Metaphysics of Emergence

Rainer E. Zimmermann

rainer.zimmermann@hm.edu

Research Programme

• Language & Space

• Theory of Spaces, Networks, Systems

• Systematical Line: Spinoza – Schelling – Bloch (Modern Dialectical Materialism)

• Methodological Line: Ontological Triad (Cognition, Communication, Cooperation) & Epistemological Triad (Spaces, Networks, Systems)

Confrontational Idea

• Emergence vs. Evolution

• Example: Cell Membranes

• David Deamer et al. (2002): The First Cell Membranes. Astrobiology 2 (4), 371-381.

Co-operation

• Thanks go in particular to José María Díaz Nafría (León), Klaus Fuchs-Kittowski (Berlin), Iain Hamilton Grant (Bristol), Wolfgang Hofkirchner (Vienna), Peter Knopp (Berlin), Jason Wirth (Seattle).

Recent Literature

• Gilles Châtelet: L’enchantement du virtuel. Ed. Charles Alunni, Cathérine Paoletti, Rue d’Ulm (ENS), Paris, 2010.

• Louis H. Kauffman: Eigenforms and Quantum Physics (at the Foerster 100th birthday jubilee, U Vienna 2011)

• Richard Healey: Gauging What’s Real. Oxford University Press, 2010

• John Baez, Javier P. Muniain: Gauge Fields, Knots, and Gravity. World Scientific, 1994.

Preliminary Remarks

• The Concept of Motion (Epistemological rather than Ontological)

• Hence: Evolutionary Systems are models of the wordly substratum (Matter: Urstoff = Arist. hypokeimenon), not models of substance (ousía) as the world‘s ground.

• Metaphysical difference: worldly categories vs. conditions of substance

Preliminary Remarks

• (Modern) Attributes of Substance:• energy-matter vs. information-structure• http://www.mdpi.com/2078-2489/3/3/472• New Ethics Proved in Geometrical Order: Spinozist

Reflexions on Evolutionary Systems• (Emergent Publications (Az.), 2010).• Nothingness as Ground, and Nothing but Ground• (Northwestern University Press, forthcoming 2013)• [with Simon M. Wiedemann] Kreativität und Form

(Glasperlenspiel) (Springer, 2012)

Emergence

• Every resultant is clearly traceable in its components, because these are homogeneous and commensurable. It is otherwise with emergents, when, instead of adding measurable motion to measurable motion, or things of one kind to other individuals of their kind, there is a co-operation of things of unlike kinds. The emergent is unlike its components insofar as these are incommensurable, and it cannot be reduced to their sum or their difference. (Lewes 1875)

Emergence

• (1) radical novelty (features not previously observed in systems);

• (2) coherence or correlation (meaning integrated wholes that maintain themselves over some period of time); structural stability, interaction of micro- and macro-levels (upward&downward causation (supervenience), top-down&bottom-up);

• (3) product of a dynamical process (it evolves).

Emergence

Continuous Models (Keller/Segel; Prigogine)(Selbstreferenz & poetische Praxis, 1991)

(a, ): amoebae/acrasine density

a/t = – (D1) + (D2a),

/t = – k1 + k-1c + a f() + D 2

k: rate constants for acrasin-acrasinase reactions, eqns. for c and skipped (complex building)

Emergence

Slime Mold Aggregation (Dictyostellum discoideum)

Emergence

• Matrix representation of operator formulation:

• E11 = – (D1), E12 = (D2) – /t,

• E21 = p() + D 2 – /t, E22 = f(),

• E x = 0. (x = (,a))

Emergence

• E E* = N(E) Negation Operator (Negator)

• Instability (Onset of Aggregation) requires new structural stability! Hence:

• E* E** = N(E*) = NN(E) = N2(E)

• Negation of the Negation

• If E = N0(E), then the following diagram is consistent:

Emergence

• 1 (structurally stable state) N(E) 2 (unstable state)• • N2(E)• • 4 … 3 (stable again)

• Sandwich structures: Schelling (PP)! The potential must be loaded with concrete power in order to become actualized. (Transition from micro to macro levels!)

• Metaphysical perspective: Nothingness that is loaded with power becomes non-being. Non-being that is actualized becomes Being.

Interlude: Systemic Perspective

1. Network: Dynamical Core of Interactions (Transport of Information software)

2. Space: Mean Free Path of Interactions (Domain of Influence software/hardware)

3. System: Boundary Operator as defining the region of interaction with the environment (software/hardware)

Interlude: Systemic Perspective

• However: These categories are actually absent in absolute terms. They are simply technical ordering principles so as to make modeling possible at all.

• The systemic perspective is nothing but epistemological.

