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A Garden of Models Steps Toward Growing the Topology of the Possible In Public Policy Modeling Carl Tollander carl@plektyx.com 4th Lake Arrowhead Conference on Human Complex Systems April 25-29, 2007

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4/28/2007 2 of 19 Build a model Composed of statements about Changing object classes With changing relationships When background setting and geometry is dynamic What we usually start out doing… …but over time, much more of our task demands… Simulate a model Composed of statements about A population of given objects With known relationships In some specified geometry. Modeling Complexity is a Complex Activity!

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4/28/2007 3 of 19 Public Policy Making - Some Observations Policies are constraints that mediate the evolution of future system (community) physical and social structure. New candidate policies must be situated relative to a mix of other existing and contemplated policies. In novel situations where new policies are contemplated, the availability and semantics of requisite data are likely to be in some flux. Policy mix is cross-jurisdictional and multi-constituency. Policy makers no longer directly control information availability, analyses and tempo.

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4/28/2007 4 of 19 Multi-source, continuously refined, environmental data Heterogeneous, Highly dynamic Constraint Sets Policy Mix Constituency Mix Emergent Community Structure Some Implementation Challenges Representation of emergent structure Composability and reusability Model Maintenance Validation, verification, calibration Messy,Contingent Constantly Evolving Messy,Contingent Adaptive Modeling Problem

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4/28/2007 5 of 19 Approaching Adaptive Modeling Improve ways to relate informal notions about models and structure to a variety of formal representations. Leverage knowledge about growth and regeneration toolkits from developmental biology, industrial design, CAS practice…. Derek Wise (UCR Math) defines mathematical gadgets as: Specifying some stuff, Equipped with structure, Satisfying some properties Stuff Structure Properties Two-stage modeling process Adaptive Structure Modeling Models Of Agents (structure agents continuously co-create model) (domain agents, familiar ABM methodology and analysis)

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4/28/2007 6 of 19 Toolkits and Emergent Structure Toolkits mediate the development of future system structure Switching Encapsulating Promoting, Inhibiting, Repressing Repairing Genetic toolkits, e.g. HOX (Caporale, Margulis, Carrol) Artificial Genomes for auto styling (BiosGroup, Plektyx) RNA shape space (Fontana, et al) Evolution of banking in Renaissance Florence (Padgett) Usually multiple toolkits, overlapping, multi-purpose… They emerge, evolve, disappear…

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4/28/2007 7 of 19 Creating Topologies of the Possible Agents carrying policy toolkits co-construct (grow) ensembles of possible model topology Adaptive Structure Modeling Models of Agents Well-situated “spot” ABMs created from this topology when needed for analysis. Still messy, contingent, constantly evolving… A Community Resource: Self-maintaining, easier validatation, Increased policy transparency, interoperability, componentry. Faster, more targeted ABM creation. But…

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4/28/2007 8 of 19 Garden of Models: Research Program in Adaptive Modeling How can heterogeneous populations of structure-building agents jointly and continuously create, regenerate and navigate a common model context? Jointly grown model structure Jointly grown model structure Models runnable in existing modeling frameworks A A A A A A A A A A D D D D D D D D D D D D Dynamic Heterogeneous Structure-building Policy Agents Dynamic Heterogeneous Data

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4/28/2007 9 of 19 Resartus Testbed Purpose: test computational embodiments of Garden of Models research program in order to drive effort towards a well- engineered Policymaker’s Workbench software architecture and implementation. –Models building models –Policies as structure-building agency –Agents with identity and multiple agency –Heterogeneous agents, heterogeneous policies

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4/28/2007 10 of 19 Background independence of emergent structure Stuff, Structure, Properties Category Theory Rich Partial Equivalence, detection and navigation Structure Agent Scheduling Emergent Structure Model Feeds Workbench user interaction mechanisms Toolkit packaging and exchange in Workbench Resartus areas of investigation

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4/28/2007 11 of 19 Category Theory - a set of gadgets useful for working with complex structure Category - objects + morphisms (transformations) that preserve structure of the objects. Functor - bundle of transformations between categories: object to object, morphism to morphism. N-category - category of categories, internal morphisms all functors. Natural Transformations - transformations between paths (functors of functors) that are equivalent. Equivalence - items are equivalent if there is a transformation between them (many available kinds of transformations) Resartus areas of investigation - Category Theory

