Complex Systems and the Evolution of Life

  • Klaus Mainzer


How can one explain the emergence of order in the Darwinian evolution of life? In the history of philosophy and biology, life was explained teleologically by non-causal (“vital”) forces aiming at some goals in nature. In a famous quotation Kant said that the “Newton for explaining a blade of grass” could never be found (Sect. 3.1). Boltzmann could show that living organisms are open dissipative systems which do not violate the second law of thermodynamics: Maxwell’s demons are not necessary to explain the arising order of life in spite of the increasing entropy and disorder in closed systems according to the second law. Nevertheless, in the statistical interpretation from Boltzmann to Monod the emergence of life is only a contingent event, a local cosmic fluctuation at the boundary of the universe (Sect. 3.2). In the framework of complex systems the emergence of life is not contingent, but necessary and lawful in the sense of dissipative self-organization. The growth of organisms and species is modeled as the emergence of macroscopic patterns caused by nonlinear (microscopic) interactions of molecules, cells, etc., in phase transitions far from thermal equilibrium (Sect. 3.3). Even ecological populations are understood as complex dissipative systems of plants and animals with mutual nonlinear interactions and metabolism with their environment (Sect. 3.4). Spencer’s idea that life is determined by a structural evolution with increasing complexity seems to be mathematized by complex dynamical systems. Is the “Newton of life” found? The theory of complex dynamical systems does not explain what life is, but it can model how forms of life can arise under certain conditions. Thus, the existence of our life is still a wonder for us as well as for our ancestors, even if we shall eventually model the complex dynamics of life.


Phase Portrait Predator Fish Dissipative Structure Slime Mold Prey Fish 
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  1. 3.1
    For historical sources of Sect. 3.1 compare Mainzer, K.: Die Philosophen und das Leben. In: Fischer, E.P., Mainzer, K. (eds.): Die Frage nach dem Leben. Piper: München (1990) 11–44Google Scholar
  2. 3.
    Diels-Kranz (see Note 2, Chapter 2) 12 A 30Google Scholar
  3. 3.
    Aristotle: Historia animalium 588 b 4Google Scholar
  4. 3.
    Aristotle: De generatione animalium II 736 b 12–15. a 35-b2Google Scholar
  5. 3.
    Descartes, R.: Discours de la méthode. Leipzig (1919/20) 39Google Scholar
  6. 3.6
    Borelli, G.A.: De motu animalium. Leipzig (1927) 1Google Scholar
  7. 3.
    Leibniz, G.W.: Monadology §64Google Scholar
  8. 3.8
    Bonnet, C.: Contemplation de la nature (1764). Oeuvres VII, 45Google Scholar
  9. 3.9
    Kant, I.: Kritik der Urteilskraft. Ed. G. Lehmann, Reclam: Stuttgart (1971) 340Google Scholar
  10. 3.10
    Goethe, J.W.: Dichtung und Wahrheit. In: Werke ( Hamburger Ausgabe) Bd. IX 490Google Scholar
  11. 3.11
    Schelling, F.W.J.: Sämtliche Werke Bd.II (ed. Schröter, M. ), München (1927) 206Google Scholar
  12. 3.12
    Darwin, C.: On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. London (1859)Google Scholar
  13. Darwin, C.: The Descent of Man, and Selection in Relation to Sex. London (1871)Google Scholar
  14. Spencer, H.: Structure, Function and Evolution (ed. Andrenski, S. ), London (1971)Google Scholar
  15. Darwin, C.: For a modern evaluation of Darwin’s position compare Richards, R.: The Meaning of Evolution. University of Chicago Press: Chicago (1992)Google Scholar
  16. 3.13
    Boltzmann, L.: Der zweite Hauptsatz der mechanischen Wärmetheorie. In: Boltzmann, L. (ed.): Populäre Schriften. Leipzig (1905) 24–46Google Scholar
  17. 3.
    Cf. Schneider, I.: Rudolph Clausius’ Beitrag zur Einführung wahrscheinlichkeitstheoretischer Methoden in die Physik der Gase nach 1856. Archive for the History of Exact Sciences 14 (1974/75) 237–261Google Scholar
  18. 3.
    Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes (see Note 43, Chapter 2)Google Scholar
  19. 3.
