Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science

Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science

Volumn , Issue , 2005, Pages 1-437

  Mainzer, Klaus ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

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EID: 85129068076     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/5770     Document Type: Book

References (455)

1. 1.1 Reichard, G.: Navaho Religion. A Study of Symbolism. 2 vols. Pantheon Books: New York (1950).
2. 1.2 Nowotny, K.A.: Beiträge zur Geschichte des Weltbildes. Farben und Weltrichtungen. Berger: Horn/Vienna (1970), p. 195.
3. 1.3 Witherspoon, G.: Language and Art in the Navajo Universe. University of Michigan Press: Ann Arbor (1977), p. 154.
4. 1.4 Brown, W.N.: A Descriptive and Illustrated Catalogue of Miniature Paintings of the Jaina Kalpasutra. Freer Gallery of Art: Washington (1934).
5. 1.5 Gopinatha Rao, T.A.: Elements of Hindu Iconography. Vol. 1. The Law Printing House: Madras (1914), Inanarnavatantra X 39. Nowotny [1.2], p. 100.
6. 1.6 I Ching — The Book of Changes. Ed. by R. Wilhelm. Diederichs: Jena (1924), repr. Düsseldorf/Cologne (1973).
7. 1.8 Mainzer, K.: Geschichte der Geometrie. B.I. Wissenschaftsverlag: Mannheim/Vienna/Zürich (1980).
8. 1.9 Kepler, J.: Collected Works. Vol. 6: Harmonice Mundi. Transl. and introduced by M. Caspar. C.H. Beck: Munich/Berlin (1939).
9. Archibald, R.C.: Golden Section. In: American Mathematical Monthly 25 (1918), pp. 232– 238;
10. Coxeter, H.S.M.: Unvergängliche Geometrie. Birkhäuser: Basel/Stuttgart (1963), p. 206.
11. 1.14 Sachs, A.: Babylonian observational astronomy. In: Philosophical Transactions of the Royal Society of London A 276 (1974), pp. 43–50;
12. van der Waerden, B.L.: Geometry and Algebra in Ancient Civilizations. Springer: Berlin/Heidelberg/New York (1983);
13. Neugebauer, O.: The Exact Sciences in Antiquity. Brown University Press: Providence (2nd ed. 1957).
14. 1.15 Needham, J.: Astronomy in Ancient and Medieval China. In: Philosophical Transactions of the Royal Society of London A 276 (1974), pp. 67–82.
15. J. Mittelstraß: Die Rettung der Phänomene. Ursprung und Geschichte eines antiken Forschungsprinzips. De Gruyter: Berlin (1962);
16. Mainzer, K.: Grundlagenprobleme in der Geschichte der exakten Wissenschaften. Universitätsverlag: Constance (1981), p. 8.
17. Hanson, N.R.: Constellations and Conjectures. Reidel: Dordrecht/Boston (1973), p. 101.
18. Bruins, E.M.: La chimie du Timée. In: Revue de Métaphysique et de Morale LVI (1951), pp. 269–282.
19. 1.19 Diels, H.: Die Fragmente der Vorsokratiker. 6th ed., revised by W. Kranz. 3 vols. Weidmannsche Verlagsbuchhandlung: Berlin (1960/1961) (abbrev.: Diels-Kranz), 12 A 10 (Pseudo-Plutarch).
20. Heisenberg, W.: Physik und Philosophie. Ullstein: Frankfurt (1970), p. 44.
21. Feng Yu-Lan: A History of Chinese Philosophy. Vol. 2: The Period of Classical Learning. Princeton University Press: Princeton (1953), p. 120.
22. 2.1 Leibniz, G.W.: Zur Analysis der Lage. In: Hauptschriften zur Grundlegung der Philosophie. Vol. 1. Ed. by E. Cassirer, transl. by A. Buchenau. Felix Meiner: Leipzig (1904), p. 73.
23. 2.2 Van der Waerden, B.L.: Algebra. Vol. 1. Springer: Berlin/Heidelberg/New York (1966), §9.
24. 2.3 Veblen, O., Young, J.W.: Projective Geometry. Vol. 1. Ginn: Boston (1918), pp. 61 ff.
25. 2.4 Weyl, H.: Symmetry. Princeton University Press: Princeton (1952).
26. 2.5 Speiser, A.: Die Theorie der Gruppen von endlicher Ordnung. Birkhäuser: Basel/Stuttgart (4th ed. 1956), §4.
27. 2.6 Shubnikov, A.V., Koptsik, V.A.: Symmetry in Science and Art. Plenum Press: New York/London (1974), pp. 79 ff.;
28. Wolf, K.L., Wolff, R.: Symmetrie. Vol. 2. Böhlau: Münster/Cologne (1956), pp. 132 f.
29. Burckhardt, J.J.: Die Symmetrie der Kristalle. Birkhäuser: Basel/Boston/Berlin (1988).
30. Klein, F.: Das Erlanger Programm. In: Gesammelte Mathematische Abhandlungen. Vol. 1. Springer: Berlin (1921), p. 463.
31. Lie, S.: Abhandlungen. Vol. 5. Teubner: Leipzig/Kristiana (1924), p. 586.
32. 2.14 Gauss, C.F.: Disquisitiones generales circa superficies curvas. In: Werke. Vol. 4. Teubner: Leipzig (1880), pp. 217 ff.;
33. 2.15 Riemann, B.: Über die Hypothesen, welche der Geometrie zu-grunde liegen. Springer: Berlin (1919).
34. Eisenhart, L.P.: Riemannian Geometry. Princeton University Press: Princeton (1926).
35. 2.17 Lie, S., Engel, F.: Theorie der Transformationsgruppen. 3 vols. Teubner: Leipzig (1888–1893).
36. 2.18 Freudenthal, H.: Lie groups in the foundations of geometry. In: Advances in Mathematics 1 (1965), pp. 145–190.
37. Cartan, E.: Les espaces riemanniens symétriques. In: Verh. Intern. Mathem.-Kongr. I. Zürich (1932), pp. 152–161;
38. Helgason, S.: Differential Geometry and Symmetric Spaces. Academic Press: New York (1962).
39. 2.20 Elliott, J.P., Dawber, P.G.: Symmetry in Physics. Vol. 1: Principles and Simple Applications. Macmillan: London/ Basingstoke (1979), chapt. 4.
40. Kaplan, D. Glass, L.: Understanding Dynamics. Springer: Berlin/Heidelberg/New York (1995), p. 210;
41. Haken, H.: Syn-ergetics. An Introduction. Springer: Berlin/Heidelberg/New York (3rd ed. 1983), pp. 106 ff.
42. Arnold, V.I.: Ordinary Differential Equations. M.I.T. Press: Cambridge Mass. (1978);
43. Hirsch, M.W., Smale, S.: Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press: New York (1974).
44. Nicolis, G. Prigogine, I.: Die Erforschung des Komplexen. Piper: München (1987), Fig. 3.18–3.19.
45. Abraham, R.H. Shaw, C.D.: Dynamics — The Geometry of Behavior. Part 4: Bifurcation Behavior. Aerial Press: Santa Cruz (1984), p. 179.
46. Thom, R.: Structural Stability and Morphogenesis. Benjamin/ Cummings: Reading Mass. (1975).
47. Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman: San Francisco (1982).
48. 2.32 Fatou, P.: Sur les équations fonctionelles. In: Bull. Soc. Math. Fr. 47 (1919/1920), pp. 161–271, 48, pp. 208–314;
49. Julia, G.: Sur l’iteration des fonctions rationelles. In: Journal des Mathématique Pure et Appliquée 8 (1918), pp. 47–245.
50. Peitgen, H.-O. Richter, P.H.: The Beauty of Fractals. Images of Complex Dynamical Systems. Springer: Berlin/ Heidelberg/New York (1986), p. 10.
51. 2.34 Douady, A., Hubbard, J.H. Iteration des polynomes quadra-tiques complexes. In: CRASH Paris 294 (1982), pp. 123–126.
52. 3.1 Mainzer, K.: Thinking in Complexity. The Computational Dynamics of Matter, Mind, and Mankind. Springer: Berlin/Heidelberg/New York (4th ed. 2004), chapt. 2.6;
53. Abar-banel, H.D.I.: Analysis of Observed Data. Springer: New York (1996);
54. Kanz, H. Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press: Cambridge (1997).
55. 3.3 Schmutzer, E.: Symmetrien und Erhaltungssätze der Physik. Akademie-Verlag: Berlin/Oxford/Braunschweig (1972), p. 56 ff.
