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Is There Anything New Under the Sun?

Instability as the Core of Emergence

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Emergence and Modularity in Life Sciences

Abstract

This chapter aims to give substance to a contemporary understanding of emergence from the perspective of the philosophy of science. Looking at progress in the natural sciences, it draws on the concept of self-organization in order to provide a characterization of emergence. From the 1960s onward, theories of self-organization (including complex systems theory, nonlinear dynamics, chaos theory, synergetics, dissipative structures, fractal geometry, and autopoiesis theory) explicitly addressed emergent behavior. Referring to those theories, this chapter enquires into the ontological core as well as into the methodological and epistemological characteristics of self-organization—and, hence, of emergence. It is asked whether there is unity in the diversity of self-organizing phenomena in nature. It will be shown that instabilities constitute the ontological core of self-organization and are, therefore, central to any semantically meaningful understanding of emergence. Besides this ontological condition for the possibility of emergence (instability), the chapter also reveals that there are three further ontological characteristics of emergence, namely, (1) novelty, (2) processuality/temporality, (3) internality (“self”). In addition, related methodological and epistemological characteristics encompass: (4) limits in reproducibility/repeatability, (5) obstacles to predictability and (6) deficits in testability and reductive describability/explainability. In sum, since instabilities play a crucial role in nature, they are essential to any present-day concept of emergence.

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Notes

  1. 1.

    Well known in the Latin statement: Nihil sub sove novum (colloquial translation at Ecclesiastes 1:9).

  2. 2.

    For instance: Conway Lloyd Morgan, Samuel Alexander, Roy W. Sellars, and William McDougall.

  3. 3.

    The concepts are often used interchangeably, although “self-organization” is broader in content than “emergence”.

  4. 4.

    This vagueness of the term has challenged philosophers such as Ansgar Beckermann, Hans Flohr, Jaegwon Kim and Manfred Stöckler to provide clarification.

  5. 5.

    The main points of the list that follows can also be found in Stephan (2007) and in more detail in Schmidt (2015). However, Stephan (2007) distinguishes between different types of emergence. As we are here less interested in semantic details and more concerned with providing a conceptual framework, we will not make further differentiations at this point.

  6. 6.

    The properties might also include aspects of information, dispositions, or risks.

  7. 7.

    Including Nonlinear Dynamics, Chaos Theory, Synergetics, Dissipative Structures, Fractal Geometry, and Catastrophe Theory.

  8. 8.

    In fact, we can observe a convergence of some sub-disciplines of physics, informatics, biology, chemistry, and medicine.

  9. 9.

    I wish to stress here at the beginning of the chapter that the same holds for social or technical complex systems.

  10. 10.

    For instance, as in a billiard system, which has become a paradigm in this regard.

  11. 11.

    Instability has, therefore, to be regarded as an empirical fact of our life-world and beyond—not just as a contingent convention.

  12. 12.

    In this regard, stability metaphysics precedes scientific methodology.

  13. 13.

    As was seen in the 19th century in the debate on the heat death of the universe.

  14. 14.

    Moreover, the various definitions and meanings of complexity—even if they do not refer to the genesis and evolution of a new pattern such as those in more geometric definitions of “complexity” via “dimensions”—refer directly or indirectly to instabilities (Atmanspacher et al. 1992; Wackerbauer et al. 1994).

  15. 15.

    The term “organization” in “self-organization” emphasizes such characteristics.

  16. 16.

    The priority of instability can also be shown for: symmetry breaking, phase transitions, time’s arrow/irreversibility, deterministic chance, randomness, chaos, turbulence, catastrophes, fractals, information loss or gain. In general, however, the same argument holds with respect to the essential role of nonlinearity in these phenomena. But nonlinearity per se does not challenge traditional physical methodology. Many systems are nonlinear but stable, for example, simple two-dimensional planetary systems. They are, like linear systems, without chaos and turbulence, without self-organization and symmetry breaking. Instability, and not nonlinearity by itself, makes the difference.

  17. 17.

    Or, more precisely, we could speak of the “onto-nomological core” of emergence (cf. Schmidt 2015).

  18. 18.

    Compare Maxwell’s (1991, p. 13) remark above, forty years earlier.