    Cf. Boltzmann, L.: Über die mechanische Bedeutung des zweiten Hauptsatzes der Wärmetheorie (1866). In: Boltzmann, L.: Wissenschaftliche Abhandlungen (ed. Hasenöhrl, F.) vol. 1 Leipzig (1909), repr. New York (1968) 9–33.Google Scholar
  20. Analytischer Beweis des zweiten Hauptsatzes der mechanischen Wärmetheorie aus den Sätzen über das Gleichgewicht der lebendigen Kraft (1871) 288–308Google Scholar
  21. 3.17
    Cf., e.g., Einstein’s famous article `Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen’. Annalen der Physik 17 (1905) 549–560Google Scholar
  22. 3.18
    Poincaré, H.: Sur les tentatives d’explication méchanique des principes de la thermodynamique. Comptes rendus de l’Académie des Sciences 108 (1889) 550–553.zbMATHGoogle Scholar
  23. Zermelo, E.: Über einen Satz der Dynamik und die mechanische Wärmetheorie. Annalen der Physik 57 (1896) 485ADSCrossRefGoogle Scholar
  24. 3.19
    Cf. Popper, K.R.: Irreversible processes in physical theory. Nature 181 (1958) 402–403ADSCrossRefGoogle Scholar
  25. Reichenbach, H.: The Direction of Time. Berkeley (1956)Google Scholar
  26. Grünbaum, A.: Philosophical Problems of Space and Time. Dordrecht (1973)Google Scholar
  27. Hintikka, J., Gruender, D., Agazzi, E. (eds.): Probabilistic Thinking, Thermodynamics and the Interaction of the History and Philosophy of Science II. Dordrecht/Boston/ London (1978)Google Scholar
  28. 3.20
    Boltzmann, L.: Der zweite Hauptsatz der mechanischen Wärmetheorie. In: Boltzmann, L.: Populäre Schriften (see Note 13 ) 26–46Google Scholar
  29. 3.21
    Boltzmann, L.: Über die Frage nach der objektiven Existenz der Vorgänge in der unbelebten Natur. In: Boltzmann, L.: Populäre Schriften (see Note 13 ) 94–119Google Scholar
  30. 3.22
    Monod, J.: Le Hasard et la Nécessité. Editions du Seuil: Paris (1970)Google Scholar
  31. 3.23
    Primas, H.: Kann Chemie auf Physik reduziert werden? Chemie in unserer Zeit 19 (1985) 109–119, 160–166CrossRefGoogle Scholar
  32. 3.24
    Bergson, H.L.: L’évolution créative. Paris (1907).Google Scholar
  33. Heitler, W.H.: Über die Komplementarität von lebloser und lebender Materie. Abhandlungen der Math.-Naturw. Klasse d. Ak. d. Wiss. u. Lit. Mainz Nr. 1 (1976) 3–21Google Scholar
  34. Driesch, A.: Philosophie des Organischen. Leipzig (1909).Google Scholar
  35. Whitehead, A.N.: Process and Reality. An Essay in Cosmology. New York (1978)Google Scholar
  36. 3.25
    Schrödinger, E.: Was ist Leben? Piper: München (1987) 133Google Scholar
  37. 3.
    Schrödinger, E.: Was ist Leben? (see Note 25) 147Google Scholar
  38. 3.27
    Thompson, W: The Sorting Demon of Maxwell (1879). In: Thompson, W: Physical Papers I-VI, Cambridge (1882–1911), V, 21–23Google Scholar
  39. 3.
