ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Poizner B. N., Sitnikova D. L. Big bifurcation: birth of mathematical modelling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 5, pp. 82-96. DOI: 10.18500/0869-6632-2000-8-5-82-96

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2000no5p082.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Nonlinear Dynamics and Humanities
Article type: 
Article
UDC: 
518:519+1(091) (4)
DOI: 
10.18500/0869-6632-2000-8-5-82-96

Big bifurcation: birth of mathematical modelling

Autors: 
Poizner Boris Nikolaevich, National Research Tomsk State University
Sitnikova Darya Leonidovna, National Research Tomsk State University
Abstract: 

What is genealogy of mathematical model — universal method of cognition? Authors took up а new interpretations of processes in European culture of XVII century. The mathematical modelling method is represented as а result of self—organization in а situation of competition and interference of esoteric, scholastic, rationalistic cognition ways. Why the last has won а victory over others? Its replicator had maximum of advantages
concerning of self—organization process forming in society.

Key words: 
-
Acknowledgments: 
The work was supported by the RFBR (project № 00-06-60195).
Reference: 
  1. Yablonsky AI. Mathematical Models in the Study of Science.М.: Nauka; 1986. 352 p. (in Russian).
  2. Evin IA. Synergy of Art. M.: Lada; 1993. 171 p. (in Russian).
  3. Knyazeva EN. Odyssey of Scientific Intelligence. M.: Institute of Philosophy of the Russian Academy of Sciences; 1995. 230 p. (in Russian).
  4. Koronovsky AA, Trubetskov DI. Nonlinear Dynamics in Action. Saratov: College; 1995. 130 p. (in Russian).
  5. Kapitsa SP, Kurdyumov SP, Malinetsky GG. Synergetics and Forecasts for the Future. М.: Nauka; 1997. 285 p. (in Russian).
  6. Moiseev NN. The Fate of Civilization. The Way of Reason. M.: Yazyki russkoi kultury; 2000. 224 p. (in Russian).
  7. Mainzer K. Thinking in Complexity: the Complex Dynamics оf Matter, Mind, and Mankind. Berlin: Springer, 1997. 362 p.
  8. Melik-Gaykazyan IV. Information and Self-Organization: Methodological Analysis. Tomsk: TPU; 1995. 180 p. (in Russian).
  9. Melik-Gaykazyan IV. Information processes and reality. M.: Nauka; 1997. 192 с.
  10. Basin MA, editor. Synergy and methods of science. Saint Petersburg: Nauka; 1998. 439 p.
  11. Poremsky VD. Strategy of Anti-Bolshevik Emigration: Selected Articles 1934-1997. M.: Posev; 1998. 276 p.
  12. Arshinov VI, Budanov VG, Voitsekhovich VE. Synergistic Paradigm. Variety of Searches and Approaches. M.: Progress-Traditsiya; 2000. 536 p.
  13. Kachak VV, Mchedlova ES. Model of interaction between two scientific areas, taking into account the limitation of exponential growth of achievements. Izvestiya VUZ. Applied Nonlinear Dynamics. 1998;6(2):85. (in Russian)
  14. Neimark YuI. The mathematical model of society allowing to answer the question on principles of its functioning, organization and operating. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(1):64-69. (in Russian).
  15. Neuymin YaG. Models in science and technology. History, theory, practice. Saint Petersburg: Nauka; 1984. 187 p.
  16. Ratnikov VS. Physical and theoretical modeling: bases, development, rationality. Kiev: Naukova Dumka; 1995. 290 p.
  17. Samarskii AA, Mikhailov AP. Mathematical modeling. Ideas. Methods. Examples. М.: Nauka; 1997. 320 p.
  18. Rosov NS. The Structure of Civilization and Trends in World Development. Novosibirsk: Novosibirsk University Publishing; 1992. 213 p.
  19. Poisner BN. Replicator is an intermediary between a person and history. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(6):83.
  20. Geodakyan VA. Systemic-evolutionary interpretation of brain asymmetry. In: System studies. Methodological problems: Yearbook 1986. M.: Nauka; 1987. С. 355-376.
  21. Sitnikova DL. Dynamics of cultural patterns in science in the image of IG Fichte and V I Vernadsky. In: Materials of the 2nd International Conference “Self-organization of natural, technogenic and social systems interdisciplinary synthesis of fundamental and applied research.” 1-4 September 1998, Almaty, Kazakhstan. Almaty: Gylym; 1998. P. 181-183.