  19. 19.

    A special case of static instability is one that shows sensitive dependence of all points in the state space. A prominent example is compound interest. Tiny differences in seed capital grow exponentially into enormous differences years later. The linear differential equation dx/dt = ax yields a solution that can be determined analytically: x(t) = x(0) · eat, with a constant Lyapunov coefficient: a > 0. Trajectories starting from a neighborhood reveal a static continuous divergence. In an open-ended state space, they need never converge to each other again. However, a closed solution does not exist for this linear differential equation. If the initial conditions are known, a calculation for all times is feasible and a prediction is possible.

  20. 20.

    Translation from German (JCS).

  21. 21.

    Today, we utilize Poincaré’s fundamental ideas to construct a specific map in order to obtain insights into the time evolution of a dynamical system—the so-called “Poincaré map”.

  22. 22.

    The term “butterfly effect”, central to the notion of “chaos”, was coined by Lorenz (1963, 1989). In addition, and in more detail, more than 15 competing notions and definitions of “chaos” exist (cp. Brown and Chua 1996, 1998). One of the most relevant chaos definitions nowadays has been suggested by Devaney (1987). Devaney requires a system’s dynamics to exhibit three features in order to be called chaotic: (a) sensitive dependence on initial conditions (unpredictability); (b) topological transitivity (non-decomposability, wholeness); and (c) denseness of periodic points (elements of regularity). Banks et al. (1992) show from a mathematical perspective for one-dimensional maps that sensitivity (a) follows from properties (b) and (c). Thus, sensitivity does not seem to be a fundamental requirement for providing an adequate understanding of dynamical instability. From an empirical perspective, Devaney’s and Banks’ definitions—focusing on (b) and (c)—are regarded as interesting but hard to determine. Unlike mathematicians, physicists mostly advocate an understanding of chaos based on sensitivity coefficients. A classical sensitivity coefficient is Lyapunov’s exponent that measures the average divergence of trajectories (“chaos coefficient”). For physics and its methodological need to deal with experimental uncertainties, a positive Lyapunov exponent is one major characteristic of dynamical instability.

  23. 23.

    Depending on the initial model class, altering a model can be performed by varying the model’s equations, the system parameters or exponents, by adding mathematical functions or by modifying the state space.

  24. 24.

    Such as trigonometric stability, stability of the first order, permanent stability, semi-permanent stability, unilateral stability, regions of stability, stability in the sense of Poisson (cp. Birkhoff 1927).

  25. 25.

    It is important to stress, as Janich does convincingly, the experimental/engineering aspects of physics: physics aims to produce experimentally reproducible phenomena, and it is based on experimentation (cp. Hacking 1983).

  26. 26.

    Bunge believes that instabilities and nonlinearity make it too difficult to assign determinism to unstable dynamics.

  27. 27.

    In the case of static instability, if the watershed is not fractal or the initial states are not located within the neighborhood of the watershed, numerical integration is feasible. Small perturbations do not make any difference in the final result. In other cases, two initial states differing by imperceptible amounts may evolve into two considerably different states. Then, if any observation error of the present state is made, an acceptable prediction of the state (to within only small tolerances) in the distant future may well be impossible. Similar conclusions hold for structural instability.

  28. 28.

    Feigenbaum cited in Gleick (1987, p. 174f). The differential equation of a deterministic system is effectively worthless since reliable predictions would require exact information.

  29. 29.

    In particular, they drive a wedge between (deterministic) laws and (prediction-relevant, single) trajectories.

  30. 30.

    It is still an ongoing debate whether testability is to be understood as a normative requirement or merely as a description of what in fact happens in science.

  31. 31.

    In this line, Woodward (2000, p. 197) has very recently claimed: “Explanation in the special sciences involves subsumption under general laws.”

  32. 32.

    In the history of the philosophy of science, there has been a strong focus on these challenges, in particular on ontological, epistemological, and methodological types of reductionism. The unification of three of the four fundamental theories in physics shows the success of explanatory reductionism.

  33. 33.

    By referring to earthquakes Hume also supports his arguments against anti-naturalist positions since phenomena that appear irregular can be generated by regular laws.

  34. 34.

