Jeffrey Goldstein, Ph.D.

Adelphi University

Garden City, New York USA

goldstei@adelphi.edu

The Self-transcending Construction of Emergence

life consciousness speciation project life consciousness speciation project

teams multi-organisms artificial life the teams multi-organisms artificial life the

InternetInternet

magnetism superfluidity magnetism superfluidity

superconductivitysuperconductivity

additional computational functionalityadditional computational functionality

dissipative structures optimal options dissipative structures optimal options

pricesprices

perception of color attractors and their perception of color attractors and their

basinsbasins

drug interactions leadership behavior drug interactions leadership behavior

software “bugs” temperature citiessoftware “bugs” temperature cities

wars scientific revolutions creative wars scientific revolutions creative

ideasideas

EXAMPLES OF EMERGENCEEXAMPLES OF EMERGENCE

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)

• Recursion• Edge of Chaos – Selection Pressures (Kauffman)• Gravitics (Ian Stewart)

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

Holland’s Sets of Equations that Change CardinalityCrutchfield’s

Calculi of Emergence

Bennett’s Logical Depth Cohen’s/Stewart’s

Existence Theorem for Emergent Phenomena

Piaget’s Logico-Mathematical Constructions

Anderson’s Constructionist Hypothesis

Fontana’s and Buss’s Computational Constructions

?

Reiser’s Transfinite Aggregates

Holland’s Sets of Equations that Change CardinalityCrutchfield’s

Calculi of Emergence

Bennett’s Logical Depth Cohen’s/Stewart’s

Existence Theorem for Emergent Phenomena

Piaget’s Logico-Mathematical Constructions

Anderson’s Constructionist Hypothesis

Fontana’s and Buss’s Computational Constructions

Gödel and Turing: Limitative Theorems

Reiser’s Transfinite Aggregates

Holland’s Sets of Equations that Change CardinalityCrutchfield’s

Calculi of Emergence

Bennett’s Logical Depth Cohen’s/Stewart’s

Existence Theorem for Emergent Phenomena

Piaget’s Logico-Mathematical Constructions

Anderson’s Constructionist Hypothesis

Fontana’s and Buss’s Computational Constructions

Cantorian Anti-diagonalization”

Reiser’s Transfinite Aggregates

Holland’s Sets of Equations that Change CardinalityCrutchfield’s

Calculi of Emergence

Bennett’s Logical Depth Cohen’s/Stewart’s

Existence Theorem for Emergent Phenomena

Piaget’s Logico-Mathematical Constructions

Anderson’s Constructionist Hypothesis

Fontana’s and Buss’s Computational Constructions

Self-transcending Constructions “STC”

Construction of anti-diagonal sequence to transcend Construction of anti-diagonal sequence to transcend

cardinality of rational numbers:cardinality of rational numbers:

Definition 1: Definition 1: RR is a 3-place relation among x,y,z represented is a 3-place relation among x,y,z represented as as DD11 and and DD22 making-up vertical and horizontal arrays of making-up vertical and horizontal arrays of

rationalsrationalsDefinition 2: A diagonal Definition 2: A diagonal FF is constructed on is constructed on DD11 and and DD22 so that so that

the mapping is a bijection the mapping is a bijection DD11 ----> > DD22

Definition 3: Definition 3: GG is the value of the diagonal is the value of the diagonal FF in in RRDefinition 4: Definition 4: STCSTC is an anti-diagonal of is an anti-diagonal of FF in in R so thatR so that((STCxyzSTCxyz = =¬ Gxyz¬ Gxyz))

NOTE: NOTE: ¬ ¬ IS A NEGATION OPERATOR WHICH ALLOWS STC IS A NEGATION OPERATOR WHICH ALLOWS STC TO TRANSCEND CARDINALITY OF RATIONALSTO TRANSCEND CARDINALITY OF RATIONALS

Formalism of STC (incl. Negation) -Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONSADAPTED FROM SIMMONS

EVOLUTION VERSUS DESIGNEVOLUTION VERSUS DESIGN

•CONTINUITY OF EVOLUTION VERSUS DISCONTINUITY OF

CONSTRUCTION

BERGSON: BERGSON: ELAN VITALELAN VITAL VERSUS VERSUS MACHINEMACHINE

•CONSTRUCTION SEEMS TO IMPLY CONSTRUCTOR

• CONSTRUCTIONS ARE THOUGHT OF AS PREDICTABLE AND DEDUCIBLE

BIAS AGAINST BIAS AGAINST CONSTRUCTIONCONSTRUCTION SCIENCE VERSUS ARTSCIENCE VERSUS ART

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 CONSTRUCTIONAL SOURCES OF NOVELTY IN NEO-OF NOVELTY IN NEO-EMERGENTISMEMERGENTISM

RECURSIVE RECURSIVE OPERATIONS, E.G., OPERATIONS, E.G., FUNCTIONAL ITERATION, FUNCTIONAL ITERATION, CROSSOVER, CROSSOVER, RECOMBINATION..RECOMBINATION.. NEGATION OPERATIONS NEGATION OPERATIONS (CHANGING VALUES ON (CHANGING VALUES ON RECURSION)RECURSION)

INTRODUCTING INTRODUCTING RANDOMNESS INTO RANDOMNESS INTO SYSTEMSYSTEM

f f cc : :IIcc x x SScc SScc (where (where ffcc is defined so that is defined so that

ffcc (t+1) = (t+1) = ffcc((IIcc(t)(t)SScc(t)); (t)); II = possible input = possible input

combinations at time t, combinations at time t, S S = states of system = states of system at time tat time t

Constrained Generating Procedures (Holland)Constrained Generating Procedures (Holland)

RECURSIONRECURSION

x f f f f x f xnn ( (. . . ( ( )). . . )) ( )0 0

FUNCTIONAL ITERATIONFUNCTIONAL ITERATION

((FEIGENBAUM’S ROUTE TO CHAOSFEIGENBAUM’S ROUTE TO CHAOS))

f f nn is the is the nnth iterate of th iterate of ff

RECURSIONRECURSION

Holland’s Genetic Holland’s Genetic Recombination Using Recombination Using Negation and RandomnessNegation and Randomness

Crossover and Mutation Negate Previous

Combination at Every Iteration

AND/OR MUTATION

Construction of anti-diagonal sequence to transcend Construction of anti-diagonal sequence to transcend

cardinality of rational numbers:cardinality of rational numbers:

Definition 1: Definition 1: RR is a 3-place relation among x,y,z represented is a 3-place relation among x,y,z represented as as DD11 and and DD22 making-up vertical and horizontal arrays of making-up vertical and horizontal arrays of

rationalsrationalsDefinition 2: A diagonal Definition 2: A diagonal FF is constructed on is constructed on DD11 and and DD22 so that so that

the mapping is a bijection the mapping is a bijection DD11 ----> > DD22

Definition 3: Definition 3: GG is the value of the diagonal is the value of the diagonal FF in in RRDefinition 4: Definition 4: STCSTC is an anti-diagonal of is an anti-diagonal of FF in in R so thatR so that((STCxyzSTCxyz = =¬ Gxyz¬ Gxyz))

NOTE: NOTE: ¬ ¬ IS A NEGATION OPERATOR WHICH ALLOWS STC IS A NEGATION OPERATOR WHICH ALLOWS STC TO TRANSCEND CARDINALITY OF RATIONALSTO TRANSCEND CARDINALITY OF RATIONALS

Formalism of STC (incl. Negation) -Formalism of STC (incl. Negation) -ADAPTED FROM SIMMONSADAPTED FROM SIMMONS

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 wildernessAnd rivers out of the desert.

-Isaiah 43:19