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Complex yet Causal Lorenzo Casini L.Casini@kent.ac.uk University of Kent

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Outline What is Complexity Simplicity Some “Complications” Crisis of Classical Thinking ? Old Metaphysics, New Epistemology Causality as Epistemic Category 2

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What is Complexity Several proposals, none is widely accepted Formal measures: Algorithmic complexity Statistical complexity … Definitions: non-Turing-computability of some models of a system (Rosen) –Formal feature of models bearing on ontology of systems 3

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Object-driven characterisations: self-organisation: “order from noise” (von Foerster), “order through fluctuations” (Prigogine) self-organised criticality (Bak) autopoiesis (Maturana & Varela) adaptation (Holland) … Subject-driven “aspects”: contextuality (Chu) observer-relativity (Gesherson-Heylighen) gap between formal models and real systems (Casti) Eclectic checklists Compositional + dynamical + adaptive + plurality of descriptions (Mitchell) 4

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No clear account of causality Sometimes complexity and causality are presented as incompatible: chaos as randomness emergence as a gap in the causal chain holism as pan-interactionism (non causal)... 5

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Simplicity In classical dynamics (Prigogine & Stengers 1984): Lawfulness –objects’ trajectories depend on dynamical laws and are deducible from these Determinism –given laws and initial conditions, past and future states are given Reversibility –given complete knowledge, time inversion can be performed by inverting velocities 6

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What is causality? Metaphysics –relation between states of the system, such that each state necessitates the state that follows and is necessitated by the state that precedes along a continuous temporal chain Epistemology –this relation that can be, in principle, known and exploited for explanation (retrodiction), prediction, intervention (velocity inversion) Simplicity Galileo: Nature is governed by “simple” laws 7

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Some “Complications” Nonlinearity –Trajectories in nonlinear systems cannot be easily deduced— many differential equations cannot be solved analytically Extreme sensitivity to initial conditions –in chaotic systems, future states depend on exact specification of initial conditions—infinitely small changes determine large changes—and cannot be calculated exactly 8

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Bifurcations and symmetry-breaking –far-from-equilibrium dissipative (nonlinear) systems can go through infinitely many stable configurations in response to infinitely small changes in some bifurcation parameter, e.g. heat (convection), growth rate (population evolution) –“chancy” fluctuations (fields, quantum fluctuations, distribution of chemical reactants) affect micro-dynamics at bifurcation points and determine (random?) choice between bifurcation branches which results in qualitative changes in macro-dynamics 9

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Crisis of Classical Thinking ? Determinism –knowledge of a state doesn’t allow exact prediction and retrodiction of other states—but these remain determined (dynamics is described by topology and computation) Irreversibility –knowledge of a macro-state doesn’t allow ideal intervention (velocity inversion at the micro-level)—but Laplace’s demon knows positions and momenta of particles at the micro-level Lawfulness –are there, but too complex for us (End of simplicity)..and causality? 10

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–An external input causes an open system to stay in/ move along/ towards/ away from /change, attractor –A state causes another state along a closed chain (e.g. limit cycle) in which an open system is “organisationally” closed (Heylighen) –A configuration of parts that follow deterministic rules of behaviour causes the “emergent” behaviour of the whole –An attractor “downwardly” causes its nearby states (its basin, or domain of attraction) to converge towards it –Components “interact”, i.e. the state of one causes (fully or partially) the state of another (Chen Nagl & Clack) … All these “modes” seem compatible with traditional metaphysics—only require complex epistemology Complexity is an observer-dependent notion a worldview a collection of techniques and models 11

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Old Metaphysics, New Epistemology Determinism without simple LAWS –any state is fully determined by some previous state –but these states are often not subsumable under strict LAWS (many dynamical “laws”, e.g. kinetics, are only contingent generalisations) “Old” epistemology (universal theories & laws) is abandoned –due to problems of deducibility, predictability, measurement, etc. “New” epistemology is embraced –Primacy of models-mediators, approximations to reality—faithful to some systems, hardly exportable to others 12

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Causality as Epistemic Category (directions for future work) Complexity reveals that notion of ‘cause’ depends first on our practices—only indirectly on our metaphysics necessary to analyse nature of this dependence Models cannot be totally faithful (openness, nonlinearities, contextuality) but abstract from details irrelevant to the purpose at hand (e.g. pretending cell metabolism is like electric circuit with few components) what’s the nature of this abstraction? Causality is an epistemic category that we confidently apply to reality if our models successfully mediate between us and reality When is a mediation successful? A mediation is successful (i.e. identifies causal structure) when satisfies 3 general desiderata—tells us what –needs to be included to “reproduce” system’s behaviour –is good predictor of system’s behaviour –can be manipulated to modify this behaviour 13

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causality is an entailment relation causal relations are inference patterns extracted from models (not from systems directly) with which we reason about systems in explanation, prediction, control This doesn’t entail denial of objectivity of causal relations— what Laplace’s demon knows Only stresses that (causal) knowledge involves necessarily approximations to, constructions of and interactions with phenomena 14

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Some figures adapted from a 2004 Lecture by Larry Liebovitch, Ph.D. Chaos BIOL/CMSC 361: Emergence 1/29/08.

Some figures adapted from a 2004 Lecture by Larry Liebovitch, Ph.D. Chaos BIOL/CMSC 361: Emergence 1/29/08.

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