56. 3.4 Noether, E.: Invariante Variationsprobleme. I. Nachrichten der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse (1918), pp. 235–257.
57. 3.5 Minkowski, H.: Raum und Zeit (Lecture 1908). In: Lorentz, H.A. Einstein, A. Minkowski, H.: Das Relativitätsprinzip. Eine Sammlung von Abhandlungen. Teubner: Leipzig/Berlin (1913), repr. Wissenschaftliche Buchgesellschaft: Darmstadt (8th ed. 1982), pp. 54–66;
58. Pension, L.: H. Minkowski and Einstein’s Theory of Relativity. In: Archiv for History of Exact Sciences 17 (1977), pp. 71–95;
59. Einstein, A.: The Meaning of Relativity. Princeton University Press: Princeton (1988).
60. 3.6 Jackson, J.D.: Classical Electrodynamics. John Wiley: New York (1975), pp. 515 ff.
61. 3.7 Weyl, H.: Raum, Zeit, Materie. Vorlesungen über allge-meine Relativitätstheorie. Springer: Berlin (1923), repr. Wissenschaftliche Buchgesellschaft: Darmstadt (1961);
62. Ehlers, J.: The Nature and Structure of Spacetime. In: Mehra, J. (ed.): The Physicist’s Conception of Nature. Reidel: Dordrecht/Boston (1973), pp. 94 ff.;
63. 3.8 Wigner, E.P.: Symmetry and Conservation Laws. In: Symmetries and Reflections. Scientific Esays of Eugene P. Wigner, Indiana University Press: Bloomington/London (1967), pp. 22 ff.;
64. Fock, V.: The Theory of Space, Time and Gravitation. Pergamon Press: New York (1959).
65. 3.9 Weinberg, S.: Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity. John Wiley: New York (1972), pp. 25 ff.;
66. Hawking, S.W. Ellis G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press: New York (1973);
67. Hawking, S.W.: A Brief History of Time. Bantam Books: New York (1988);
68. Hawking, S.W. Penrose, R.: The Nature of Space and Time. Princeton University Press: Princeton (1996).
69. 3.10 Mie, G. Grundlagen einer Theorie der Materie (I). In: Annalen der Physik 37 (1912), pp. 511–534;
70. Hilbert, D.: Die Grundlagen der Physik. In: Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1915), pp. 395–407;
71. Mehra, J.: Einstein, Hilbert, and the Theory of Gravitation. In: Mehra [3.7], pp. 137 ff.
72. Hund, F.: Geschichte der Quantentheorie. B.I. Wissenschaftsverlag: Mannheim/Vienna/Zürich (2nd ed. 1975).
73. Wigner, E.P.: Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren. Vieweg: Braunschweig (1931);
74. van der Waerden, B.L.: Die gruppentheoretis-che Methode in der Quantenmechanik. Springer: Berlin (1932).
75. Boardman, A.D, O’Connor, D.E., Young, P.A.: Symmetry and its Application in Science. MacGraw-Hill: London/New York (1973), chapt. 9;
76. Elliott, J.P., Dawber, P.G.: Symmetry in Physics. Vol. 5. Macmillan: London (1979), chapt. 5;
77. Greiner, W. Müller, B.: Theoretische Physik. Vol. 5: Quantenmechanik II: Symmetrien. Harri Deutsch: Thun/Frankfurt (1985).
78. 3.14 Itzykson, C., Zuber, J.-B.: Quantum Field McGraw-Hill: Theory. New York (1980), chapt. 2;
79. 3.15 Marshak, R.E. Riazuddin, Ryan, C.P.: Theory of Weak Interaction in Particle Physics. John Wiley: New York (1969).
80. 3.16 Lee, T.D., Yang, C.N.: Questions of Parity Conservation in Weak Interaction. In: Physical Review 104 (1956), p. 254;
81. Wu, C.S. Amber, E. Heyward, R.W. Hoppes, D.D. Hudson, R.P.: Experimental Test of Parity Conservation in Beta-Decay. In: Physical Review 105 (1957), pp. 1413–1415.
82. 3.17 Abers, E.S., Lee, B.W.: Gauge Theories. In: Physics Reports 9 C (1973), p. 1;
83. Rollnik, H.: Ideen und Experi-mente für eine einheitliche Theorie der Materie. In: Rheinisch-Westfälische Akademie der Wissenschaften Vortrag N 296. Opladen (1979), pp. 18 ff.
84. Salam, A.: Weak and electromagnetic interactions. In: Svartholm, N.: Elementary Particle Theory: Relativistic Groups and Analyticity (Nobel Symposium No. 8). Almqvist and Wiksells: Stockholm (1968), p. 367.
85. 3.19 Mainzer, K.: Symmetries of Nature. De Gruyter: Berlin/New York (1996),
86. 3.20 Bernstein, J.: Spontaneous Symmetry Breaking, Gauge Theories, the Higgs Mechanism and all that. In: Revise Reports of Modern Physics 46 (1974), pp. 7–48;
87. Davies, P.C.W.: Super-force. Simon & Schuster: New York (1984);
88. Georgi, H.: Why Unify? In: Nature 288 (Dec. 1980), pp. 649–651;
89. Georgi, H. Glashow, S.L.: Unity of all Elementary-Particle Forces. In: Physical Review Letters 32 vol. 8 (1974), pp. 438–441;
90. Glashow, S.L.: Interactions. Time-Warner Books: New York (1988);
91. Weinberg, S.: The search for unity. Notes for a history of quantum field theory. In: Daedalus 106 (4) (1977), pp. 17–35.
92. Wheeler, J.A.: A Journey into Gravity and Spacetime. Scientific American Library: New York (1990).
93. Greene, B.: The Elegant Universe. Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. W.W. Norton: New York/London (1999), p. 144, Fig. 6.2.
94. 3.23 Davies, P.C.W., Brown, J. (eds.): Superstrings: A Theory of Everything? Cambridge University Press: Cambridge Eng. (1988).
95. Kaluza, T.: Zum Unitätsproblem der Physik. Sitzungs-berichte der preußischen Akadademie der Wissenschenschaften zu Berlin (1921), pp. 966–972;
96. Klein, O.: Quantentheorie und fünfdimensionale Relativitätstheorie. Zeitschrift für Physik 37 (1926), pp. 895–906;
97. Veblen, O. Hoffmann, D.: Projective Relativity. In: Physical Review 36 (1930), p. 810.
98. Audretsch, J. Mainzer, K.: Vom Anfang der Welt. C.H. Beck: München (2nd ed. 1990), p. 98.
99. Weinberg, S.: The First Three Minutes. Basic Books: New York (1993).
100. Guth, A.H.: The Inflationary Universe. Addison-Wesley: Reading Mass. (1997).
101. 3.30 Steigman, G.: Observational tests of antimatter cosmologies. In: Annual Review of Astronomy and Astrophysics 14 (1976), pp. 339–372;
102. Toussaint, D. Treiman, S.B. Wilczek, F. Zee, A.: Matter-antimatter accounting, thermodynamics, and black-hole radiation. In: Physical Review D 19 (Febr. 1979), pp. 1036–1045.
103. Prigogine, I.: From Being to Becoming — Time and Complexity in Physical Sciences. Freemann: San Franciso (1980);
104. Boccara, N. (ed.): Symmetries and Broken Symmetries in Condensed Matter Physics. IDSET: Paris (1981).
105. 3.32 Mainzer, K.: The Little Book of Time. Copernicus: New York (2002), chapt. 5.
106. 3.33 Lorenz, E.N.: Deterministic flow. In: J. Atmos. Sci. 20 (1963), p. 130;
107. Schuster, H.G.: Deterministic Chaos. An Introduction. Physik-Verlag: Weinheim (1984), p. 9.
108. Feynman, R.P. Leighton, R.B. Sands, M.: The Feynman Lectures of Physics. Vol. II. Addison-Wesley: Reading Mass. (1965).
109. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer: Berlin (1978);
110. Davies, P.C.W.: The Physics of Time Asymmetry. Surrey University Press: London (1974);
111. Penrose R.: The Emperor’s New Mind. Oxford University Press: Oxford (1989), p. 181.
112. Lichtenberg, A.J. Libermann, M.A.: Regular and Stochastic Motion. Springer: Berlin (1982);
113. Poincaré, H.: Les Méthodes Nouvelles de la Mécanique Céleste. Gauthier-Villars: Paris (1892).
114. 3.40 Arnold, V.I.: Small denominators II. Proof of a theorem of A.N. Kolmogorov on the the preservation of conditionally-periodic motions under a small perturbation of the Hamiltonian. In: Russian Mathematical Surveys 18 (1963) p. 5;
115. Kolmogorov, A.N.: On conservation of conditionally-periodic motions for a small change in Hamiltonian function. In: Doklady Akademy Nauk USSR 98 (1954), p. 525;
116. Moser, J.: Convergent series expansions of quasi-periodic motions. In: Mathematische Annalen 169 (1967), p. 163.
117. 3.41 Birkhoff, G.D.: Nouvelles recherches sur les système dy-namiques. In: Mem. Pont. Acad. Sci. Novi Lyncaei 1 (1935), p. 85.
118. 3.42 Eckmann, J.P.: Roads to turbulence in dissipative dynamical systems. In: Rev. Mod. Phys. 53 (1981), p. 643;
119. Lanford, O.E.: Turbulence Seminar. In: Bernard, P. Rativ, T. (eds.): Lecture Notes in Mathematics 615. Springer: Berlin (1977), p. 114.
120. Landau, L.D. Lifshitz, I.M.: Course of Theoretical Physics. Vol. 5: Statistical Physics. Pergamon Press: London/Paris 1959. Landau only considered phase transitions in thermal equilibrium;
121. Brout, R.: Phase Transitions. Benjamin: New York (1965);
122. Domb, C., Green, M.S. (eds.): Phase Transitions and Critical Phenomena. 5 vols. Academic Press: London (1972–1976).
123. Haken, H.: Encyclopedia of Physics. Vol XXV/2c. Light and Matter. Springer: Berlin (1970).
124. Satter, D.: Topics in Stability and Bifurcation Theory. Springer: Berlin (1973).
125. 3.47 Guggenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer: Berlin (1983);
126. Nicolis, G. Prigogine, I.: Self-Organization in Non-Equilibrium Systems. John Wiley: New York (1977).
127. 4.1 Biggs, N.L. Loyd, E.K. Wilson, R.J.: Graph-Theory 1736–1936. Clarendon: Oxford (1990), p. 55.
128. 4.2 Partington, J.R.: A Short History of Chemistry. Macmillan: London (1965), pp. 300 ff.
129. 4.3 Kékulé, A.: Lehrbuch der organischen Chemie. Enke: Erlangen (1859a).
130. 4.4 Le Bel, J.A. van’t Hoff, J.H.: Die Lagerung der Atome im Raume. Vieweg: Braunschweig (1877).
131. 4.6 Bader, R.F.W.: Atoms in Molecules. A Quantum Theory. Clarendon Press: Oxford (1990), p. 30.
132. 4.7 Primas, H.: Chemistry, Quantum Mechanics and Reductionism. Springer: Berlin (2nd ed. 1983).
133. 4.9 Flurry, R.L.: Symmetry Groups. Theory and Chemical Applications. Englewood Cliffs: New Jersey (1980);
134. Donaldson, J.S. Ross, S.D.: Symmetry and Stereochemistry. Inter-text Books: London (1972);
135. Hollas, J.M.: Die Symmetrie von Molekülen. De Gruyter: Berlin/New York (1975).
136. Pasteur, L.: Lecons sur la dissym]’etrie moléculaire. Hachette: Paris (1861);
137. 4.11 Hückel, E.: Zur Quantentheorie der Doppelbindung. In: Zeitschrift für Physik 60 (1930), pp. 423–456;
138. Woodward, R.B. Hoffmann, R.: The Conservation of Orbital Symmetry. Verlag Chemie: Weinheim (1970).
139. Mandelkern, L.: Introduction to Macromolecules. Springer: New York (1983).
140. Heisenberg, W.: Die Plancksche Entdeckung und die philosophischen Grundlagen der Atomlehre. In: Heisenberg, W.: Wandlungen in den Grundlagen der Naturwissenschaft. Hirzel: Stuttgart (1959), p. 183.
141. Sund, H.: Evolution und Struktur der Proteine. Universitätsverlag: Konstanz (1968);
142. Fasold, H.: Die Struktur der Proteine. Verlag Chemie: Weinheim (1973);
143. Dickerson, R.E. Geis, I.: Struktur und Funktion der Proteine. Verlag Chemie: Weinheim (1975).
144. Ingram, V.M.: The Hemoglobins in Genetics and Evolution. Columbia University Press: New York/London (1975).
145. 4.17 Eisenberg, D.: X-ray crystallography and enzyme structure. In: Boyer, P.H. (ed.): The Enzymes. Structures and Control I. Academic Press: New York/London (1970), pp. 7 ff.
146. Quack, M.: Die Symmetrie von Zeit und Raum und ihre Verletzung in molekularen Prozessen. In: Akademie der Wissenschaften (Berlin) Jahrbuch 1990–1992. De Gruyter: Berlin (1993), p. 469;
147. Quack, M.: Molecular spectra, reaction dynamics, symmetries and life. In: Chimia 57 (2003), pp. 147–160.
148. 4.19 Quack, M.: On the measurement of parity violating energy difference between enantiomers. In: Chemical Physics Letters 132 No. 2 (1986), pp. 147–153.
149. Morozov, L.L. Goldanskii, V.I.: Violation of symmetry and self-orgranization in prebiological evolution. In: Krinsky, V.I. (ed.): Self-Organization. Autowaves and Structures far from Equilibrium. Springer: Berlin (1984), pp. 224–232.
150. 4.22 Mainzer, K.: Symmetry and complexity — fundamental concepts of research in chemistry. In: Hyle. An International Journal for the Philosophy of Chemistry 3 (1997), pp. 29–49.
151. Misra, B.: Nonequi-librium Entropy, Lyapunov Variables, and Ergodic Properties of Classical Systems. Proceedings of the National Academy of Sciences of the United States of America 75 (1978), pp. 1627– 1631;
152. Misra, B. Prigogine, I. Courbage, M.: P.N.A.S. (1979), pp. 4768–4772;
153. B. Misra, M. Courbage (1978): Physica 104A (1980), pp. 359–377;
154. B. Misra, I. Prigogine: Letters Mathe. Phys. 7 (1983), pp. 421–428.
155. Scott, S.C.: Chemical Chaos. Oxford University Press: Oxford (1961);
156. Schneider, F.W. Münster, A.F.: Nichtlineare Dynamik in der Chemie. Spektrum Akademischer Verlag: Hei-delberg/Berlin/Oxford (1996).
157. 4.25 Müller, A.: Struktur-Vielfalt im Nanokosmos. In: Akademie-Journal. Magazin der Union der deutschen Akademien der Wissenschaften 1 (2003), p. 20;
158. 248 cluster. In: Nature 48 (1999), p. 397.
159. 4.26 Whitesides, G.M., Mathias, J.P., Seto, C.T.: Molecular self-asembly and nanochemistry: A chemical strategy for the synthesis of nanostructures. In: Science 254 (1991), pp. 1312–1319.
160. 4.27 Feynman, R.: There’s plenty of room at the bottom. In: Miniaturization 282 (1961), pp. 295–296.
161. Drexler, K.E.: Nanotechnology summary. In: Encyclopedia Britannica’s Science and the Future Yearbook 162 (1990);
162. Drexler, K.E.: Nanosystems Molecular Machinery, Manufacturing, and Computation. John Wiley & Sons: New York (1992).
163. Newcome, G.R. (ed.): Advances in Dendritic Macromolecules JAI Press: Greenweech Conn. (1994).
164. 60. In: Science 242 (1988), pp. 1017–1022;
165. Smalley, R.W.: Great balls of carbon: The story of Buckminsterfullerene. In: The Sciences 31 (1991), pp. 22–28.
166. 4.31 Müller, A.: Supramolecular inorganic species: An expedition into a fascinating rather unknown land mesoscopia with interdisciplinary expectations and discoveries. In: J. Molecular Structure 325 (1994), p. 24;
167. 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), pp. 1–11.
168. Christie, B.: Spektrum der Wissenschaft Spezial 2 (2002), p. 22.
169. 5.1 Monod, J.: On symmetry and function in biological systems. In: Engström, A. Strandberg, B. (eds.): Symmetry and Function of Biological Systems at the Macromolecular Level. Proceedings of the 11th Nobel Symposium 1968. Almqvist and Wiksell: Stockholm (1968), pp. 15–27.
