Difference between revisions of "Pluralism"
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The [[Pluralism]], as idea of simplicity, had been used to guess the asymptotic behaviour of [[tetration]] and [[arctetration]] at $\pm \mathrm i \infty$ |
The [[Pluralism]], as idea of simplicity, had been used to guess the asymptotic behaviour of [[tetration]] and [[arctetration]] at $\pm \mathrm i \infty$ |
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Revision as of 10:27, 4 December 2018
Pluralism (плюрализм) is the last axiom among the TORI axioms set [1][2][3] Pluralism, postulated as compulsory for the scientific concept, declares, that mutually-contradicted concepts may coexist in science, but specifies their subordination:
If two concepts satisfying first 5 TORI axioms, have some common range of validity, then, in this range, the simplest of them has priority.
Concepts, that use complicated formalism to describe simple phenomena, have low priority. The simple concepts, that are applicable to the case, should be considered first.
Occam razor
The ideas of pluralism and simplicity are not new.
They are discussed and applied during centuries.
Some links are suggesed at http://en.wikipedia.org/wiki/Occam's_razor
Tetration and other Superfunctions
The Pluralism, as idea of simplicity, had been used to guess the asymptotic behaviour of tetration and arctetration at $\pm \mathrm i \infty$ [4].
The same idea can be applied to other superfunctions [5].
Certain postulates about of simplicity of the superfunction and the abelfunction lead to uniqueness of the solution.
In particular, tetration not only exist, but also is unique super exponential, that have simple behaviour at infinity.
[6][7][8]:
.. we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an infinite number of solutions, and there is no agreement as to which solution is "best. We will approach the problem by first solving Abel's functional equation $\alpha(e^x) = \alpha(x) + 1$ by perturbing the exponential function so as to produce a real fixed point, allowing a unique holomorphic solution. We then use this solution to find a solution to the unperturbed problem. However, this solution will depend on the way we first perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.
Several examples of search for simplest concept (and to choose it) are mentioned in article Place of science in the human knowledge [9].
References
- ↑ http://www.scirp.org/journal/PaperInformation.aspx?PaperID=36560 http://mizugadro.mydns.jp/PAPERS/2013jmp.pdf D.Kouznetsov. TORI axioms and the applications in physics. Journal of Modern Physics, 2013, v.4, p.1151-1156.
- ↑ http://pphmj.com/abstract/5076.htm D.Kouznetsov. Support of non-traditional concepts. Far East Journal of Mechanical Engineering and Physics, 1, No.1, p.1-6 (2010)
- ↑ http://ufn.ru/tribune/trib120111 D.Kouznetsov. Place of science and physics in the human knowledge. Physics-Uspekhi, v.181, Трибуна, p.1-9 (2011, in Russian)
- ↑ http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html
D.Kouznetsov. Solutions of F(z+1)=exp(F(z)) in the complex z plane. Mathematics of Computation, 78 (2009) 1647-1670 - ↑
http://www.ils.uec.ac.jp/~dima/BOOK/443.pdf D.Kouznetsov. Superfunctions. 2017.
http://mizugadro.mydns.jp/BOOK/444.pdf D.Kouznetsov. Superfunctions. 2018. (41742154 bytes) - ↑ http://www.springerlink.com/content/u7327836m2850246/ http://mizugadro.mydns.jp/PAPERS/2011uniabel.pdf H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2011)
- ↑ http://dx.doi.org/10.11568/kjm.2016.24.1.81 William Paulsen. Finding the natural solution to $f(f(x)) = \exp(x)$ Korean J. Math. Vol 24, No 1 (2016) pp.81-106.
- ↑ http://myweb.astate.edu/wpaulsen/tetration2.pdf http://link.springer.com/article/10.1007/s10444-017-9524-1 William Paulsen and Samuel Cowgill. Solving $F(z+1)=b^{F(z)}$ in the complex plane. Advances in Computational Mathematics, 2017 March 7, p. 1–22. .. we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an infinite number of solutions, and there is no agreement as to which solution is "best. We will approach the problem by first solving Abel's functional equation $\alpha(e^x) = \alpha(x) + 1$ by perturbing the exponential function so as to produce a real fixed point, allowing a unique holomorphic solution. We then use this solution to find a solution to the unperturbed problem. However, this solution will depend on the way we first perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.
- ↑
http://budclub.ru/k/kuznecow_d_j/2010mestoe.shtml D.Kouznetsov. Place of Science in the human knowledge (2010).
http://ufn.ru/tribune/trib120111 Д.Кузнецов. Место науки и физики в человеческом знании. Трибуна УФН, 2010–2011, No.110. (In Russian)
Keywords
TORI, TORI axiom, Philosophy, Place of science in the human knowledge, Religion, Science