    Prigogine, I.: Time, irreversibility and structure. In: Mehra, J. (ed.): The Physicist’sGoogle Scholar
  40. Conception of Nature. D. Reidel: Dordrecht/Boston (1973) 589Google Scholar
  41. 3.29
    Eigen, M.: The origin of biological information. In: Mehra, J. (ed.): The Physi- cist’s Conception of Nature (see Note 28 ) 607.Google Scholar
  42. Fig. 3.2 shows a so-called coat gene obtained by nuclease digestion of phage MS2-RNA (Min Jou, W., Haegemann, G., Ysebaert, M., Fiers, W: Nature 237 (1972) 82). This gene codes for a sequence of 129 amino acids. The structure is further spatially folded. Also compare Perel- son, A.S., Kauffman, S.A. (eds.): Molecular Evolution on Ragged Landscapes: Proteins, RNA, and the Immune System. Santa Fé Institute Studies in the Sci- ences of Complexity, Proceedings vol. 9. Addison-Wesley: Redwood City (1990)Google Scholar
  43. 3.30
    For a survey cf. Depew, D.J., Weber, B.H.: Evolution at a Crossroads. The New Biology and the New Philosophy of Science. MIT Press: Cambridge, MA (1985)Google Scholar
  44. Ebeling, W., Feistel, R.: Physik der Selbstorganisation und Evolution. Akademie-Verlag: Berlin (1982)Google Scholar
  45. Haken, H., Haken-Krell, M.: Entstehung von biologischer Information und Ordnung. Wissenschaftliche Buchgesellschaft: Darmstadt (1989).Google Scholar
  46. Hofbauer, L.: Evolutionstheorie und dynamische Systeme. Mathematische Aspekte der Selektion. Springer: Berlin (1984)zbMATHGoogle Scholar
  47. 3.
    Eigen, M.: Homunculus im Zeitalter der Biotechnologie — Physikochemische Grundlagen der Lebensvorgänge. In: Gross, R. (ed.): Geistige Grundlagen der Medizin. Springer: Berlin (1985) 26, 36 for Fig. 3.4a—d.Google Scholar
  48. Maynard Smith, J.: Optimization theory in evolution. Annual Review of Ecological Systems 9 (1978) 31–56CrossRefGoogle Scholar
  49. Mainzer, K.: Metaphysics of nature and mathematics in the philosophy of Leibniz. In: Rescher, N. (ed.): Leibnizian Inquiries. University Press of America: Lanham/New York/London (1989) 105–130Google Scholar
  50. 3.32
    Dyson, F.: Origins of Life. Cambridge University Press: Cambridge (1985)Google Scholar
  51. 3.33
    Kauffman, S.: Autocatalytic sets of proteins. Journal of Theoretical Biology 119 (1986) 1–24CrossRefGoogle Scholar
  52. 3.34
    For a survey cf. Kauffmann, A.S.: Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press: Oxford (1992)Google Scholar
  53. 3.35
    Haken, H.: Synergetics (see Note 4, Chapter 1 ) 310Google Scholar
  54. 3.
    Hess, B., Mikhailov, A.: Self-organization in living cells. In: Science 264 (1994) 223–224Google Scholar
  55. Hess, B., Mikhailov, A.: Ber. Bunsenges. Phys. Chem. 98 (1994) 1198–1201 (extended version)Google Scholar
  56. 3.37
    Susman, M.: Growth and Development. Prentice-Hall: Englewood Cliffs, NJ (1964)Google Scholar
  57. Prigogine, I.: Order through fluctuation. In: Jantsch, E., Waddington, C.H. (eds.): Evolution and Consciousness. Human Systems in Transition. Addison-Wesley: London (1976) 108Google Scholar
  58. 3.38
    Gerisch, G., Hess, B.: Cyclic-AMP-controlled oscillations in suspended dictyostelium cells: Their relation to morphogenetic cell interactions. Proc. Natl. Acad. Sci. 71 (1974) 2118Google Scholar
  59. 3.39
    Rosen, R.: Dynamical System Theory in Biology. Wiley-Interscience: New York (1970)zbMATHGoogle Scholar
  60. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Bahavior (see Note 14, Chapter 2) 110 for Figs. 3. 5Google Scholar
  61. 3.40
    Meinhardt, H., Gierer, A.: Applications of a theory of biological pattern formation based on lateral inhibition. J. Cell. Sci. 15 (1974) 321 (Figs. 3. 7–8 )Google Scholar
  62. Meinhardt, M.: Models of Biological Pattern Formation. Academic Press: London (1982)Google Scholar
  63. 3.41
    For a survey compare Gerok, W. (ed.): Ordnung und Chaos in der belebten und unbelebten Natur. Verhandlungen der Gesellschaft Deutscher Naturforscher und Ärzte. 115. Versammlung (1988), Stuttgart (1989)Google Scholar
