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Meta-Systems, Complexity, and Emergence Kent D. Palmer CSER 2008 080404 kent@palmer.name http://archonic.net http://holonomic.net

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Papers for CSER Conference The Failure of Systems Engineering as an approach toward Complex Adaptive Systems in our major Customers Eyes: –Analysis of the Capstone Concept for Joint Operations and its relation to Meta-systems Theory Emergence and Complexity in relation to General Schemas Theory –A point of discussion within the Systems Science Enabler Technical Working Group of INCOSE

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Meta-system Primer This brief primer will help readers to understand the papers associated with this conference In order to understand the points of my paper it is necessary to explain Meta- systems in relation to Systems Meta-systems offer a different way to look at things than Systems

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Two different Schemas Meta-System System of Systems System (Super-system) Sub-system

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What is a Schema A projected organization of envelopes of spacetime which is a template for the pre-understanding of perceptual objects The term System is over-used and has lost its meaning. To get that meaning back we must compare it with other similar concepts of the same type that have a family resemblance but at different scales The history of the term Schema is discussed by Umberto Eco in Kant and the Platypus –By Schema we mean what he calls the Mathematical and Geometrical Schemas, not the many other meanings of the term he mentions. This is the most basic type of schema, i.e. the type that allows us to reference an object in spacetime.

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System and Meta-system Formalization Turning Machine Representation (Gurevich Abstract State Machine) System Application Normal Turing Machine System dynamics with negative feedback Meta-system Operating System Universal Turing Machine System dynamics with positive feedback

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Bataille Accursed Share General Economy Meta-system International waters Lawlessness of the high seas Piracy, reflaging ships, contraband and smuggling Restricted Economy System Nation states control what is within their borders, ideally Really the state is a meta-system inside = black and grey markets, barter and gift

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Nested Systems and Meta-systems Russian Dolls: Shells are systems Spaces are meta-systems

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Meta-system Characteristics + Positive Feedback + - Positive Feedback - SYSTEM Negative feedback loop Singularity > Folds continuity and discontinuity (Rene Thom Catastrophe Theory)

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Meta-System Partitions System Anti-System OriginSink Source Boundary Horizon ARENA

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Perceptual / Conceptual Gestalt –System Flow –Process Proto-gestalt –Meta-system Proto-flow –Meta-process

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Open-Scape HORIZON G G G G No movement One point of view PG PG=Proto-gestalt G= Gestalt

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Gestalt vs Flow Reference in background Flowing In Foreground Background foreground

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Proto-gestalt / Proto-flow G G G G PG F F F F Streams in a River Static-dynamicDynamic-Static view PF=Proto-flow F= Flow PF Bank Reference Line

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Emergence and Complexity are Orthogonal It is possible to have both simplicity and Emergence, such as in atoms It is possible to have both complexity and de-emergence which some call complications. We normally see dynamic complexity leading to emergent effects but this is not an intrinsic relation between the two properties

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Complex systems do not capture the concept of the meta-system Systems Theory Complex Systems Complex Adaptive Systems Chaotic Systems Meta-systems Theory Complex Meta-systems Complex Adaptive Meta- systems Chaotic Meta-systems

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Emergence and Schemas are Orthogonal Any Schema (System or Meta-system) can either be seen as emergent or de-emergent De-emergence or Emergence can be upward or downward in the self-nesting of a single schema The transition to another schema from a particular schema can either be emergent or supervenient Supervenience means homeomorphic without new emergent properties appearing Sub-venience is mapping in the opposite direction, down instead of up

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Emergence De-Emergence Complexity Simplification Schema Meta-schema Super-Schema Sub-schema Reduction Complication Supervenience Subvenience Nesting of Schemas Transition between Schemas Homeomorphism Essential Difference as Novelty Set to Mass Transition Set to Set or Mass to Mass Transition START Pick: Position in Hierarchy of Schemas Complexity/Complication ratio Sameness/Difference ratio

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Exploring the Design Landscape Nesting of Schemas Transition between Schemas Homeomorphism Essential Difference Set to Mass Transition Set to Set or Mass to Mass InitialDesign FinalDesign AlternativeDesign AlternativeDesign

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SE should be grounded on Systems Theory Systems Engineering Discipline Systems Theory

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Complementary Disciplines Systems Engineering Discipline Systems Theory Meta-systems Engineering Discipline Meta-systems Theory Emergent Engineering

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EXCESS LACK Produces Emergence or De-emergence Regardless of Schema

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System/Meta-system vs Emergence/De-emergence Emergent System Emergent Meta-SystemDe-emergent System De-emergent Meta-system Move to the outer environment Move to the inner environment An environment with emergent properties of its own without becoming a system Next higher or lower level of system

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Hierarchy of Schemas Pluriverse Kosmos World Domain Meta-system Reflexive social Autopoietic Symbiotic Dissipative Ordering System Form Pattern Monad Facet Emergent Engineering deals with all the schematic levels within reach of experience ExperientialScaffolding

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Schemas and Dimensions Pluriverse 8 to 9 Kosmos 7 to 8 World 6 to 7 Domain 5 to 6 Meta-system 4 to 5 System 3 to 4 Form 2 to 3 Pattern 1 to 2 Monad 0 to 1 Facet -1 to 0 General Rule: Two dimensions per Schema and Two Schemas per dimension String Theory 10 -- 11 Heterochronic 12 --14 Max area Max volume Hyper-sphere volumes and areas infinity

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Holonomic Systems Meta-system = Whole less than the sum of its parts Reflexive Autopoietic Dissipative System = Whole greater than sum of is parts Special System = Whole exactly equal to sum of parts

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Emergent Meta-system Sedenion Algebra Zero Divisors Octonion Algebra Quaternion Algebra Complex Algebra Real Algebra <<lost conjugate << lost commutative << lost associative << lost division Lower Energy

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Meta-system Primer End Kent D. Palmer kent@palmer.name http://archonic.net http://holonomic.net

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