    This point is, in fact, the nucleus of the classic deductive-nomological account of explanation (cp. Hooker 2004).

  35. 35.

    For an in-depth discussion see, most prominently: Chaitin (1971, 1987, 2001).

  36. 36.

    For example, see Crutchfield et al. (1986), Devaney (1987), Peitgen et al. (1992), and Jackson (1989).

  37. 37.

    Of course, nonlinear techniques such as nonlinear data analysis, phase space reconstruction, surrogate data analysis, and other tools provide some options to find deterministic structures and separate them from white noise.

  38. 38.

    See the six characteristics described in the first part of this article, in particular the methodological and epistemological characteristics 4–6, such as non-reproducibility/non-repeatability (4), unpredictability (5), and irreducibility (6).

  39. 39.

    Prediction and time’s arrow are twins. And time is a necessary condition for the possibility of scientific experience.

  40. 40.

    For a brief history from a different point of view, see: Holmes (2005). In general, these challenges—and the related problems—can also be observed in the nineteenth century in the realm of hydrodynamics (cf. Darrigol 2006; Swinney and Gollub 1981).

  41. 41.

    An analysis of the historical development can be found in Aubin and Dalmedico (2002).

  42. 42.

    For an introduction to Duhem’s philosophy of instability see, Schmidt (2017).

  43. 43.

    “Deduction is sovereign mistress, and everything has to be ordered by the rules she imposes” (ibid., 266). A “deduction is of no use to the physicist so long as it is limited to asserting that a given rigorously true proposition has for its consequence the rigorous accuracy of some other proposition” (Duhem 1991, p. 143).

  44. 44.

    Further, Prigogine stresses that Duhem was pioneering in his reflection on instabilities, but–according to Prigogine–Duhem went too far in his general critique concerning the ultimate uselessness of “unstable deductions”. Duhem assessed instabilities in a negative sense only, as a threat to classical-modern physical methodology.

  45. 45.

    However, a proper methodology of the sort that works for stable objects is, and will always remain, impossible.

  46. 46.

    The traditional quantitative, metrically oriented stability dogma has been replaced by weaker, more qualitative topological characteristics.

  47. 47.

    Some of these deserve to be mentioned: entropies, information theory parameters, Lyapunov exponent, scaling exponents, lengths of transients, fractal dimensions, renormalization theory parameters, topological characteristics, structure of stable and unstable periodic trajectories, existence of chaos or hyper-chaos, parameters of basin boundaries, types of bifurcations, parameters of chaos control theory, power and Fourier spectra, phenomenological analysis of patterns, etc. Some of these properties are well known from solid state physics, fluid and plasma physics, meteorology, or statistical thermodynamics. What is new is (a) that these properties are necessary to empirically test (complex dynamical) models with just a few degrees of freedom and (b) that the model-theoretical discussion is deepened by the acceptance that nature can be structurally unstable.

  48. 48.

    The assumption required for the existence of such shadow trajectories is that the system is hyperbolic. How serious this restriction to hyperbolicity might be is still a matter of ongoing research.

  49. 49.

    The shift in terminology is not just rhetoric. Rather, it indicates a modeling turn in the sciences. For a philosophical account of models, see Redhead (1980), Morgan and Morrison (1999), and Hartmann and Frigg (2006). However, these authors already diagnose such a model-orientation in the realm of non-unstable objects.

  50. 50.

    It is interesting that an epistemological and methodological discussion on the structure of mathematical models is taking place within the sciences today, as part of the progress of the sciences themselves. Well-established ideas of philosophy of science are not an add-on—they can be considered as an intrinsic element of sciences. Instability and complexity carry philosophical thought, such as the reflection on the criteria for scientific evidence, truth or objectivity, into the very heart of sciences.

  51. 51.

    In his seminal book “Knowledge and Human Interest”, Habermas (1972) exemplifies this point and encourages a broader perception of the value dimension of research programs in general and among the public. However, in spite of its relevance to our late-modern technoscientific age, in the mainstream of the philosophy of science, Habermas’ central point was—and still is—neglected and disregarded.

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Schmidt, J.C. (2019). Is There Anything New Under the Sun?. In: Wegner, L., Lüttge, U. (eds) Emergence and Modularity in Life Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-06128-9_1

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