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4/28/2007 12 of 19 Agents use policy constraints to detect, establish, degrade or navigate rich partial equivalence in a model based on policy constraints. In practical terms, these constraints take the form of one or more N-categories, called Horizons, which describe the depth and scope of the policy. Comparing two N-categories for equivalence with respect to a Horizon yields a (possibly empty) functor, which constitutes new agent-navigable structure in the growing model. Properties of a policy horizon determine the role of the equivalence vis-à-vis toolkits, i.e., promote, inhibit, repress, activate, etc. Resartus areas of investigation - Rich Partial Equivalence

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4/28/2007 13 of 19 A a An Agent carries one or more horizons, which are its agencies. Agency can be delegated, rewarded, recombined, etc. a a On opportunity, Agent may select one or more of its agencies for the situation at hand. Policy agents Constituency agents The identity of an agent is the sum of its agencies and any heuristics for their application. Resartus areas of investigation - Agency and Identity

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4/28/2007 14 of 19 Finding Equivalence A a a a C1C1 C2C2 A a a a C1C1 C2C2 A a a a C1C1 C2C2 EaEa EaEa ! EaEa ! ? ? A a a a C1C1 C2C2 A a a a C1C1 C2C2 A a a a C1C1 C2C2 ? ? EaEa ? EaEa ! Navigating Equivalence Resartus areas of investigation - Equivalence Examples

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4/28/2007 15 of 19 Since we don’t know what local topologies we will find, we must minimize pre- specification of that topology in the scheduler. A a a a A a a a Random jumps in category-memory space (a là Tierra, StarCat) Resartus areas of investigation - Scheduling Structure Agents

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4/28/2007 16 of 19 Similar to RSS (syndicated) news feeds on the Web. Aggregator Feed Aggregator Feed Aggregator Feed Difference: Feeds are/deliver Categories (new local model topologies) Aggregation is (here) an adaptive modeling process containing structure-building agents. Resartus areas of investigation - Model Feeds

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4/28/2007 17 of 19 CAP Workbench for cross-jurisdictional policy in rural communities Policy Component Webs - distributed policy making. Multiple language implementation of Resartus elements. Learning - Hierarchical Reactive Planning –Agent learns choice of horizon –Path equivalence / plan equivalence Advanced Schedulers (e.g. Cartan-geometry based) Analytic Journalism - modeling possible story spaces Model recombination Future Directions

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4/28/2007 18 of 19 Category Theory Very fast introduction by John Baez: http://math.ucr.edu/home/baez/planck/node5.htmlhttp://math.ucr.edu/home/baez/planck/node5.html Notions of Equivalence by Barry Mazur: http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf Research Programs and Mathematics Corfield, David, “How Mathemeticians may Fail to be Fully Rational”, 2006 http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf Wise, Derek, “Properties, Structure and Stuff”, UCR Quantum Gravity Seminar notes, Spring, 2004, http://math.ucr.edu/home/baez/qg-spring2004/s04week01.pdf http://math.ucr.edu/home/baez/qg-spring2004/s04week01.pdf Developmental and Molecular Biology, Constructive Social Models (Toolkits, etc.) Caporale, Helena Lynnn, “Darwin in the Genome: Molecular Strategies in Biological Evolution”, McGraw-Hill, 2003 Carroll, Sean B., “Endless Forms Most Beautiful: The New Science of Evo Devo”, W.W. Norton Company, 2005 Margulis, Lynn and Dorion Sagan, “Acquiring Genomes: A Theory of the Origins of Species”, Basic Books, 2002 Padgett, John, and Paul McLean, “Organizational Invention and Elite Transformation: The Birth of Partnership Systems in Renaissance Florence”, AJS Volume 111 Number 5 (March 2006): pp 1463-1568 B. M. R. Stadler, P. F. Stadler, G. Wagner and W. Fontana “The Topology of the Possible: Formal spaces underlying patterns of evolutionary change”, Journal of Theoretical Biology, 213 (2), 241-274 (2001) References

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4/28/2007 19 of 19 How to transform structural asymmetry to ‘gradients’ (non-commutative flows along equivalence) Organizations of dimensionality vs. ‘levels’? Next implementation languages after Java? Relationships vs Transformations? More meta the model the lower the required cognition? Some General Questions

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