170. Jenken, M.: The biological and philosophical definitions of life. In: Acta biotheoretica 24 (1975), pp. 14–21.
171. 5.2 Sitte, P.: Symmetrien bei Organismen. In: Biologie in unserer Zeit 6 (1884), p. 165;
172. Klug, A.: Point groups and the design of aggregates. In: Engström [5.1], p. 427.
173. 5.3 Gierer, A.: Physik der biologischen Gestaltbildung. In: Naturwissenschaften 68 (1981), pp. 245–251.
174. 5.4 Weberling, F.: Symmetrie der Pflanzen. In: Stork, H. (ed.): Symmetrie. Aulis: Cologne (1985), pp. 175 ff.;
175. Frey, A.: Geometrische Symmetriebetrach-tungen. In: Flora 120 (1926), pp. 87–98;
176. Troll, W.: Sym-metriebetrachtungen in der Biologie. In: Studium generale 2 (1949), pp. 240–259.
177. 5.5 Weberling, F.: Morphologie der Blüten und der Blütenstände. Eugen Ulmer: Stuttgart (1981).
178. 5.6 Steiner, G.: Spiegelsymmetrie der Tierkörper. In: Naturwis-senschaftliche Rundschau 32 (1979), pp. 481–485;
179. 5.7 Doczi, C.: The Power of Limits. Shambhala Publications: Boulder Colorado (1981).
180. 5.8 Haeckel, E.: Kunstformen der Natur. Verlag des Bibliographis-chen Instituts: Leipzig/Vienna (1899).
181. 5.9 Thompson, D.W.: On Growth and Form. Birkhäuser: Basel (1973).
182. 5.10 Depew, D.J., Weber, B.H. (eds.): Evolution at a Crossroads. The New Biology and the New Philosophy of Science. M.I.T. Press: Cambridge Mass. (1985);
183. Eberling, W. Feistel, R.: Physik der Selbstorganisation und Evolution. Akademischer Verlag: Berlin (1982);
184. Haken, H. Haken-Krell, M.: Entstehung von biologischer Information und Ordnung. Wissenschaftliche Buchgesellschaft: Darmstadt (1989);
185. Hofbauer, L.: Evolutionstheorie und dynamische Systeme. Mathematische Aspekte der Selektion. Springer: Berlin (1984).
186. Eigen, M. Schuster, P.: The Hypercycle: A Principle of Natural Self-Organization. Springer: Berlin (1979).
187. 5.12 Levin, S.A.: Complex adaptive systems: Exploring the known, the unknown and the unknowable. In: Bulletin of the American Mathematical Society 40 (2002), pp. 3–19;
188. 5.13 Eigen M., Winkler, R.: Das Spiel. Naturgesetze steuern den Zufall. Piper: Munich/Zürich (1975), pp. 272 ff.;
189. Küppers, B.-O.: Der Ursprung biologischer Information. Piper: Munich/Zürich (1986), pp. 214 ff.
190. 5.14 Eigen, M.: Self-organization of matter and the evolution of biological macromolecules. In: Naturwissenschaften 58 (1971), p. 465;
191. 5.15 Wright, S.: “Surfaces” of selection value. In: Proceedings of the National Academy of Sciences of the United States of America 58 (1967), p. 165;
192. Die Entstehung des Lebens. In: Natur 3 (1983), p. 68;
193. Eigen, M.: Homunculus im Zeitalter der Biotech-nologie — Physikochemische Grundlagen der Lebensvorgänge. In: Gross, R. (ed.): Geistige Grundlagen der Medizin. Springer: Berlin (1985), pp. 24 ff.
194. Yakushevich, L.V.: Nonlinear Physics of DNA. John Wiley: Chichester (1998);
195. Krumhansl, J.A.: The intersection of nonlinear science, molecular biology, and condensed matter physics. Viewpoints. In: Peyrard, M. (ed.): Nonlinear Excitations in Biomolecules. Springer: Berlin (1995), pp. 1–9.
196. Watson, J.D.: Molecular Biology of the Gene. Benjamin: New York (1970).
197. Kauffmann, A.S.: Origins of Order. Self-Organization and Selection in Evolution. Oxford University Press: Oxford (1992).
198. Baas, N.A.: Emergence, Hierarchies, and Hyperstructures. In: Langton, C.G. (ed.): Artificial Life III. Addison-Wesley: Reading Mass. (1994).
199. Nicolis, J.S.: Dynamics of Hierarchical Systems. An Evolutionary Approach. Springer: Berlin (1986);
200. Voorhees, B.H.: Axiomatic theory of hierarchical systems. In: Behavioral Science 28 (1983), pp. 24–34;
201. Rosen, R.: Dynamical System Theory in Biology. Wiley-Interscience: New York (1970).
202. Meinhardt, M.: Models of Biological Pattern Formation. Academic Press: London (1982).
203. Meinhardt, H. Gierer, A.: Application of a theory of biological pattern formation based on lateral inhibition. In. Journal of Cell Science 15 (1974), p. 321.
204. 5.24 Bassingthwaite, J.B., van Beek, J.H.G.M.: Lightning and the heart: Fractal behavior in cardiac function. In: Proceedings of the IEEE 76 (1988), p. 696.
205. 5.25 Goldberger, A.L., Bhargava, V., West, B.J.: Nonlinear dynamics of the heartbeat. In: Physica 17D (1985), pp. 207–214;
206. Winfree, A.T.: When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton University Press: Princeton (1987).
207. 5.26 Churchland, P.S., Sejnowski, T.J.: Perspectives in cognitive neuroscience. In: Science 242 (1988), pp. 741–745.
208. van Essen, D., Maunsell, J.H.R.: Two-dimensional maps of the cerebral cortex. In: Comparative Neurobiology 191 (1980), pp. 255–281.
209. Hubel, D.H. Wiesel, T.N.: Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. In: Journal of Physiology 160 (1962), pp. 106–154.
210. Kandel, E.R. Schwartz, J.: Principles of Neural Science. Elsevier: New York (1985).
211. 5.27 Hodgekin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. In: Journal of Physiology 117 (1952), pp. 500–544.
212. Huxley, A.F.: Can a nerve propagate a subthreshold disturbance? In: Journal of Physiology 148 (1959), pp. 80P–81P;
213. Scott, A.C.: Neuroscience. A Mathematical Primer. Springer: New York (2002).
214. Hebb, D.O.: The Organization of Behavior. John Wiley: New York (1949).
215. 5.31 von der Malsburg, C.: Self-Organization of orientation sensitive cells in the striate cortex. In: Kybernetik 14 (1973), pp. 85–100;
216. Wilshaw, D.J. von der Malsburg, C.: How patterned neural connections can be set up by self-organization. In. Proceedings of the Royal Society series B 194 (1976), pp. 431–445.
217. 5.32 Barlow, H.B.: Single units and sensatioperceptual psychology. In: Perception 1 (1972), p. 371.
218. 5.33 Singer, W.: The role of synchrony in neocortical processing and synaptic plasticity. In: Domany, E. van Hemmen, L. Schulten, K. (eds.): Model of Neural Networks II. Springer: Berlin (1994).
219. 5.34 Mainzer, K.: Philosophical concepts of computational neuroscience. In: Eck-miller, R. Hartmann, G. Hauske, G. (eds.): Parallel Processing in Neural Systems and Computers. North-Holland: Amster-dam/New York (1990), pp. 9–12;
220. Flohr, H.: Brain processes and phenomenal consciousness. A new and specific hypothesis. In: Theory & Psychology 1 (1991), p. 248;
221. Scott, A.C.: Stairway to the Mind. Copernicus: New York (1995).
222. 5.35 Freeman, W.: Noise-induced first-order phase transitions in chaotic brain activity. In: International Journal of Bifurcation and Chaos 9 No. 11 (1999), pp. 2215–2218;
223. Freeman, W. et al.: A neurobiological theory of meaning in perception I–V. In: International Journal of Bifurcation and Chaos 13 (2003);
224. 5.37 Rettenmeyer, C.W.: Behavioral studies of army ants. In: University of Kansas Science Bulletin 44 (1963), p. 281;
225. Prigogine, I.: Order through fluctuation: Self-organization and social system. In: Jantsch, E. Waddington, C.H. (eds.): Evolution and Consciousness. Human systems in transition. Addison-Wesley: London (1976), p. 108.