  22. Poizner BN, Sosnin EA. Experience in classifying subjects of self-organization of matter and information. Izvestiya VUZ. Applied Nonlinear Dynamics. 1998;6(3):74-86.
  23. Rozov SM. Darwinism and epistemology: genetics and memetics. In: On the Shadow Side. Materials for the history of the seminar by M.A. Rozov on epistemology and philosophy of science in Novosibirsk Akademgorodok. Novosibirsk: Novosibirsk University Publishing; 1996. P. 311-338.
  24. Klix F. Erwachendes Denken. Berlin: VEB Deutscher Verlag der Wissenschaften; 1980. 291 p. (in German).
  25. Aveni AF. Empires of Time: Calendars, Clocks, and Cultures. New York: Basic Books Inc.; 1989. 393 p.
  26. Toporov VN. Numbers. In: Myths of the peoples of the world. Encyclopedia. Vol. 2. M.: Sovetskaya Enziklopediya; 1980. P. 629-631.
  27. Poisner BN. Chaos, order, time in ancient world paintings. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(3-4):97-109.
  28. Dahan-Dalmedico А, Peiffer J. Une histoire des mathématiques: Routes et dédales. M.: Points; 1986. 320 p. (in French).
  29. Rassell B. Wisdom of the West: a historical survey of Western Philosophy in its social and political settings. London: Rathbone Books; 1959. 416 p.
  30. Lyubishchev AA. Lines of Democritus and Plato in the History of Culture. Saint Petersburg: Aleteja; 2000. 256 p.
  31. Nalimov VV. I’m Throwing Away My Thoughts. On the Way and at a Crossroads. М.: Progress- Traditsiya; 2000. 344 p.
  32. Dmitriev IS. Unknown Newton. Silhouette Against the Background of the Era. Saint Petersburg: Aleteja; 1999. 784 p.
  33. Yates FA. The Rosicrucian Enlightenment. London: Routledge Classic; 1972. 290 p.
  34. Semenov A. Encyclopedia of Mysticism. Saint Petersburg: Litera; 1997. 478 p.
  35. Vasilev S, Nugatov V. Encyclopedia of mystical terms. М.: Lockid; 1998. 576 p.
  36. Biedermann G. Encyclopedia of symbols. М.: Resspublika; 1996. 335 p.
  37. Gaydenko PP. Evolution of the concept of science (XVII-XVIII c.). Formation of scientific programs of modern times. M.: Nauka; 1987. 447 p.
  38. Catasonov VN. Metaphysical mathematics of the XVII century. М.; Nauka; 1993. 41 p.
  39. Dubnishcheva GYa. Retrophysics in the Mirror of Philosophical Reflection. М.: INFRA-M; 1997. 334 p.
  40. Gritsanov AA. The newest philosophical dictionary. Minsk: Skakun; 1998. 896 p.
  41. Ilichev  LF, Fedoseev PN, Kovalev SM, Panov VG, editors. Philosophical Encyclopedic Dictionary. М.: Sovetskaya entsiklopediya; 1989. 815 p.
  42. Bagno VE. Christ’s Troubadour. In: Lyul R. A book about a loving and beloved. A book about the Order of Chivalry. A book about animals. Ramon’s song. Saint Petersburg: Nauka; 2003. P. 241-244.
  43. Holl MP. The Secret Teachings of All Ages: an Encyclopedic Outline of Masonic, Hermetic, Qabbalistic and Rosicrucian Symbolical Philosophy. New York : Jeremy P. Tarcher/Penguin; 2003. 751 p.
  44. Dimont MI. Jews, God and History. New York: Signet; 1962. 472 p.
  45. Ladorenko OO. Classic Jewish mysticism. В:Kasavina IT, editor. Knowledge beyond science. Mysticism, hermeticism, astrology, alchemy, magic in the intellectual traditions of the I-XIV centuries.M.: Respublica; 1996. P. 435-441.
  46. Lightman M. Cabal. Secret Jewish teaching. Часть 1-3. Novosibirsk: Interbook; 1993. 166 p.
  47. Holl MP. The Secret Teachings of All Ages: an Encyclopedic Outline of Masonic, Hermetic, Qabbalistic and Rosicrucian Symbolical Philosophy. New York : Jeremy P. Tarcher/Penguin; 2003. 751 p.
  48. Glazerson M. The Mystical Of The Festivals. Jerusalem: Gesharim; 2000. 158 p.
  49. Stepanov AM. Explanatory dictionary on esotericism, occultism and parapsychology. M.: Istoki; 1997. 336 p.
  50. Khimik IA. Artistic culture of primitive society. Reader. St. Petersburg: Slavija; 1994. 416 p.
  51. Kasavin IT. Magic: its imaginary discoveries and true secrets. In: Kasavin IT, editor. Misconception?: Diversity of Extrascientific Knowledge. М.: Politizdat; 1990. P. 58-81. (in Russian).
  52. Kasavin IT. Magic as a parallel humanities XVIII-XIX c. In: Hermeticism, magic, natural philosophy in European culture XIII-XIX c. M.: Kanon+; 1999. P. 675-676. (in Russian).
