Skip to main content
SpringerLink
Log in
Book cover

Thinking in Complexity pp 15–78Cite as

Complex Systems and the Evolution of Matter

  • Chapter

  • 189 Accesses

Abstract

How can order arise from complex, irregular, and chaotic states of matter? In classical antiquity philosophers tried to take the complexity of natural phenomena back to first principles. Astronomers suggested mathematical models in order to reduce the irregular and complex planetary orbits as they are experienced to regular and simple movements of spheres. Simplicity was understood, still for Copernicus, as a feature of truth (Sect. 2.1). With Newton and Leibniz something new was added to the theory of kinetic models. The calculus allows scientists to compute the instaneous velocity of a body and to visualize it as the tangent vector of the body’s trajectory. The velocity vector field has become one of the basic concepts in dynamical systems theory. The cosmic theories of Newton and Einstein have been described by dynamical models which are completely deterministic (Sect. 2.2).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. For historical sources of Sect. 2.1 compare Mainzer, K.: Symmetries in Nature. De Gruyter: New York (1994) (German original 1988 ) Chapter 1

    Google Scholar 

  2. Diels, H.: Die Fragmente der Vorsokratiker, 6th ed., revised by W. Kranz, 3 vol. Berlin (1960/1961) (abbrev.: Diels-Kranz), 12 A 10 (Pseudo-Plutarch)

    Google Scholar 

  3. Diels-Kranz 13 A 5, B 1

    Google Scholar 

  4. Diels-Kranz 22 B 64, B 30

    Google Scholar 

  5. Heisenberg, W: Physik und Philosophie. Ullstein: Frankfurt (1970) 44

    Google Scholar 

  6. Diels-Kranz 22 B8

    Google Scholar 

  7. Diels-Kranz 31 B8

    Google Scholar 

  8. Heisenberg, W: Die Plancksche Entdeckung und die philosophischen Grundlagen der Atomlehre, in: Heisenberg, W: Wandlungen in den Grundlagen der Naturwissenschaften. S. Hirzel: Stuttgart (1959) 163

    Google Scholar 

  9. Cf. also Hanson, N.R.: Constellations and Conjectures. Boston (1973) 101

    Google Scholar 

  10. Hanson, N.R. (see Note 9, 113) carried out corresponding calculations.

    Google Scholar 

  11. Bohr, H.: Fastperiodische Funktionen. Berlin (1932)

    Google Scholar 

  12. Forke, A.: Geschichte der alten chinesischen Philosophie. Hamburg (1927) 486;

    Google Scholar 

  13. Fêng Yu-Lan: A History of Chinese Philosophy vol. 2: The Period of Classical Learning. Princeton NJ (1953) 120

    Google Scholar 

  14. Mainzer, K.: Geschichte der Geometrie. B. I. Wissenschaftsverlag: Mannheim/ Wien/Zürich (1980) 83

    Google Scholar 

  15. Edwards, C.H.: The Historical Development of the Calculus. Springer: Berlin (1979) 89

    Book  MATH  Google Scholar 

  16. Mainzer, K.: Geschichte der Geometrie (see Note 13) 100

    Google Scholar 

  17. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Behavior Part 1. Aerial Press: Santa Cruz (1984) 20

    Google Scholar 

  18. Audretsch, J., Mainzer, K. (eds.): Philosophie und Physik der Raum-Zeit. B.I. Wissenschaftsverlag: Mannheim (1988) 30

    Google Scholar 

  19. Audretsch, J., Mainzer, K. (eds.): Philosophie und Physik der Raum-Zeit (see Note 15 ) 40

    Google Scholar 

  20. Weyl, H.: Raum, Zeit, Materie. Vorlesung über Allgemeine Relativitätstheorie. Wissenschaftliche Buchgesellschaft: Darmstadt (1961) (Reprint of the 5th Edition (1923)) 141

    Google Scholar 

  21. Mach, E.: Die Mechanik. Historisch-kritisch dargestellt. Wissenschaftliche Buchgesellschaft: Darmstadt (1976) (Reprint of the 9th Edition (1933)) 149

    Google Scholar 

  22. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Behavior (see Note 14 ) 57

    Google Scholar 

  23. Ruelle, D.: Small random pertubations of dynamical systems and the definition of attractors. Commun. Math. Phys. 82 (1981) 137–151

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Behavior (see Note 14 ) 45

    Google Scholar 

  25. For an analytical elaboration cf. Stauffer, D., Stanley, H.E.: From Newton to Mandelbrot. A Primer in Theoretical Physics. Springer: Berlin (1990) 26

    Google Scholar 

  26. Nicolis, G., Prigogine, I.: Die Erforschung des Komplexen (see Chapter 1, Note 3 ) 132

    Google Scholar 

  27. Abraham, R.H., Shaw, C.D.: Dynamics — The Geometry of Behavior (see Note 14) 168, 174

    Google Scholar 

  28. For an analytical elaboration cf. Mainzer, K.: Symmetries in Nature (see Note 1) Chapter 3. 31

    Google Scholar 

  29. Stauffer, D., Stanley, H.E.: From Newton to Mandelbrot (see Note 19 ) 24

    Google Scholar 

  30. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer: Berlin (1978)