226. 5.38 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. M.I.T. Press: Cambridge Mass. (1988), pp. 75–105;
227. Schneider, E.D.: Thermodynamics, ecological succession, and natural selection: A common thread. In: Weber [5.38], pp. 107–138.
228. 6.1 Hobbes, T.: The Elements of Law Natural and Politic (1640). Ed. by F. Tönnies. Simpkin, Marshall, and Co.: London (1889);
229. Gough, J.W.: The Social Contract. A Critical Study of its Development. Clarendon Press: Oxford (1957).
230. 6.2 Meek, R.L.: The interpretation of the “Tableau économique”. In: Economica 27 (1960), pp. 322–347.
231. 6.3 Smith, A.: An Inquiry into the Nature and Causes of the Wealth of Nations. Ed. By E. Cannan. The University of Chicago Press: Chicago (1976).
232. 6.4 Mayr, O.: Adam Smith und das Konzept der Regelung. In: Troitzsch, U. Wohlauf, G. (eds.): Technikgeschichte. Suhrkamp: Frankfurt (1980), p. 245.
233. 6.5 Walras, L.: Principe d’une théorie mathématique de l’echange. In: Journal des Economistes 33 (1874), pp. 1–21;
234. Hicks, J.: Léon Walras. In: Classics and Moderns. Collected Essays on Economic Theory. Vol. III. Basil Blackwell: Oxford (1983), pp. 85–95.
235. 6.6 von Neuman, J. Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press: Princeton (1943).
236. 6.7 Shubik, M.: Game Theory and Related Approaches to Social Behavior. John Wiley: New York (1964).
237. 6.8 Nash, J.: Noncooperative games. In: Annals of Mathematics 54 (1951), pp. 289–295.
238. 6.9 van Damme, E.: Stability and Perfection of Nash Equlibrium. Springer: Berlin (1987);
239. Bicchieri, C.: Game theory: Nash equilibrium. In: Floridi, L. (ed.): Philosophy of Computing and Information. Blackwell: Oxford (2004), pp. 289–304.
240. Harsanyi, J. Selten, R.: A General Theory of Equilibrium Selction in Games. M.I.T. Press: Cambridge Mass. (1987).
241. Hofbauer, J. Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press: Cambridge (1998).
242. 6.12 Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press: Cambridge (1982).
243. 6.14 Weidlich, W.: Synergetic modelling concepts for sociodynamics with application to collective political opinion formation. In: Journal of Mathematical Sociology 18 (1994), pp. 267–291.
244. Henderson, J.M. Quandt, R.E.: Microeconomic Theory — A Mathematical Approach. McGraw-Hill: London (1980);
245. Nicholson, W.: Microeconomic Theory — Basic Principles and Extensions. The Dryden Press: Fort Worth Texas (1992);
246. Varain, H.R.: Microeconomic Analysis. W.W. Norton: New York (1992).
247. Simon, H.A.: Models of Bounded Rationality. 2 vols. M.I.T. Press: Cambridge Mass. (1982).
248. Sterman, J.D.: Business Dynamics. Systems Thinking and Modeling for a Complex World. McGraw-Hill: Boston (2000);
249. Weidlich, W.: Sociodynamics. A Systematic Approach to Mathematical Modelling in the Social Sciences. Taylor & Francis: London (2002);
250. Auyang, S.Y.: Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics. Cambridge University Press: Cambridge (1998);
251. Wei-Bin Zhang: Synergetic Economics — Time and Change in Non-linear Economics. Springer: Berlin (1991);
252. Goodwin, R.M.: Chaotic Economic Dynamics. Oxford University Press: New York (1990);
253. Anderson, P.W., Pines, D. (eds.): The Economy as an Eolving Complex System. Addison-Wesley: Redwood City (1988).
254. 6.18 Weidlich, W., Braun, M.: The master equation approach to nonlinear economics. In: Journal of Evolutionary Economics 2 (1992), pp. 233–265.
255. 6.19 Mayntz, R.: The influence of natural science theories on contemporary social science. In: Dierkes, M. Bievert, B. (eds.): European Social Science in Transition. Campus: Frankfurt (1992), pp. 27–79.
256. Tönu, P.: Nonlinear Economic Dynamics. Springer: Berlin (1992);
257. Barnett, W.A., Geweke, J., Shell, K. (eds.): Economic Complexity. Chaos, Sunspots, Bubbles, and Nonlinearity. Cambridge University Press: Cambridge (1990);
258. Brian Arthur, W., Durlauf, N.S., Lane, D.L. (eds.), The Economy as an Evolving Complex System II. Proceedings Volume of the Santa Fé Institute. Vol. XXVII. Addison-Wesley: Reading Mass. (1997);
259. Lorenz, H.-W.: Nonlinear Dynamical Economics and Chaotic Motion. Springer: Berlin (1989).
260. Dendrinos, D.S. Sonis, M.: Chaos and Socio-Spatial Dynamics. Springer: Berlin (1990);
261. Pumain, D.: Spatial Analysis and Population Dynamics. John Libbey Eurotext: Mon-trouge/London/Wien (1991);
262. Lee, E.S.: A theory of migration. In: Demography (1966), pp. 47–57.
263. 6.23 Haag, G., Dendrinos, D.S.: Toward a stochastic dynamical theory of location: (A) A nonlinear migration process. In: Geographical Analysis 15 (1983), pp. 269–286.
264. Weidlich, W., Haag, G. (eds.): Interregional Migration — Dynamic Theory and Comparative Analysis. Springer: Berlin (1988);
265. 6.26 Allen, P.M.: Self-organization in the urban system. In: Schieve, W.C. Allen, P.M. (eds.): Self-Organization and Dissipative Structures. Applications in the Physical and Social Sciences. University of Texas Press: Austin (1982), pp. 142–146.
266. Batty, M. Longley, P.A.: Fractal Cities. Academic Press: London (1994);
267. Frankhauser, P.: La fractalité des structures ur-baines. Anthropos: Paris (1994).
268. 6.28 Frankhauser, P., Sadler, R.: Fractal analysis of urban structures. In: Natural Structures — Principles, Strategies and Models in Architecture and Nature. Proceedings of the Internernational Symposium SFB 230. Vol. II. (1992), pp. 57–65.
269. 6.29 White, R., Engelen, G.: Cellular automata and fractal urban form. A cellular modelling approach to the evolution of urban land-use oatterns. In: Environment and Planning A 25 (1993), pp. 1175–1199;
270. White, R., Engelen, G.: Cellular automata as the basis of integrated dynamic regional modelling. In: Environment and Planning B 24 (1997), pp. 235–246;
271. White, R., Engelen, G.: The use of constrained cellular automata of high-resolution modelling of urban land-use dynamics. In: Environment and Planning B. Planning and Design 24 (1997), pp. 323–343.
272. Helbing, D.: Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes. Kluwer Academic Publishers: Dordrecht (1995).
273. 6.31 Beynon, J., Dunkerley, D. (eds.): Globalization: The Reader. Athlone: London (2000);
274. O’Rourke, K. Williamson, J.: Globalization and History. M.I.T. Press: Cambridge Mass. (1999);
275. Lechner, F., Boli, J. (eds.): The Globalization Reader. Blackwell: Oxford (2000).
276. 6.32 Boswell, T.: Hegemony and Bifurcation Points in World History. In: Bornschier, V. Chase-Dum, C. (eds.): The Future of Global Conflict. Sage: London (1999), pp. 263–284.
277. Therborn, G.: European Modernity and Beyond. The Trajectory of European Societies 1945–2000. Sage: London (1995).
278. Kaufmann, S.A.: The Origins of Order — Self-Organization and Selection in Evolution. Oxford University Press: Oxford (1993).
279. Deacon, B.: Global Social Policy: International Organizations and the Future of Welfare. Sage: London (1997).
280. Marx, K. Engels, F.: Das Kommunistische Manifest. Studien-texte 4. Fink: Munich (1969).
281. Novotny, H.: Eigenzeit. Entstehung und Strukturierung eines Zeitgefühls. Suhrkamp: Frankfurt (1989).
282. Friedman, M.: A Theory of the Consumption Function. Princeton University Press: Princeton (1957).
283. 6.40 von Weizsäcker, C.C.: Logik der Globalisierung. Van-denhoeck & Ruprecht: Göttingen (2003).
