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A Garden of Models Steps Toward Growing the Topology of the Possible In Public Policy Modeling

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A Garden of ModelsSteps Toward Growing the Topology of the Possible In Public Policy Modeling

Carl Tollander

4th Lake Arrowhead Conference on Human Complex Systems

April 25-29, 2007

Modeling Complexity is a Complex Activity!

What we usually start out doing…

Simulate a model

Composed of statements about

A population of given objects

With known relationships

In some specified geometry.

- Build a model
- Composed of statements about
- Changing object classes
- With changing relationships
- When background setting and geometry is dynamic

- Composed of statements about

…but over time,

much more of our task demands…

- 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.

Policy Mix

Heterogeneous,

Highly dynamic

Constraint

Sets

Multi-source,

continuously refined, environmental

data

Emergent

Community

Structure

Constituency Mix

Adaptive Modeling Problem

Messy,

Contingent

Constantly Evolving

- Some Implementation Challenges
- Representation of emergent structure
- Composability and reusability
- Model Maintenance
- Validation, verification, calibration

Models

Of Agents

Adaptive

Structure

Modeling

Two-stage modeling process

(structure agents continuously co-create model)

(domain agents, familiar ABM methodology and analysis)

Improve ways to relate informal notions about models and structure to a variety of formal representations.

Derek Wise (UCR Math) defines mathematical gadgets as:

- Specifying some stuff,
- Equipped with structure,
- Satisfying some properties

Stuff

Structure

Properties

Leverage knowledge about growth and regeneration toolkits from developmental biology, industrial design, CAS practice….

- Toolkits
- mediate the development
- of future system structure
- Switching
- Encapsulating
- Promoting,
- Inhibiting,
- Repressing
- Repairing

Artificial Genomes for auto styling (BiosGroup, Plektyx)

Genetic toolkits, e.g. HOX

(Caporale, Margulis, Carrol)

Usually multiple toolkits, overlapping, multi-purpose…

They emerge, evolve, disappear…

RNA shape space (Fontana, et al)

Evolution of banking in Renaissance Florence (Padgett)

Creating Topologies of the Possible

Still messy, contingent, constantly evolving…

But…

- A Community Resource:
- Self-maintaining, easier validatation,
- Increased policy transparency, interoperability, componentry.
- Faster, more targeted ABM creation.

Agents carrying policy toolkits co-construct (grow) ensembles of possible model topology

Well-situated “spot” ABMs created from this topology when needed for analysis.

Adaptive Structure Modeling

Models of Agents

How can heterogeneous populations of structure-building

agents jointly and continuously create, regenerate

and navigate a common model context?

Models runnable in existing modeling frameworks

D

D

A

Dynamic

Heterogeneous

Structure-building

Policy

Agents

Dynamic

Heterogeneous

Data

A

Jointly grown

model structure

D

A

D

A

A

D

D

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

- 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 - Category Theory

- 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 - Rich Partial Equivalence

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 - Agency and Identity

On opportunity,

Agent may select

one or more of

its agencies for the

situation at hand.

An Agent carries one or more horizons, which are its agencies.

Agency can be delegated, rewarded, recombined, etc.

a

A

a

a

- Policy agents
- Constituency agents

The identity of an agent is the sum of its agencies and any heuristics for their application.

a

a

a

a

a

a

A

A

A

A

A

A

a

a

a

a

a

a

a

a

a

a

a

a

Resartus areas of investigation - Equivalence Examples

Navigating Equivalence

?

?

C1

C1

C2

C2

!

C1

Ea

?

Ea

!

C1

C2

C2

Ea

C1

!

Ea

Ea

C1

C2

C2

a

a

A

A

a

a

a

a

Resartus areas of investigation - Scheduling Structure Agents

Since we don’t know what local topologies we will find, we must minimize pre-specification of that topology in the scheduler.

Random

jumps in

category-memory

space

(a là Tierra,

StarCat)

Resartus areas of investigation - Model Feeds

Similar to RSS (syndicated) news feeds on the Web.

Feed

Feed

Feed

Aggregator

Feed

Feed

Aggregator

Feed

Feed

Aggregator

Feed

- Difference:
- Feeds are/deliver Categories (new local model topologies)
- Aggregation is (here) an adaptive modeling process containing structure-building agents.

Future Directions

- 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

References

Category Theory

Very fast introduction by John Baez: http://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

Research Programs and Mathematics

Corfield, David, “How Mathemeticians may Fail to be Fully Rational”, 2006 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

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)

Some General Questions

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?