  53. Vanderhill E. Mystics of the XXth Century. Encyclopedia. M.:Mif; 1996. 522 p.
  54. Shvarts F, Puasson A, Blavatskaya EP. Theories and symbols of alchemists. М.: Novyi Akropol; 1995. 192 p.
  55. Puasson A, Morozov NA, Shvarts F, Eliade M, Jung KG. Theory and symbols of alchemy. Great Doing. Kiev: Novyi Akropol; 1995. 288 p.
  56. Bogutskii K. Гермес Трисмегист и герметическая традиция Востока и Запада. Киев: Ирис; М.: Алетейа; 1998. 625 p.
  57. Mead GRS. Thrice-Greatest Hermes. London: Theosophical Publ. Society; 1906. 288 p.
  58. Kudryavtsev OF. Hermes Bowl: Humanistic thought of the Renaissance and hermetic tradition. M.: Jurist; 1996. 336 p.
  59. Tomberg V. Meditations on the Tarot: A Journey into Christian Hermeticism. London: TarcherPerigee; 2002. 688 p.
  60. Yates FA. Giordano Bruno and the Hermetic Tradition. Chicago: University of Chicago Press; 1964. 466 p.
  61. Platonic philosophical lexicon. In: Tsyba AV, editor. Academy. Materials and Research on the History of Platonism. Interuniversity collection. no 2. St.Petersburg: St. Petersburg University Publishing; 2000. P. 329-360. (in Russian).
  62. Josten CH. A Translation of John Dee's "Monas Hieroglyphica" (Antwerp, 1564), with an Introduction and Annotations. Ambix. 1964;12(2–3):84–221. DOI:10.1179/000269864790223101.
  63. Paracelsus Т. The Archidoxes of Magic. Whitefish: Kessinger Publishing; 2007. 188 p.
  64. Hartmann F. Paracelsus And The Substance Of His Teachings. London: Kegan Paul, Trench, Trubner & Co. Ltd; 1997. 311 p.
  65. Akhutin AV. The Concept of “Nature” in Antiquity and in Modern Times. М.: Nauka; 1988. 208 p. (in Russian).
  66. Danilov YuA. Michael Faraday. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(1):95-101. (in Russian).
  67. Sedova TA. Old Pinakothek in Munich. М.: Iskusstvo; 1990. 278 p.
  68. Kinelev VG, Mironov VB. Education, Upbringing, Culture in the History of Civilizations. М.: VLADOS; 1988. 520 p. (in Russian).
  69. Deleuze G. The Fold: Leibniz and the Baroque. Minnesota: University of Minnesota Press; 1992. 192 p.
  70. Bely А. Self-Conscious Soul. М.: Kanon+; 1999. 560 p.
  71. Shirokova NS. Celtic Culture and the Nordic Tradition of Antiquity.St. Petersburg.: Evrasiya; 2000. 352 p. (in Russian).
  72. Ancient Wisdom and Secret Sects. London: Littlehampton Book Services Ltd; 1989. 160 p.
  73. Boult JE. Vasily Kandinsky and Theosophy. In: Avtonomova NB, Sarabianov DV, Turchin VS, editors. The Multifaceted World of Kandinsky. M.: Nauka; 1998. P. 30-42; Pravoverova LL. Movement through space and time. Worlds A. Bely and V. Kandinsky. Chelovek. 2000;3:93-104. (in Russian).
  74. Ivanov VV. Foreword by the editor of the English edition. In: Ronen О. The Silver Age as an Intention and Fiction. M.: United humanitarian publishing house; 2000. P. 11. (in Russian).
  75. Trubetskov DI. Fluctuations and Waves for the Humanities: Textbook for Universities. Saratov: College; 1997. 392 p.
  76. Malinetskii GG. Chaos. Structures. Computing Experiment: Introduction to Nonlinear Dynamics. М.: Nauka; 1997. 255 p.
  77. Stepin VS. Science, religion and modern problems of cultural dialogue. In: Reason and Existence: Analysis of Scientific and Non-Scientific Forms of Thinking. St. Petersburg: Russian Christian Humanitarian Institute; 1999. P. 21-34. (in Russian).
  78. Moiseev NN. Modern education: the problem of synthesis of humanitarian and natural science knowledge. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(1):93-94.
  79. Poizner VN, Sosnin EA. Synthesis of synthesizing sciences and integration of university education with fundamental research. In: Integration of the educational process and basic research: innovative strategies and technologies: Proc. All-Russian Scientific and Practical Conference. Vol. 1. 20-21 April 2000, Tomsk, Russia. Tomsk: Tomsk University Publishing; 2000. P. 99. (in Russian).
  80. Kasavin IT. To the concept of ultimate experience. In: Reason and existence: Analysis of scientific and non-scientific forms of thinking. St. Petersburg: Russian Christian Humanitarian Institute; 1999. P. 388-400. (in Russian).
Received: 
28.08.2000
Accepted: 
10.11.2000
Published: 
07.02.2001
  • 243 reads