• But for human beings, the epistemology is also ontological. (Sandkühler, HHHolz)

• Hence: The onto-epistemic result is useful after all. It adequately maps the relationship between cognition and communication – but not the world as it really is!

Emergence

• Short Excursion into Topoi

• Essentially, a topos is a category plus an additional structure including initial and terminal objects, push-outs and pull-backs such that the following diagram commutes:

Emergence

• 1. Category

• A category C is a class of objects ob(C) and a class of morphisms mor(C) such that each morphism has a unique source and target object, respectively. Also, for every three objects a, b, c there is a binary operation of the form mor(a, b) x mor(b, c) mor(a, c) called composition such that associativity and left and right identity laws are valid.

• 2. Additional Structure …

Emergence

Emergence

• Generic Conjectures:

• NEG is the category of negators with the objects being the structurally stable world states and the morphisms being the negators themselves.

• Conjecture 1: NEG is a topos.• GAME is the category of games with the objects being

positions of agents in their utility space and the morphisms being the strategies of agents.

• Conjecture 2: NEG and GAME are generically isomorphic.

• (Because essentially, strategies act as negators among agents or their positions, respectively.)

Emergence

• Continuous scheme:• o = coefficient, x = differential operation• ox + ox + … + ox = 0,• … …,• ox + ox + … + ox = 0.

Sleeping variables: their o = 0. (the x are actually there)

Field of possibilities: their x = 0. (the x may come later)

Emergence

• Differential operators relatively simple case, but useful entry

• From physical structures to micro-organisms and to populations in biology similar approaches

• Most complex but best-known everyday example of emergence:

Emergence

Emergence

Emergence

• Note that both these states are stable, hence they can only be states 1 and 3 of the appropriate sandwich structure.

• In other words: The child must be the negation of the negation of the adults.

• Only strict case of individuality! (different from other animals)

Emergence

Emergence

• Analysis of necessary and sufficient conditions.

• Aristotelian: enérgeia/entelecheia (actuality) vs. possibility

• possibility: katà tò dynatón vs. dynámei ón

• (being according to possibility („I‘ll do my best“)/being in possibility: the potential to become something)

Emergence

• concepts• 1. thinkability in logical sense• 2. adequacy with respect to formal experience

(in the epistemic sense)• 3. relationship between possibility and actuality

(in the metaphysical sense)• types• 1. what is not yet• 2. what is contingent• 3. what is included in the necessary

Emergence

• Bloch‘s Aristotelian interpretation:• „Actualizing is thus to activate subjective

potential in order to produce consequences of the objectively-real possible.“ (EM 255; my translation)

• (Aristotle, Physics, 201b.3-5): „The becoming actualized of what is possible in so far as it is possible [of the being in possibility], this is obviously motion.“ (… he tou dynatou, he dynatón, entelécheia phaneròn óti kínesis estin.)

Emergence

• Cusanus: God is everything in complicated manner (omnia complicite);

• Hence: It is necessary to unfold what is folded (explicari in mundo)

Emergence

• Shifts of Possibility (Bloch)• 1. the formally possible (that can be thought)• 2. the matter-of-fact objectively possible (that can be:

problematic judgement)• 3. the possible according to matter and object (that can

become, independent of its knowledge)• active can be (power: Vermögen) vs. passive can

become (potentiality)[subjective vs. objective factor: open power vs. Open potentiality]

• 4. the objectively real possible (the substratum = matter/dynámei ón/Urstoff)

Emergence

• Social, psychological, biological (chemical as well as physical) factors shape the field of possibilities.

Emergence

• Rosetta stone of universal isomorphisms (conjecture)

• NEG OPS … GAME SOCS

• Emergence shows up in terms of initial and terminal objects. (0 A, a: 1 A)

• An element of a set A is any mapping whose codomain is A and whose domain is 1.

Emergence

• particle annihilation & creation n = ( n!)-1/2 (a†)n n

• an = n n – 1• a†n = (1 n) n + 1• a0 = 0

k = ak†0

Emergence

• From Quantum Gravity to the DNA (Lou Kauffman)

• Temperley-Lieb algebra/Artin braid group/Jones polynomial of invariants of knots and links

• creation operator cup := a†: C V V• annihilation operator cap := <a: V V C in

order to define the computation of a link amplitude (state sum) of type:

• Z = <cupMcap

Emergence

• Motivation:

• • + = in t/x co-ordinates

Emergence

• Categorification of Quantum Physics

• Jeffrey C. Morton, Jamie Vicary: The Categorified Heisenberg Algebra I: A Combinatorial Representation.

• http://arxiv.org/pdf/1207.2054v1.pdf

Emergence

• A. Kock, G. E. Reyes: Fractional Exponent Functors and Categories of Differential Equations. (1998)

• http://home.imf.au.dk/kock/ODE55.pdf