284. Dunning, J.H.: The Globalization of Business. Routledge: London (1993).
285. Von Hayek, F.A.: Notes on the evolution of systems of rules of conduct. In: von Hayek, F.A.: Studies in Philosophy and Economics. Routledge: London (1967), pp. 66–81;
286. O’Briek, R. Goetz, A.M. Scholte, J.A. Williams, M.: Consulting Global Governance. Cambridge University Press: Cambridge Mass. (2000);
287. Weiss, T.G.: Governance, good governance and global governance. Conceptual and actual challenges. In: Third World Quarterly 21 (2000), pp. 795–814.
288. Easterly, W.: The Effect of IMF and World Bank Programs on Poverty. Oxford University Press: Oxford (2001);
289. Dunkley, G.: The Free Trade Adventure: The WTO, GATT and Globalism. A Critique. Zed: London (1999).
290. Meadows, D.H. et al.: The Limits to Growth. Universe Books: New York (1972);
291. Randers, J. Meadows, D.: System Simulation to Test Environmental Policy I: A Sample Study of DDT Movement in the Environment. M.I.T. Press: Cambridge Mass. (1971).
292. 6.46 Siebert, H.: Ökonomische Theorie der Umwelt. Mohr: Tübingen (1978);
293. Mainzer, K. (ed.): Ökonomie und Ökologie/Economie et Ecologie. Haupt: Bern (1993).
294. Castles, F.G.: Ethnicity and Globalization. Sage: London (2000).
295. Chua, A.: World on Fire. Doubleday: New York (2003).
296. 6.49 Kant, I: Zum ewigen Frieden (1795). In: Kants gesammelte Schriften. Ed. by Königlich Preußische Akademie der Wissenschaften. Bd. VIII. De Gruyter: Berlin (1912/1923).
297. Holden, B. (ed.): Global Democracy: Key Debates. Routledge: London (2000);
298. Beck, U.: World Risk Society. Polity Press: Cambridge Mass. (2000).
299. Dierkes, M. Berthoin Antal, A. Child, J. Nonaka I.: Handbook of Organizational Learning & Knowledge. Oxford University Press: Oxford (2001);
300. Mainzer, K.: Vom Komplexitäts-zum Kreativitätsmanagement. Auf Talentsuche in der Wissens-gesellschaft. In: Götz, K. (ed.): Personalarbeit der Zukunft. Managementkonzepte DaimlerChrysler. Vol. 27. Hampp Verlag: Munich (2002), pp.13–25.
301. 7.1 Shannon, C.E. Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press: Chicago (1949);
302. Cover T. Thomas, J.: Elements of Information Theory. John Wiley & Sons: New York (1991).
303. 7.2 Carrington, G.: Basic Thermodynamics. Oxford University Press: Oxford (1994).
304. 7.3 Deco, G., Schürmann, B.: Information Dynamics. Foundations and Applications. Springer: Berlin (2001), chapt. 3.
305. 7.4 Jaynes, E.T.: Information theory and statistical mechanics. In: Physical Review 106 (1957), p. 620.
306. 7.5 Ebeling, W. Freund, J. Schweitzer, F.: Komplexe Struk-turen: Entropie und Information. Teubner: Stuttgart/Leipzig (1998).
307. 7.6 Benett, C.H.: Quantum information and computation. In: Physics Today 10 (1995), pp. 24–30.
308. 7.7 von Weizsäcker, C.F.: Aufbau der Physik. Dtv: Munich (3rd ed. 1994).
309. 7.8 Feistel, R. Eberling, W.: Evolution of Complex Systems. Kluwer: Dordrecht (1989);
310. Klimontovich, Y.: Statistical Theory of Open Systems. Kluwer: Dordrecht (1995).
311. 7.9 Adamii, C.: Learning and Complexity in Genetic Auto-Adaptive Systems. In: Physica D 80 (1995), pp. 154–170.
312. 7.10 Eberling, W., Volkenstein, M.V.: Entropy and the evolution of biological information. In: Physica A 163 (1990), p. 398.
313. 7.11 Sagan, C.: Die Drachen von Eden. Das Wunder der men-schlichen Intelligenz. Droemer Knaur: Munich/Zurich (1978):
314. Gould, S.J.: The Book of Life. W.W. Norton: New York (1993).
315. Churchland, P.S. Sejnowski, T.J.: The Computational Brain. M.I.T. Press: Cambridge Mass. (1992);
316. 7.13 Hölldobler, B.: Vom Verhalten zum Gen. Die Soziobi-ologie eines Superorganismus. In: Nova Acta Leopoldina NF 76303 (1997), pp. 205–223.
317. Wheeler, W.M.: The ant-colony as an organism. In: Journal of Morphology 22 (1911), pp. 307–325.
318. Mainzer, K.: KI — Künstliche Intelligenz. Grundlagen in-telligenter Systeme. Wissenschaftliche Buchgesellschaft: Darmstadt (2003).
319. 7.16 Hawking, S.W.: The Universe in a Nutshell. Bantam Books: New York (2001). The path integral was suggested in a paper of Hawking during the 17th International Conference on General Relativity and Gravitation: July 25, 2004 at Dublin.
320. 7.17 Turing, A.M.: On computable numbers, with an application to the “Entscheidungsproblem.” In: Proceedings of the London Mathematical Society Series 2 42 (1936), pp. 103–105;
321. Teuscher, C. (ed.): Alan Turing: The Life and Legacy of a Great Thinker. Springer: Berlin (2004).
322. Wegener, I.: Complexity Theory. Limiting Factors on the Efficiency of Algorithms. Springer: Berlin (2004);
323. Hromkovic, J.: Theoretical Computer Science. Introduction to Automata, Computability, Complexity, Algorithmics, Randamization, Communication, and Cryptography. Springer: Berlin (2004);
324. Homer, S. Selman, A.L.: Computability and Complexity Theory. Springer: New York (2001).
325. 7.19 Chaitin, G.J.: On the length of programs for computing finite binary sequences. In: Journal of the ACM 13 (1966), pp. 547– 569;
326. Chaitin, G.J.: The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning. Springer: New York (1998);
327. Calude, C.S.: Information and Randomness. An Algorithmic Perspective. Springer: New York (2nd ed. 2002).
328. Hirvensalo, M.: Quantum Computing. Springer: New York (2nd ed. 2004).
329. 7.22 Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. In: Proc. Roy. Soc. A 400 (1985). pp. 97–117.
330. 7.23 Bouwmeester, A.E., Zeilinger, A. (eds.): The Physics of Quantum Information. Springer: Berlin (2000);
331. Nielsen, M.A. Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press: Cambridge (2001);
332. Lo, H.-K., Popesku, S., Spiller, T. (eds.): Introduction to Quantum Computation and Information. World Scientific: Singapore (1998).
333. 7.24 Audretsch, J., Mainzer, K. (eds.): Wieviele Leben hat Schrödingers Katze? Zur Physik und Philosophie der Quantenmechanik. Spektrum: Heidelberg (1996).
334. 7.25 Adleman, L.M.: Molecular computation of solutions to com-binatorical problems. In: Science 266 (1994), pp. 1021–1024;
335. Lipton, R.J.: DNA solutions of hard computational problems. In: Science 268 (1995), pp. 542–545.
336. 7.26 von Neumann, J.: The Computer and the Brain. Yale University Press: New Haven (1958);
337. Burks, A.W. (ed.): Essays on Cellular Automata. University of Illinois Press: Urbana-Champaign Ill. (1970).
338. 7.27 Wolfram, S.: Universality and complexity in cellular automata. In: Farmer, D. Toffoli, T. Wolfram, S. (eds.): Proceedings of an Interdisciplinary Workshop. North-Holland: Amsterdam (1984).
339. 7.28 Mainzer, K.: Komplexität in der Natur. In: Nova Acta Leopoldina NF 76 No. 303 (1997), pp. 165–189.
340. Wolfram, S.: A New Kind of Science. Wolfram Media Inc.: Champaign, Ill. (2002), p. 443.
341. 7.31 McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. In: Bulletin of Mathematical Biophysics 5 (1943), pp. 115–133.
342. 7.32 Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization in the brain. In: Psychological review 65 (1958), pp. 386–408.
343. Minsky, M. Papert, S.A.: Perceptrons. M.I.T Press: Cambridge Mass. (1969) (expanded ed. 1988).
344. 7.34 Hopfield, J.J.: Neural Network and physical systems with emergent collective computational abilities. In: Proceedings of the National Academy of Sciences 79 (1982), pp. 2554–2558.
