: how are approaches to research different or the same: in the past, now, in the future?

• Sander: cross-disciplinary science is very important now because useful tools are already out there

Sander: What is the greatest "big miss" you've had?

• Sid: preferential attachment model, was studying in context of citations and observed power laws, but thought not interesting
• Sander: mentioned in a 1974 paper something that implied that the universe would collapse, didn't follow through with that thought
• Simon: if you rediscover something, don't feel stupid, you're in good company

Cole: Is one of the goals of complex systems to unify scientific language?

• Anne: yes, it is very important; example of diffusion (of innovation, beliefs, epidemics, etc.)