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Jeffrey Goldstein, Ph.D. Adelphi University Garden City, New York USA goldstei@adelphi.edu The Self-transcending Construction of Emergence

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life consciousness speciation project teams multi-organisms artificial life the Internet magnetism superfluidity superconductivity additional computational functionality dissipative structures optimal options prices perception of color attractors and their basins drug interactions leadership behavior software bugs temperature cities wars scientific revolutions creative ideas EXAMPLES OF EMERGENCE EXAMPLES OF EMERGENCE

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Self-transcending Constructions in Neo-emergentism

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Drives Behind Emergence: Candidates Blumenbach: Bildungstrieb Spencer: Increasing Heterogeneity Bergson: Creative Evolution/Elan Vital Alexander: Nisus (Connatus from Spinoza) Whitehead: Processual De Chardin: Eschatological Thermodynamics: Self-organization Based On Minimum or Maximum Entropy Production or So-called Fourth Law of Thermodynamics (information theoretic) Recursion Edge of Chaos – Selection Pressures (Kauffman) Gravitics (Ian Stewart)

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Construction, not Process Not a Metaphysics Based on the Already Given (Structures, Dynamics, Properties) Not Subjugation to Process or Temporal Flow Non-Oppositional Based on Constructional Resources and Operations Free Act of Creativity but Not Order for Free

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Reisers Transfinite Aggregates Hollands Sets of Equations that Change Cardinality Crutchfields Calculi of Emergence Bennetts Logical Depth Cohens/Stewarts Existence Theorem for Emergent Phenomena Piagets Logico- Mathematical Constructions Andersons Constructionist Hypothesis Fontanas and Busss Computational Constructions ?

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Reisers Transfinite Aggregates Hollands Sets of Equations that Change Cardinality Crutchfields Calculi of Emergence Bennetts Logical Depth Cohens/Stewarts Existence Theorem for Emergent Phenomena Piagets Logico- Mathematical Constructions Andersons Constructionist Hypothesis Fontanas and Busss Computational Constructions Gödel and Turing: Limitative Theorems

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Reisers Transfinite Aggregates Hollands Sets of Equations that Change Cardinality Crutchfields Calculi of Emergence Bennetts Logical Depth Cohens/Stewarts Existence Theorem for Emergent Phenomena Piagets Logico- Mathematical Constructions Andersons Constructionist Hypothesis Fontanas and Busss Computational Constructions Cantorian Anti- diagonalization

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Reisers Transfinite Aggregates Hollands Sets of Equations that Change Cardinality Crutchfields Calculi of Emergence Bennetts Logical Depth Cohens/Stewarts Existence Theorem for Emergent Phenomena Piagets Logico- Mathematical Constructions Andersons Constructionist Hypothesis Fontanas and Busss Computational Constructions Self- transcending Constructions STC

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Construction of anti-diagonal sequence to transcend cardinality of rational numbers: Definition 1: R is a 3-place relation among x,y,z represented as D 1 and D 2 making-up vertical and horizontal arrays of rationals Definition 2: A diagonal F is constructed on D 1 and D 2 so that the mapping is a bijection D 1 --> D 2 Definition 3: G is the value of the diagonal F in R Definition 4: STC is an anti-diagonal of F in R so that (STCxyz =¬ Gxyz) NOTE: ¬ IS A NEGATION OPERATOR WHICH ALLOWS STC TO TRANSCEND CARDINALITY OF RATIONALS Formalism of STC (incl. Negation) - ADAPTED FROM SIMMONS

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EVOLUTION VERSUS DESIGN EVOLUTION VERSUS DESIGN CONTINUITY OF EVOLUTION VERSUS DISCONTINUITY OF CONSTRUCTION BERGSON: ELAN VITAL VERSUS MACHINE BERGSON: ELAN VITAL VERSUS MACHINE CONSTRUCTION SEEMS TO IMPLY CONSTRUCTOR CONSTRUCTIONS ARE THOUGHT OF AS PREDICTABLE AND DEDUCIBLE BIAS AGAINST CONSTRUCTION SCIENCE VERSUS ART SCIENCE VERSUS ART

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Construction, not Process Not a Metaphysics Based on the Already Given (Structures, Dynamics, Properties) Not Subjugation to Process or Temporal Flow Non-Oppositional Based on Constructional Resources and Operations Free Act of Creativity but Not Order for Free

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CONSTRUCTIONAL SOURCES OF NOVELTY IN NEO-EMERGENTISM RECURSIVE OPERATIONS, E.G., FUNCTIONAL ITERATION, CROSSOVER, RECOMBINATION.. NEGATION OPERATIONS (CHANGING VALUES ON RECURSION) NEGATION OPERATIONS (CHANGING VALUES ON RECURSION) INTRODUCTING RANDOMNESS INTO SYSTEM

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f c :I c x S c S c (where f c is defined so that f c (t+1) = f c (I c (t)S c (t)); I = possible input combinations at time t, S = states of system at time t Constrained Generating Procedures (Holland) RECURSION

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FUNCTIONAL ITERATION FUNCTIONAL ITERATION ( FEIGENBAUMS ROUTE TO CHAOS ) ( FEIGENBAUMS ROUTE TO CHAOS ) f n is the nth iterate of f RECURSION

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Hollands Genetic Recombination Using Negation and Randomness Crossover and Mutation Negate Previous Combination at Every Iteration AND/OR MUTATION

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Construction of anti-diagonal sequence to transcend cardinality of rational numbers: Definition 1: R is a 3-place relation among x,y,z represented as D 1 and D 2 making-up vertical and horizontal arrays of rationals Definition 2: A diagonal F is constructed on D 1 and D 2 so that the mapping is a bijection D 1 --> D 2 Definition 3: G is the value of the diagonal F in R Definition 4: STC is an anti-diagonal of F in R so that (STCxyz =¬ Gxyz) NOTE: ¬ IS A NEGATION OPERATOR WHICH ALLOWS STC TO TRANSCEND CARDINALITY OF RATIONALS Formalism of STC (incl. Negation) - ADAPTED FROM SIMMONS

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Thou sendeth forth Thy spirit, they are created; And Thou renewest the face of the earth. – Psalm 104:30 Whose Name stands for I am that I am says, Look, I am doing a new thing; It springs forth right now, do you not perceive it? I create a path out of the wilderness And rivers out of the desert. -Isaiah 43:19

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