The Self-transcending Construction of Emergence Jeffrey Goldstein, Ph.D. Adelphi University Garden City, New York USA goldstei@adelphi.edu EXAMPLES OF EMERGENCE 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 Self-transcending Constructions in Neo-emergentism • • • • • • • 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) 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 Reiser’s Transfinite Aggregates Bennett’s Logical Depth Fontana’s and Buss’s Computational Constructions Crutchfield’s Calculi of Emergence Anderson’s Constructionist Hypothesis ? Cohen’s/Stewart’s Existence Theorem for Emergent Phenomena Holland’s Sets of Equations that Change Cardinality Piaget’s LogicoMathematical Constructions Reiser’s Transfinite Aggregates Bennett’s Logical Depth Fontana’s and Buss’s Computational Constructions Crutchfield’s Calculi of Emergence Anderson’s Constructionist Hypothesis Gödel and Turing: Limitative Theorems Piaget’s LogicoMathematical Constructions Cohen’s/Stewart’s Existence Theorem for Emergent Phenomena Holland’s Sets of Equations that Change Cardinality Reiser’s Transfinite Aggregates Bennett’s Logical Depth Fontana’s and Buss’s Computational Constructions Crutchfield’s Calculi of Emergence Anderson’s Constructionist Hypothesis Cantorian Antidiagonalization” Cohen’s/Stewart’s Existence Theorem for Emergent Phenomena Holland’s Sets of Equations that Change Cardinality Piaget’s LogicoMathematical Constructions Reiser’s Transfinite Aggregates Bennett’s Logical Depth Fontana’s and Buss’s Computational Constructions Crutchfield’s Calculi of Emergence Anderson’s Constructionist Hypothesis Selftranscending Constructions “STC” Piaget’s LogicoMathematical Constructions Cohen’s/Stewart’s Existence Theorem for Emergent Phenomena Holland’s Sets of Equations that Change Cardinality Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONS 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 D1 and D2 making-up vertical and horizontal arrays of rationals Definition 2: A diagonal F is constructed on D1 and D2 so that the mapping is a bijection D1 --> D2 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 BIAS AGAINST CONSTRUCTION SCIENCE VERSUS ART EVOLUTION VERSUS DESIGN •CONSTRUCTION SEEMS TO IMPLY CONSTRUCTOR •CONTINUITY OF EVOLUTION VERSUS DISCONTINUITY OF CONSTRUCTION BERGSON: ELAN VITAL VERSUS MACHINE • CONSTRUCTIONS ARE THOUGHT OF AS PREDICTABLE AND DEDUCIBLE 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 CONSTRUCTIONAL SOURCES OF NOVELTY IN NEO-EMERGENTISM RECURSIVE OPERATIONS, E.G., FUNCTIONAL ITERATION, CROSSOVER, RECOMBINATION.. NEGATION OPERATIONS (CHANGING VALUES ON RECURSION) INTRODUCTING RANDOMNESS INTO SYSTEM RECURSION Constrained Generating Procedures (Holland) f c :Ic x Sc Sc (where fc is defined so that fc (t+1) = fc(Ic(t)Sc(t)); I = possible input combinations at time t, S = states of system at time t RECURSION FUNCTIONAL ITERATION (FEIGENBAUM’S ROUTE TO CHAOS) xn f ( f (... f ( f ( x0 ))...)) f ( x0 ) n f n is the nth iterate of f Holland’s Genetic Recombination Using Negation and Randomness AND/OR MUTATION Crossover and Mutation Negate Previous Combination at Every Iteration Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONS 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 D1 and D2 making-up vertical and horizontal arrays of rationals Definition 2: A diagonal F is constructed on D1 and D2 so that the mapping is a bijection D1 --> D2 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 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