345. Rummelhart, D.E. Smolensky, P. McClelland, J.L. Hinton, G.E.: Schemata and sequential thought processes. In: McClelland, J.L. Rumelhart, D.E. (eds.): Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol.2: Applications. M.I.T Press: Cambridge Mass. (1986);
346. Churchland, P.S.: Neurophilosophy. Toward a Unified Science of the Mind-Brain. M.I.T. Press: Cambridge Mass. (1988), p. 465.
347. Chua, L.O.: CNN: A Paradigm for Complexity. World Scientific: Singapore (1998);
348. Mainzer, K.: CNN and the evolution of complex information systems in nature and society. In: Tetzlaff, R. (ed.): Cellular neural networks and their applications. Proceedings of the 7th IEEE International CNN Workshop. World Scientific: Singapore (2002), pp. 483–497.
349. 7.37 Chua, L.O., Yang, L.: Cellular neural networks: Theory. In: IEEE Transactions on Circuits and Systems 35 (1988), pp. 1257–1272;
350. Chua, L.O., Yang, L.: Cellular neural networks: Applications. In: IEEE Transactions on Circuits and Systems 35 (1988), pp. 1273–1290.
351. 7.38 Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing: Foundations and Applications. Cambridge University Press: Cambridge (2002), p. 7 (Fig. 2.1), p. 8 (Fig. 2.2);
352. Mainzer, K.: Cellular neural networks and visual computing: Foundations and applications according to the book of Leon O. Chua and Tamá Roska. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 1 (2003), pp. 1–6.
353. Mainzer, K.: Computerphilosophie zur Einführung. Junius Verlag: Hamburg (2003).
354. Dadam, P.: Verteilte Datenbanken und Client/Server-Systeme. Springer: Berlin (1996), p. 26;
355. Mainzer, K.: Computernetze und virtuelle Realität. Springer: Berlin (1999), p. 31.
356. 7.42 Itoh, M., Chua, L.O.: Star cellular neural networks for associative and dynamic memories. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14 5 (2004), pp. 1725–1772.
357. 7.44 Christos, G.: Memory and Dreams. Rutgers University Press: New Brunswic/New Jersey/London (2003).
358. Bollobás, B.: Random Graphs. Academic Press: London (1985);
359. Albert, R. Barabási, A.-L.: Statistical mechanics of complex networks. In: Reviews of Modern Physics 74 1(2002), pp. 47–97.
360. Watts, D.J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press: Princeton NJ (1999).
361. Wasserman, S. Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press: Cambridge (1994).
362. 7.50 Halabi, B.: Internet-Routing-Architekturen: Grundlagen, Design und Implementierung. Carl Hanser Verlag: Munich (1998);
363. Calvert, K.M., Doar, M.B., Zegura, E.W.: Modeling Internet topology. In: IEEE Transactions Communication 1 (1997), p. 160.
364. 7.51 Fukuda, K., Takayasu, H., Takayasu, M.: Spatial and temporal behavior of congestion in internet traffic. In: Fractals 7 1 (1999), p. 67.
365. Mainzer, K. Büchs, M. Kundish, D. Pyrka, P.: Physical and virtual mobility: Analogies between traffic and virtual highways. In: Mayinger, F. (ed.): Mobility and Traffic in the 21st Century. Springer: Berlin (2001), pp. 243–318.
366. Takayasu, M. Takayasu, H. Sato, T.: Critical behaviors and 1/f noise in information traffic. In: Physica A 233 (1996), Fig. 1, p. 825.
367. 7.54 Crestani, F., Pasi, G. (eds.): Soft Computing in Information Retrieval: Techniques and Applications. Physica Verlag (Springer): Heidelberg (2000).
368. 7.55 Weiser, T.: The computer for the 21st century. In: Scientific American 9 (1999), p. 66;
369. Norman, D.A.: The Invisible Computer. Cambridge University Press: Cambridge (1998).
370. Mainzer, K.: Self-organization and emergence in complex dynamical systems. Interdisciplinary perspectives for organic computing. In: 34. Jahrestagung der Gesellschaft für Informatik. INFORMATIK 2004 Ulm.
371. Hofmann, P.E.H. et al.: Evolutionäre E/E-Architekturen. Vision einer neuartigen Elektronik-Architektur für Fahrzeuge. DaimlerChrysler: Esslingen (2002).
372. 8.1 Aristotle: The Categories, On Interpretation, Prior Analytics. Harvard University Press: Cambridge Mass. (1938).
373. 8.2 Bochenski, I.M. Church, A. Goodman, N.: The Problem of Universals. A Symposium. Notre Dame, Indiana (1956);
374. Quine, W.V.O.: Ontological Relativity and other Essays. Columbia University Press: New York/London (1969).
375. 8.3 Bourbaki, N.: Elements of Mathematics: Theory of Sets. [Éléments de Mathématique: Théorie des Ensembles]. Hermann: Paris (1968);
376. Scheibe, E.: Invariance and covariance. In: Agassi, J. Cohen, R.S. (eds.): Scientific Philosophy Today. Kluwer: Boston (1981), pp. 311–331.
377. 8.5 Carnap, R.: Der logische Aufbau der Welt. Weltkreis: Berlin (1928), repr. Meiner: Hamburg (1974).
378. 8.6 van Fraassen, B.C.: Laws and Symmetry. Clarendon Press: Oxford (1989)
379. Mainzer, K.: Symmetry of Nature. De Gruyter: Berlin/New York (1996) [German: 1988], chapt. 5.3.
380. 8.7 P. Suppes [e.g., What is a scientific theory? In: Morgenbesser, S. (ed.): Philosophy of Science Today. Basic Books: New York (1967)]
381. Suppe, F.: The Semantic Conception of Theories and Scientific Realism. University of Illinois Press: Urbana Ill. (1988);
382. Giere, R.: Understanding Scientific Reasoning. Holt, Rinehart, and Winston: New York (1979). Stegmüller emphasized structuralism as “non-statement view” in Stegmüller, W.: The Structuralistic View of Theories. Springer: Berlin (1979);
383. Moulines, C.U.: Approximate application of theories. In: Erkenntnis 10 (1976), pp. 201–227.
384. 8.8 Scheibe, E.: Struktur und Theorie in der Physik. In: Audretsch, J. Mainzer, K. (eds.): Philosophie und Physik der Raum-Zeit. B.I. Wissenschaftsverlag: Mannheim (2nd ed. 1996), pp. 103–120.
385. 8.9 Ludwig, G.: Die Grundstrukturen einer physikalischen Theorie. Springer: Berlin (1978), §10, §12.
386. Derrida, J. Rorty, R.: Objectivity, Relativism and Truth. Philosophical Papers I. Cambridge University Press: Cambridge (1991).
387. Emch, G.G.: Mathematical and Conceptual Foundations of 20th Century Physics. North-Holland: New York/Oxford (1984).
388. Mainzer, K.: System. An introduction to systems science. In: Floridi, L. (ed.): Philosophy of Computing and Information. Blackwell Publishing: Oxford (2004), pp. 28–39.
389. Bergson, H.: Durée et simultanété. A propos de la théorie d’Einstein. Félix Alcan: Paris (1922).
390. 8.19 Sowa, J.F.: Knowledge Representation. Logical, Philosophical, and Computational Foundations. Brooks/Cole: Pacific Grove (2000).
391. Broy, M., Steinbrüggen, R.: Modellbildung in der Informatik. Springer: Berlin (2004).
392. Petri, C.A.: Kommunikation mit Automaten. [Diss. University of Bonn]. Bonn (1962);
393. Best, E. Devillers, R. Koutny, M.: Petri Net Algebra. Springer: Berlin (2001).
394. Huntley, H.E.: The Devine Proportion: A Study in Mathematical Beauty. Dover: New York (1970).
395. Hambidge, J.: Dynamic Symmetry. The Greek Vase. Yale University Press: New Haven (1920);
396. Stecchini, L.C.: Notes on the relation of ancient measure to the great pyramid. In: Tomkins, P.S. (ed.): The Secrets of the Great Pyramid. Harper & Row: New York (1978), p. 368;
397. Dominguez, M.A.: La Architectura Precolumbina en Mexico. Mexico D.F., Orion (1956).
398. Diels, H.: Antike Technik. Teubner: Leipzig/Berlin (1924), pp. 15f.
399. von Steuben, H.: Der Kanon des Polyklet. Doryphoros und Amazone: Tübingen (1973).
400. Knell, H.: Grundzüge der griechischen Architektur. Wissenschaftliche Buchgesellschaft: Darmstadt (1980).
401. Kepes, G. (ed.): Symmetry, Rhythm. George Braziller: New York (1966).
402. 8.29 Michell, G.: Der Hindu-Tempel. Bauformen und Bedeutung. DuMont: Cologne (1979), p. 71 ff.;
403. Brown, P.: Indian Architecture. Vol. 1: Buddhist and Hindu Periods. Tara-porevala: Bombay (5th ed. 1965);
404. Michaels, A.: Beweisverfahren in der vedischen Sakralgeometrie. Ein Beitrag zur Entstehungsgeschichte von Wissenschaft. Franz Steiner: Wiesbaden (1978).
405. 8.30 Doczi, G.: The Power of Limits. Shambhala: Boulder Colorado (1981), pp. 134 ff.
406. 8.31 Vogt-Gögnil, U.: Die Moschee-Grundformen sakraler Baukunst. Artemis: Zurich (1978), pp. 111 f.
407. 8.32 Golvin, L.: Essai sur l’architecture religieuse Musulmane. 3 vols. Klincksieck: Paris (1970–1974).
408. Panofsky, E.: Architecture and Scholasticism. Faber and Faber: Latrobe (1951).
409. Siebenhühner, H.: Deutsche Künstler am Mailänder Dom. Bruckmann: Munich (1944);
410. Bascape, G. Mezzanotte, P.: Il Duomo di Milano. Bramante: Milan (1965);
411. Acker-mann, J.S.: Ars sine scientia nihil est. In: The Art Bulletin XXXI (1949), pp. 84–111.
412. 8.35 de Bruyne, E.: Etudes d’esthétique médiévale. 3 vols. De Tempel: Brugge (1946).
413. Alberti, L.B.: De re aedicatoria. Nicolaus Laurentii Alamani: Florence (1485), IX, p. 5.
414. 8.38 Vasari, G.: Le vite de più eccelenti pittori scultori ed architet-tori. Florence (1550). Ed. by G. Milanesi. Sansoni: Florence (1878), I, pp. 168 f.
415. Lücke, Th.: Leonardo da Vinci. Tagebücher und Aufzeichnun-gen. Asmus: Leipzig (1940), p. 480.
416. Steiner, R.A.: Theorie und Wirklichkeit der Kunst bei Leonardo da Vinci. Fink: Munich (1979);
417. Clagett, M.: Leonardo da Vinci and the Medieval Archimedes. In: Physis 11 (1969), pp. 100–151;
418. Feldhaus, F.M.: Leonardo der Techniker und Erfinder. Eugen Diederichs: Jena (2nd ed. 1922);
419. Giustini, P.A.: Da Leonardo a Leibniz. La rivoluzione scientifica. Trevisini: Milan (1976);
420. Mittelstraß, J.: Leonardo-Welt. Über Wissenschaft, Forschung und Verantwor-tung. Suhrkamp: Frankfurt (1992).
421. 8.41 Pedretti, C.: A Chronology of Leonardo da Vinci’s Architectural Studies after 1500. E. Droz: Geneva (1962), pp. 143 ff.
422. 8.44 Pacioli, L.: De divina proportione. Venice (1509), repr. Officina Bodoni: Milan (1956).
423. 8.46 Pirenne, M.H.: The Scientific Basis of Leonardo da Vinci’s Theory of Perspective. In: British Journal for the Philosophy of Science 3 (1952), pp. 169–185.
424. 8.47 Schröder, E.: Kunst und Geometrie. Dürers künstlerisches Schaffen aus der Sicht seiner “Underweysung”. Akademie-Verlag: Berlin (1980), pp. 34 ff.
425. Wittkower, R.: Architectural Principles in the Age of Hu-manism. Alec Tiranti: London (1962);
426. Kambartel, W.: Symmetrie und Schönheit. Über mögliche Voraussetzun-gen des neueren Kunstbewußtseins in der Architekturtheorie Claude Perraults. Fink: Munich (1972).
427. Werker, W.: Studien über Symmetrie im Bau der Fugen und die motivische Zusammengehörigkeit der Präludien und Fugen des “Wohltemperierten Klaviers” von J.S. Bach. Breitkopf & Härtel: Leipzig (1922).
428. 8.50 Werner, E.: Grundsätzliche Betrachtungen über Symmetrie in der Musik des Westens. In: Studia Musicologia 11 (1969), p. 486;
429. Mehner, K.: Beiträge zum Symmetriebegriff in der Musik. In: Beiträge der Musikwissenschaft 13 (1971), p. 11.
430. Rameau, J.P.: Traité de l’harmonie. Ballard: Paris (1722) [English: Dover: New York 1971].
431. Eimert, H.: Lehrbuch der Zwölftontechnik. Breitkopf & Härtel: Wiesbaden (1966).
432. Budden, F.J.: The Fascination of Groups. Cambridge University Press: Cambridge (1972);
433. Claus, R.: Symmetrie in der Musik. Zur Anwendung gruppentheoretischer Methoden. In: Preisinger, A. (ed.): Symmetrie. Springer: Vienna/New York (1980), p. 70, p. 76.
434. Solomon, L.J.: Symmetry as a Determinant of Musical Composition [Diss. West Virginia State University]. Morgan-town West Virginia (1973).
435. Schönberg, A.: Herz und Hirn in der Musik. In: Schönberg, A.: Gesammelte Schriften. Ed. by I. Voitech. Vol. 1. Suhrkamp: Frankfurt (1976), pp. 104–122.
436. 8.61 Metzinger, J.: Le cubisme était né. Souvenirs. Présance: Paris (1972):
437. Apollinaire, G.: Le peinture cubiste. Paris (1913).
438. Klee, P.: Das bildnerische Denken. Schriften zur Form-und Gestaltlehre. Ed. by J. Spiller. Schwabe: Basel (1964), p. 79.
439. Klee, P.: Exakte Versuche im Bereich der Kunst. In: Bauhaus. Zeitschrift für Bau und Gestaltung 2 No. 2/3 (1928).
440. Kandinsky, W.: Punkt und Linie zu Fläche. Beitrag zur Analyse der malerischen Elemente. Bauhaus Book No. 9. Albert Langen: Munich (1926), repr. Benteli: Bern-Bümplitz (7th ed. 1973).
441. Kandinsky, W.: Rückblicke. Klein: Baden-Baden (1955), p. 25.
442. Klee, P.: Beiträge zur bildnerischen Formlehre. Ed. by J. Glaesemer. Paul Klee-Stiftung [Kunstmuseum Bern]: Basel (1979).
443. Kagan, A.: Paul Klee: Art and Music. Cornell University Press: Ithaca N.Y. (1983);
444. Düchting, H.: Paul Klee. Malerei und Musik. Prestel: Munich (2001).
445. Gropius, W.: Der stilbildende Wert industrieller Bauformen. In: Jahrbuch des Deutschen Werkbundes (1914), p. 29.
446. Le Corbusier: Vers une Architecture. In: Conrads, U. (ed.): Programme und Manifeste zur Architektur des 20. Jahrhun-derts. Bauwelt Fundamente. Vol. 1. Berlin (1964).
447. 8.70 Le Corbusier: Urbanisme. In: Conrads [8.69].
448. Schumacher, F.: Sozialer Städtebau. In: Kulturpolitik. Jena (1919).
449. 8.72 Frampton, K.: Die Architektur der Moderne. Deutsche Verlagsanstalt: Stuttgart (1983),
450. Jencks, C.: Die Sprache der postmodernen Architektur. Deutsche Verlagsanstalt: Stuttgart (1978).
451. Lyotard, J.-F.: Das postmoderne Wissen. Ein Bericht. Impuls & Association: Bremen (1982);
452. Habermas, J.: Die Moderne — ein unvollendetes Projekt. Theodor W. Adorno Preis 1980. In: Habermas, J.: Kleine politische Schriften I–IV. Suhrkamp: Frankfurt (1981).
453. Adorno, T.W.: Ästhetische Theorie. Suhrkamp: Frankfurt (1970), p. 237.
454. Steller, E.: Computer und Kunst. Programmierte Gestaltung: Wurzeln und Tendenzen neuer Ästhetik. B.I. Wissenschaftsverlag: Mannheim (1992).
455. 8.77 Picture of the theme issue “Cognition and Complex Brain Dynamics” (ed. by P. beim Graben, D. Saddy, J. Kurths) in: International Journal of Bifurcation and Chaos 14 No. 2 (2004).