Possibility of the identification of calculative irreducible systems
Keywords:
simulation, billiard problem, strange attractor, fractal, calculative irreducible systemAbstract
Case history. A performance search, reflecting the state of the calculative irreducible systems (CIS) (reflecting points systems), led the scientists to the study of the geometric properties of strange attractors, which tend to have сantor or fractal structure repeating itself on a smaller scale. Object of study. Calculative irreducible systems. Results and discussion. We consider a Lorentz billiard task. On the basis of theoretical research and experimentation, it is argued that the global instability of the system takes place even when there is only one ball on the table, provided that at least one of the pool table walls is convex to the inside. It becomes apparent, global instability leads to the fact that the behavior of the system becomes chaotic (unpredictable) and the whole entire phase space is filled evenly. Identification of such systems can only be done by reference to literature and art, as only the mind and intuition, can display the nuances that occur in these systems. In this regard, an intermediary, in the identification of calculative irreducible systems, is the process of the hypotheses creating about their possible behavior in different situations. Since all these actions are assigned to the researcher, he is also responsible for the of heuristics prcedures formulation, which are intended to achieve the necessary credibility of the hypotheses. For each system are put relevant only to its hypothesis and heuristics procedures forward. Nevertheless, there is a list of the main hypotheses, which are included in the analysis of practice any system (even a calculative irreducible), these are hypothesis: of their potential falsifiability, confirmation, simplicity, beauty, and explanation. Conclusions. It is shown that the identification of calculative irreducible systems can only be done by reference to literature and the arts, because only mind and intuition of man can reflect all possible nuances that occur in these systems.
References
СПИСОК ИСПОЛЬЗОВАННЫХ ИСТОЧНИКОВ
Большаков В. І. Часткова компенсація неповноти формальної аксіоматики при ідентифікації структури металу / В. І. Большаков,
Ю. І. Дубров // Вісник НАН України. - 2016. - № 3. – С. 76-80.
http://dspace.nbuv.gov.ua/handle/123456789/95437
Lorentz H. A. The motion of electrons in metallic bodies II. Royal Netherlands Academy of Arts and Sciences / H. A. Lorentz. − 1905. − (7): − Рр. 585-593.
Синай Я. Г. Динамические системы с упругими отражениями /
Я. Г. Синай // Успехи математических наук. - 1970. - Т. 25. - Вып. 2. - С. 45-53.
Дубров Ю. И. Исследования имитационной модели «бильярдной задачи», а также ее применение в практике преподавания синергетики / Ю.И. Дубров // Математика. Компьютер. Образование. − Дубна. − 1998. − С. 71-83.
Дубров Ю. І. Наука як система, що самоорганізується /
Ю. І. Дубров // Вісник НАН України. -2000. - № 2. - С. 16–22.
Успенский В. А. Теорема Гёделя о неполноте : монография /
В. А. Успенский. - Москва : Наука, 1982. - 112 c.
Большаков Вад. І. Про неповноту формальної аксіоматики в задачах ідентифікації структури металу / Вад. І. Большаков,
В. І. Большаков, Ю. І. Дубров // Вісник НАН України. - 2014. - № 4. – С. 55–59.
Большаков В. И. Вычислительно неприводимые системы и пути их идентификации / В. И. Большаков, Ю. И. Дубров // Металознавство та термічна обробка металів. - Дніпропетровськ : ДВНЗ ПДАБА, 2014. -
№ 1. - С. 19-42.
REFERENCES
Bol'shakov V. I. and Dubrov Yu.I. O vozmozhnosti identifikatsii vychislitel'no neprivodimykh sistem [Possibility of the identification of computationally irreducible systems]. Vіsnik NAN Ukraїni [Bulletin of the National Academy of Sciences of Ukraine]. 2014, no. 12, pp. 45-48. (in Ukrainian).
Lorentz H.A. The motion of electrons in metallic bodies II. Royal Netherlands Academy of Arts and Sciences, 1905, (7), рр. 585-593.
Sinay Yа.G. Dinamicheskiye sistemy s uprugimi otrazheniyami [Dynamical systems with elastic reflections]. Uspekhi matematicheskih nauk [Successes of Mathematical Sciences]. 1970, 25 (2), pp. 45-53. (in Russian).
Dubrov Yu.I. Issledovaniya imitacionnoj modeli «bil'yardnoj zadachi», a takzhe ee primenenie v praktike prepodavaniya sinergetiki [Research of simulation model "billiard problem", as well as its application in practice, synergy of teaching]. Matematika. Komp'yuter. Obrazovanie. [Computer. Mathematics. Education]. Dubna, 1998, pp. 71-83. (in Russian).
Dubrov Yu.I. Nauka yak systema, shcho samoorhanizuyetʹsya [Science as a self-organizing system]. Vіsnik NAN Ukraїni [National Library of Ukraine]. 2000, (2), pp. 16-22. (in Ukrainian).
Uspenskiy V.A. Teorema Godelya o nepolnote [Gödel's incompleteness theorem]. Moscow : Nauka Publ., 1982, 112 p. (in Russian).
Bol’shakov Vad.I., Bol’shakov V.I. and Dubrov Yu.I. Pro nepovnotu formalʹnoyi aksiomatyky v zadachakh identyfikatsiyi struktury metalu [On the incompleteness of formal axiomatics in the problems of identification of the metal structure]. Vіsnik NAN Ukraїni [National Library of Ukraine]. 2014. (4): 55-59. (in Ukrainian).
Bol’shakov V.I. and Dubrov Yu.I. Vychislitel'no neprivodimyye sistemy i puti ikh identifikatsii [Computational irreducible systems and ways of their identification]. MTOM [Metal Science & Heat Treatment of Metals]. 2014, (1), pp. 19-42. (in Russian).
Downloads
Published
Issue
Section
License
Authors that are published in this journal agree to follow the conditions:
Authors reserve the right to the authorship of his work and cede the right to the journal of first publication of this work on conditions of the license under the Creative Commons Attribution License, which allows others to distribute it freely with the obligatory reference to the author of the original work and the first publication of the work in this journal.
