Difference between revisions of "Pluralism"
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http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf <br> |
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http://mizugadro.mydns.jp/PAPERS/analuxp99.pdf |
http://mizugadro.mydns.jp/PAPERS/analuxp99.pdf |
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| − | D.Kouznetsov. Solutions of F(z+1)=exp(F(z)) in the complex |
+ | D.Kouznetsov. Solutions of F(z+1)=exp(F(z)) in the complex z plane. Mathematics of Computation, 78 (2009) 1647-1670 |
</ref>. Then, the same idea is applied to other [[superfunctions]] |
</ref>. Then, the same idea is applied to other [[superfunctions]] |
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<ref> |
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</ref>. |
</ref>. |
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| − | Certain postulates about of simplicity of |
+ | Certain postulates about of simplicity of the [[superfunction]] and [[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. |
<ref> |
<ref> |
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| + | http://www.springerlink.com/content/u7327836m2850246/ |
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| − | http://myweb.astate.edu/wpaulsen/tetration2.pdf |
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| + | http://mizugadro.mydns.jp/PAPERS/2011uniabel.pdf |
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| − | http://link.springer.com/article/10.1007/s10444-017-9524-1 |
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| + | H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2011) |
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| − | 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 |
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</ref><ref> |
</ref><ref> |
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http://myweb.astate.edu/wpaulsen/tetration2.pdf |
http://myweb.astate.edu/wpaulsen/tetration2.pdf |
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http://link.springer.com/article/10.1007/s10444-017-9524-1 |
http://link.springer.com/article/10.1007/s10444-017-9524-1 |
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| − | William Paulsen and Samuel Cowgill. Solving F(z+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 |
</ref> |
</ref> |
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| − | Some examples of search for simplest concept are mentioned in article [[Place of science in the human knowledge]]. |
+ | Some examples of search for simplest concept (and to choose it) are mentioned in article [[Place of science in the human knowledge]]. |
==References== |
==References== |
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Revision as of 10:03, 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
Superfunctions
The Pluralism as idea of simplicity, had been used to guess the asymptotic behaviour of the natural tetration at $\pm \mathrm i \infty$ [4]. Then, the same idea is applied to other superfunctions [5].
Certain postulates about of simplicity of the superfunction and 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]
Some examples of search for simplest concept (and to choose it) are mentioned in article Place of science in the human knowledge.
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
http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
http://mizugadro.mydns.jp/PAPERS/analuxp99.pdf 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://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
Keywords
TORI, TORI axiom, Philosophy, Place of science in the human knowledge, Religion, Science