    MATH  Google Scholar 

  31. Davies, P.C.W.: The Physics of Time Asymmetry. Surrey University Press: London (1974)

    Google Scholar 

  32. Penrose, R.: The Emperor’s New Mind. Oxford University Press: Oxford (1989) 181

    Google Scholar 

  33. Lichtenberg, A.J., Liebermann, M.A.: Regular and Stochastic Motion. Springer: Berlin (1982)

    Google Scholar 

  34. Schuster, H.G.: Deterministic Chaos. An Introduction. Physik-Verlag: Weinheim (1984) 137

    MATH  Google Scholar 

  35. Poincaré, H.: Les Méthodes Nouvelles de la Méchanique Céleste. Gauthier-Villars: Paris (1892)

    Google Scholar 

  36. Arnold, V I: Small Denominators II, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally-periodic motions under a small perturbation of the Hamiltonian, Russ. Math. Surveys 18 (1963) 5

    Google Scholar 

  37. Kolmogorov, A.N.: On Conservation of Conditionally-Periodic Motions for a Small Change in Hamilton’s Function, Dokl. Akad. Nauk. USSR 98 (1954) 525

    MathSciNet  Google Scholar 

  38. Moser, J.: Convergent series expansions of quasi-periodic motions, Math. Anm. 169 (1967) 163

    Google Scholar 

  39. Cf. Arnold, V.I.: Mathematical Methods of Classical Mechanics (see Note 22)

    Google Scholar 

  40. Schuster, H.G.: Deterministic Chaos (see Note 23), 141

    Google Scholar 

  41. Hénon, M., Heiles, C.: The applicability of the third integral of the motion: Some numerical experiments, Astron. J. 69 (1964) pp. 73

    Article  Google Scholar 

  42. Schuster, H.G.: Deterministic Chaos (see Note 23), 150.

    Google Scholar 

  43. Figures 2.16a—d from M.V. Berry in S. Jorna (ed.), Topics in nonlinear dynamics, Am. Inst. Phys. Conf. Proc. vol. 46 (1978)

    Google Scholar 

  44. For mathematical details compare, e.g. Staffer, D., Stanley, H.E.: From Newton to Mandelbrot (see Note 19 ), 83

    Google Scholar 

  45. Mainzer, K.: Symmetrien der Natur (see Note 1), 423

    Google Scholar 

  46. Primas, H., Müller-Herold, U.: Elementare Quantenchemie. Teubner: Stuttgart (1984) with an elementary introduction to the Galileo-invariant quantum mechanics (Chapter 3)

    Google Scholar 

  47. Audretsch, J., Mainzer, K. (eds.): Wieviele Leben hat Schrödingers Katze? B. I. Wissenschaftsverlag: Mannheim (1990)

    Google Scholar 

  48. Gutzwiller, M.C.: Chaos in Classical and Quantum Mechanics. Springer: Berlin (1990)

    MATH  Google Scholar 

  49. Friedrich, H.: Chaos in Atomen, in: Mainzer, K., Schirmacher, W. (eds.): Quanten, Chaos und Dämonen (see Note 1 of Chapter 1)

    Google Scholar 

  50. Friedrich, H., Wintgen, D.: The hydrogen atom in a uniform magnetic field, Physics Reports 183 (1989) 37–79

    Article  MathSciNet  ADS  Google Scholar 

  51. Birkhoff, G.D.: Nouvelles recherches sur les systèmes dynamiques, Mem. Pont. Acad. Sci. Novi Lyncaei 1 (1935) 85

    Google Scholar 

  52. Enz, C.P.: Beschreibung nicht-konservativer nicht-linearer Systeme I—II, Physik in unserer Zeit 4 (1979) 119-126, 5 (1979) 141–144 (II)

    Google Scholar 

  53. Lorenz, E.N.: Deterministic nonperiodic flow, J. Atoms. Sci. 20 (1963) 130

    Article  ADS  Google Scholar 

  54. Schuster, H.G.: Deterministic Chaos (see Note 23) 9

    Google Scholar 

  55. Eckmann, J.P.: Roads to turbulence in dissipative dynamical systems, Rev. Mod. Phys. 53 (1981) 643

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Computer simulation of Fig. 2.21 from Lanford, O.E., Turbulence Seminar, in: Bernard, P., Rativ, T. (eds.): Lecture Notes in Mathematics 615, Springer: Berlin (1977) 114