  64. Mainzer, K.: Chaos und Selbstorganisation als medizinische Paradigmen. In: Deppert, W., Kliemt, H., Lohff, B., Schaefer, J. (eds.): Wissenschaftstheorien in der Medizin. De Gruyter: Berlin/New York (1992) 225–258Google Scholar
  65. 3.42
    Bassingthwaighte, J.B., van Beek, J.H.G.M: Lightning and the heart: Fractal behavior in cardiac function. Proceedings of the IEEE 76 (1988) 696CrossRefGoogle Scholar
  66. 3.43
    Goldberger, A.L., Bhargava, V., West, B.J.: Nonlinear dynamics of the heartbeat. Physica 17D (1985) 207–214MathSciNetzbMATHGoogle Scholar
  67. Goldberger, A.L., Bhargava, V., West, B.J.: Nonlinear dynamics in heart failure: Implications of long-wavelength cardiopulmonary oscillations. American Heart Journal 107 (1984) 612–615CrossRefGoogle Scholar
  68. Ree Chay, T., Rinzel, J.: Bursting, beating, and chaos in an excitable membrance model. Biophysical Journal 47 (1985) 357–366ADSCrossRefGoogle Scholar
  69. Winfree, A.T.: When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton (1987)Google Scholar
  70. Guevara, M.R., Glass, L., Schrier, A.: Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214 (1981) 1350Google Scholar
  71. 3.44
    Cf. Johnson, L.: The thermodynamic origin of ecosystems: a tale of broken symmetry. In: Weber, B.H., Depew, D.J., Smith, J.D. (eds.): Entropy, Information, and Evolution. New Perspectives on Physical and Biological Evolution. MIT Press. Cambridge, MA (1988) 75–105Google Scholar
  72. Schneider, E.D.: Thermodynamics, ecological succession, and natural selection: a common thread. In: Weber, B.H., Depew, D.J., Smith, J.D. (eds.): Entropy, Information, and Evolution (see Note 42) 107138Google Scholar
  73. 3.45
    Odum, E.P.: The strategy of ecosystem development. Science 164 (1969) 262–270ADSCrossRefGoogle Scholar
  74. Margalef, R.: Perspectives in Ecological Theory. University of Chicago Press: Chicago (1968)Google Scholar
  75. 3.46
    Lovelock, J.E.: The Ages of Gaia. Bantam (1990)Google Scholar
  76. Schneider, S.H., Boston, P.J. (eds.): Scientists on Gaia. MIT Press: Cambridge, MA (1991)Google Scholar
  77. Pimm, S.: The Balance of Nature, University of Chicago Press: Chicago (1991)Google Scholar
  78. 3.
    Cf. Rosen, R.: Dynamical System Theory in Biology (see Note 37)Google Scholar
  79. Freedmann, H.I.: Deterministic Mathematical Models in Population Ecology. Decker: New York (1980)Google Scholar
  80. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Behavior (see Note 14, Chapter 2 ) 85Google Scholar
  81. 3.48
    Lotka, A.J.: Elements of Mathematical Biology. Dover: New York (1925)Google Scholar
  82. Volterra, V.: Leçons sur la théorie mathématique de la lutte pour la vie. Paris (1931)Google Scholar
  83. Haken, H.: Synergetics (see Note 4, Chapter 1) 130, 308Google Scholar
  84. 3.49
    Rettenmeyer, C.W.: Behavioral studies of army ants. Kansas Univ. Bull. 44 (1963) 281Google Scholar
  85. Prigogine. I.: Order through Fluctuation: Self-Organization and Social System. In: Jantsch, E., Waddington, C.H. (eds.): Evolution and Consciousness (see Note 35 ) 111Google Scholar
  86. 3.50
    Prigogine, I., Allen, P.M.: The challenge of complexity. In: Schieve, W.C., Allen, P.M.: Self-Organization and Dissipative Structures. Applications in the Physical and Social Sciences. University of Texas Press: Austin (1982) 28Google Scholar
  87. Wicken, J.S.: Thermodynamics, evolution, and emergence: Ingredients of a new synthesis. In: Weber, B.H., Depew, D.J., Smith, J.D. (eds.): Entropy, Information, and Evolution (see Note 42 ) 139–169Google Scholar

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© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Klaus Mainzer
    • 1
  1. 1.Lehrstuhl für Philosophie und WissenschaftstheorieUniversität AugsburgAugsburgGermany

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