    Google Scholar 

  57. Mandelbrot, B.B.: The Fractal Geometry of Nature, Freeman: San Fransisco (1982)

    MATH  Google Scholar 

  58. Grassberger, P.: On the Hausdorff dimension of fractal attractors, J. Stat. Phys. 19 (1981) 25

    Google Scholar 

  59. Lichtenberg, A.J., Liebermann, M.A.: Regular and Stochastic Motions (see Note 23)

    Google Scholar 

  60. Collet, P., Eckmann, J.P.: Iterated Maps of the Interval as Dynamical Systems, Birkhäuser: Boston (1980) (see Figures 2. 22–24 )

    Google Scholar 

  61. Großmann, S., Thomae, E.: Invariant distributions and stationary correlation functions of one-dimensional discrete processes, Z. Naturforsch. 32 A (1977) 353

    Google Scholar 

  62. Feigenbaum, M.J.: Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978) 25

    Article  MathSciNet  ADS  MATH  Google Scholar 

  63. Mainzer, K.: Symmetrien der Natur (see Note 1)

    Google Scholar 

  64. Cf. Nicolis, G., Prigogine, I.: Die Erforschung des Komplexen (see Note 3, Chapter 1 ) 205

    Google Scholar 

  65. Cf. Prigogine, I.: From Being to Becoming — Time and Complexity in Physical Sciences, Freemann: San Fransisco (1980)

    Google Scholar 

  66. Introduction to Thermodynamics of Irreversible Processes, Wiley: New York (1961)

    Google Scholar 

  67. Fig. 2.27 from Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures of Physics vol. II., Addison-Wesley (1965)

    Google Scholar 

  68. Haken, H.: Synergetics (see Note 4, Chapter 1 ) 5

    Google Scholar 

  69. Haken, H.: Synergetics (see Note 4, Chapter 1 ) 202

    Google Scholar 

  70. Haken, H.: Advanced Synergetics. Instability Hierarchies of Self-Organizing Systems and Devices. Springer: Berlin (1983) 187

    MATH  Google Scholar 

  71. Weinberg, S.: Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity. Wiley: New York (1972)

    Google Scholar 

  72. Cf. Mainzer, K.: Symmetrien der Natur (see Note 1) Chapter 4

    Google Scholar 

  73. Curie, P.: Sur la Symétrie dans les Phénomènes Physiques, Journal de Physique 3 (1894) 3

    Google Scholar 

  74. Audretsch, J., Mainzer, K. (eds.): Vom Anfang der Welt. C.H. Beck: München (21990) Mainzer, K.: Symmetrien der Natur (see Note 1) 515Fritzsch, H.: Vom Urknall zum Zerfall. Die Welt zwischen Anfang and Ende. Piper: München (1983) 278

    Google Scholar 

  75. Hawking, S.: A Brief History of Time. From the Big Bang to Black Holes. Bantam Press: London (1988)

    Google Scholar 

  76. Hoyle, F., Burbridge, G., Narlikar, J.V.: A quasi-steady state cosmological model with creation of matter. Astrophys. Journal 410 (1993) 437457

    Google Scholar 

  77. Audretsch, J., Mainzer, K. (eds.): Vom Anfang der Welt (see Note 48 ) 165

    Google Scholar 

  78. Whitesides, G.M., Mathias, J.P., Seto, C.T.: Molecular self-assembly and nanochemistry: A chemical strategy for the synthesis of nanostructures. Science 254 (1991) 1312–1319

    Article  ADS  Google Scholar 

  79. Newkome, G.R. (ed.): Advances in Dendritic Macromolecules. JAI Press: Greenwich, Conn. (1994)

    Google Scholar 

  80. Curl, R.F., Smalley, R.E.: Probing C60. Science 242 (1988) 1017–1022

    Google Scholar 

  81. Smalley, R.W.: Great balls of carbon: The story of Buckminsterfullerene. The Sciences 31 (1991) 22–28

    Google Scholar 

  82. Müller, A.: Supramolecular inorganic species: An expedition into a fascinating rather unknown land mesoscopia with interdisciplinary expectations and discoveries, J. Molecular Structure 325 (1994) 24

    Article  Google Scholar 

  83. Angewandte Chemie (International Edition in English) 34 (1995) 2122–2124

    Google Scholar 

  84. Müller, A., Mainzer, K.: From molecular systems to more complex ones. In: Müller, A., Dress, A., Vögtle, F. (Eds.): From Simplicity to Complexity in Chemistry–and Beyond. Vieweg: Wiesbaden (1995) 1–11

    Google Scholar 

  85. Dry, C.M.: Passive smart materials for sensing and actuation. Journal of Intelligent Materials Systems and Structures 4 (1993) 415

    Article  Google Scholar 

  86. Amato, I.: Animating the material world. Science 255 (1992) 284–286

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Philosophie und Wissenschaftstheorie, Universität Augsburg, Universitätsstrasse 10, D-86135, Augsburg, Germany

    Professor Dr. Klaus Mainzer

Authors
  1. Professor Dr. Klaus Mainzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mainzer, K. (1997). Complex Systems and the Evolution of Matter. In: Thinking in Complexity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13214-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-13214-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-13216-6

  • Online ISBN: 978-3-662-13214-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation