2018年6月5日火曜日

世界最高のIQを持つ女性 vs 数学者軍団 (1/2)

2018年06月05日(火)NEW !
テーマ：教育

組み込みエンジニアの現場力養成ドリル（5）：
世界最高のIQを持つ女性 vs 数学者軍団 (1/2)
問題を考える上で感覚（直感）の役目も大きなものですが、感覚だけに頼ると論理的な結果が見えにくくなることがあります。有名な問題を例に、組み込みエンジニアとして同問題に取り組むべきか、考えてみましょう。
[山浦恒央　東海大学大学院組込み技術研究科非常勤講師（工学博士），TechFactory]

　これまで、長編問題が続いたので、今回は、「ひとやすみ」的な軽い問題を解いていただきます。今回は、30年前のアメリカで実際に起きた「世界最高のIQを持つ女性と数学・統計学者軍団の戦い」を取り上げます。

今回の問題の背景

　アメリカの新聞の1つとして、毎週日曜日に発行されている「Parade」紙があります（週刊誌風ですが、広告が満載のいわゆるサンデー・ペーパーです）。初発行は1941年。読者はアメリカ全土に3200万人もいるそうです。日本で最大の発行部数を持つ新聞は読売新聞で、2018年4月時点の発行部数は約847万部です。週刊と日刊の違いはありますが、「Parade」紙の影響力は絶大といえます。

　Parade紙の名物コラムが1986年から連載が始まった「Ask Marilyn」で、日本語に訳すと『マリリンに聞いてみよう』でしょう。これは「世界で最も高いIQの持ち主」としてギネスブックに載ったマリリン・ボス・サヴァント（Marilyn vos Savant）さんが、読者からのあらゆる質問に答えるコラムです。ギネスブックには1986年から1989年まで、「世界最高のIQの持ち主」として彼女の名前が載りました。ただし、1990年以降、ギネスブックは「IQ値は信頼性が低い」として、IQ記録は取り上げていません。

　美貌と頭脳を兼ね備えたマリリンを困らせようと（姓の「savant」が「学者」を意味する単語であることも関係しているかもです）、人生相談から、政治経済、物理学、読者が作った難問パズル、地球温暖化への見解まで、読者はありとあらゆる質問を送りました。その中からマリリンは毎週1つを取り上げて、鮮やかに答えるのです。

　1990年9月9日号で、読者から「テレビのゲーム・ショー『Let's Make A Deal』で、3つのドアの後ろにある高級車を選ぶ場合、どうすれば高級車が当たる確率を大きくできるか？」との質問を取り上げました。多分、読者は「1＋1がなぜ2になるのか？」みたいな、「常識的ゆえに難解な問題」だと思い、マリリンを困らせようと思ったのでしょう。

　『Let's Make A Deal』は、1964年から始まり、今でも続く人気テレビ番組で、出場者が簡単なゲームをして、うまくいけば高級車や海外旅行をプレゼントしてもらえる趣向の古典的なショーです。その中の有名なゲームとして、「3つのドアと高級車」があります。

ドアの向こうは高級車かヤギか（写真はイメージです）

　出場者の前にはドアが3枚あり、1つには高級車が、残りの2つにはヤギが隠れています。挑戦者はドアを1枚選び、そこに高級車があれば、それをもらえます。トリッキーなのは、挑戦者が1枚選んで開ける前に、司会者のモンティ・ホールが、ヤギのいる別のドアを開けてみせ、「ここにはヤギがいる。今なら、もう1枚のドアに選び直してもよい」と言うことです。

問題編（制限時間30分）

　さて、この「3枚のドア」で、高級車をもらえる確率を最大にするには、挑戦者は最初に選んだドアに固執すべきか、替えるべきでしょうか？http://techfactory.itmedia.co.jp/tf/articles/1806/04/news002.html

ゼロ除算の発見は日本です：

∞？？？

∞は定まった数ではない・

人工知能はゼロ除算ができるでしょうか：

とても興味深く読みました：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

ゼロ除算関係論文・本

https://ameblo.jp/syoshinoris/entry-12370797278.html

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\begin{document}

\title{\bf Announcement410 : What is mathematics? -- beyond logic; for great challengers on the division by zero\\

(2018.１.30.)}

\author{{\it Institute of Reproducing Kernels}\\

Kawauchi-cho, 5-1648-16,\\

Kiryu 376-0041, Japan\\

}

\date{\today}

\maketitle

The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0=1/0=z/0=0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotelēs (BC384 - BC322) and Euclid (BC 3 Century - ), and the division by zero is since Brahmagupta (598 - 668 ?).

In particular, Brahmagupta defined as $0/0=0$ in Brāhmasphuṭasiddhānta (628), however, our world history stated that his definition $0/0=0$ is wrong over 1300 years, but, we showed that his definition is suitable.

For the details, see the references and the site: http://okmr.yamatoblog.net/

We wrote a global book manuscript \cite{s18} with 154 pages

and stated that the division by zero is trivial and clear, and in the last section of the manuscript we stated as follows:

\bigskip

{\bf Conclusion}

\medskip

Apparently, the common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on derivatives we have a great missing since $\tan (\pi/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero.

This book is an elementary mathematics on our division by zero as the first publication of books for the topics. The contents have wide connections to various fields beyond mathematics. The author expects the readers write some philosophy, papers and essays on the division by zero from this simple source book.

The division by zero theory may be developed and expanded greatly as in the author's conjecture whose break theory was recently given surprisingly and deeply by Professor Qi'an Guan \cite{guan} since 30 years proposed in \cite{s88} (the original is in \cite {s79}).

We have to arrange globally our modern mathematics with our division by zero in our undergraduate level.

We have to change our basic ideas for our space and world.

We have to change globally our textbooks and scientific books on the division by zero.

\bigskip

However, we have still curious situations and opinions for us on the division by zero; in particular, the two great challengers Jakub Czajko and Ilija Barukčić on the division by zero in connection with physics stated that we do not have the definition of the division $0/0$, however $0/0=1$.

They seem to think that a truth is based on physical objects and is not on our mathematics. In such a cases, we will not be able to continue discussions on the division by zero more, because for mathematicians, they will not be able to follow their logics more. However, then we will ask for the question that what are the values and contributions of your articles and discussions. We will expect some contributions, of course.

This question will reflect to mathematicians contrary. We stated for the estimation of mathematisc in \cite{s97}: Mathematics is the collection of relations and, good results are fundamental,

beautiful, and give

great good impacts to human beings.

With this estimation, we stated that the Euler formula

e^{\pi i} = -1

is the best result in mathematics in details in:

\medskip

No.81, May 2012(pdf 432kb)

www.jams.or.jp/kaiho/kaiho-81.pdf

\medskip

In order to show the importance of our division by zero and division by zero calculus we are requested to show their importance.

It seems that the long and mysterious confusions for the division by zero is on the definition. --

Indeed, when we consider the division by zero $a/0$ in the usual sense of the fundamental equation $0 \cdot z= a$, we have immediately the simple contradiction, however, we have such cases may happen, in particular, in mathematical formulas and physical formulas on the universe.

\bibliographystyle{plain}

\begin{thebibliography}{10}

\bibitem{bar}

I. Barukčić,

Dialectical Logic – Negation Of Classical Logic,

http://vixra.org/abs/1801.0256

\bibitem{jake}

J. Czajko, Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces,

Available online at www.worldscientificnews.com

WSN 92(2) (2018) 171-197

\bibitem{guan}

Q. Guan, A proof of Saitoh's conjecture for conjugate Hardy H2 kernels, arXiv:1712.04207.

\bibitem{kmsy}

M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,

New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,

Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.

\bibitem{ms16}

T. Matsuura and S. Saitoh,

Matrices and division by zero　z/0=0,

Advances in Linear Algebra \& Matrix Theory, {\bf 6}(2016), 51-58

Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt

\\ http://dx.doi.org/10.4236/alamt.2016.62007.

\bibitem{ms18}

T. Matsuura and S. Saitoh,

Division by zero calculus and singular integrals. (Submitted for publication)

\bibitem{mms18}

T. Matsuura, H. Michiwaki and S. Saitoh,

$\log 0= \log \infty =0$ and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.

\bibitem{msy}

H. Michiwaki, S. Saitoh and M.Yamada,

Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. {\bf 6}(2015), 1--8. http://www.ijapm.org/show-63-504-1.html

\bibitem{mos}

H. Michiwaki, H. Okumura and S. Saitoh,

Division by Zero $z/0 = 0$ in Euclidean Spaces,

International Journal of Mathematics and Computation, {\bf 2}8(2017); Issue 1, 2017), 1-16.

\bibitem{osm}

H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,

Journal of Technology and Social Science (JTSS), {\bf 1}(2017), 70-77.

\bibitem{os}

H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).

\bibitem{o}

H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.

\bibitem{os18}

H. Okumura and S. Saitoh,

Applications of the division by zero calculus to Wasan geometry.

(Submitted for publication).

\bibitem{ps18}

S. Pinelas and S. Saitoh,

Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.

\bibitem{romig}

H. G. Romig, Discussions: Early History of Division by Zero,

American Mathematical Monthly, Vol. {\bf 3}1, No. 8. (Oct., 1924), pp. 387-389.

\bibitem{s97}

T. M. Rassias, Editor, Nonlinear Mathematical 　 Analysis and Applications, HadronicPress,Palm Harbor,FL34682-1577,USA:ISBN1-57485-044-X,1998, 　 pp.223–234: Nonlinear transforms and analyticity of functions, Saburou Saitoh.

\bibitem{s79}

S. Saitoh, The Bergman norm and the Szeg$\ddot{o}$ norm, Trans. Amer. Math. Soc. {\bf 249} (1979), no. 2, 261--279.

\bibitem{s88}

S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in Mathematics Series, {\bf 189}. Longman Scientific \& Technical, Harlow; copublished in the United States with John Wiley \& Sons, Inc., New York, 1988. x+157 pp. ISBN: 0-582-03564-3

\bibitem{s14}

S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/

\bibitem{s16}

S. Saitoh, A reproducing kernel theory with some general applications,

Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182. (Springer) .

\bibitem{s17}

S. Saitoh, Mysterious Properties of the Point at Infinity、

arXiv:1712.09467 [math.GM](2017.12.17).

\bibitem{s18}

S. Saitoh, Division by zero calculus (154 pages: draft): （http://okmr.yamatoblog.net/）

\bibitem{ttk}

S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.

\end{thebibliography}

\end{document}

List of division by zero:

\bibitem{os18}

H. Okumura and S. Saitoh,

Remarks for The Twin Circles of Archimedes in a Skewed Arbelos by H. Okumura and M. Watanabe, Forum Geometricorum.

Saburou Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM]

Hiroshi Okumura and Saburou Saitoh

The Descartes circles theorem and division by zero calculus.　２０１７．１１．１４

https://arxiv.org/abs/1711.04961

L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.

M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,

New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,　Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.

T. Matsuura and S. Saitoh,

Matrices and division by zero　z/0=0,

Advances in Linear Algebra \& Matrix Theory, 2016, 6, 51-58

Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt

\\ http://dx.doi.org/10.4236/alamt.2016.62007.

T. Matsuura and S. Saitoh,

Division by zero calculus and singular integrals. (Submitted for publication).

T. Matsuura, H. Michiwaki and S. Saitoh,

$\log 0= \log \infty =0$ and applications. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.)

H. Michiwaki, S. Saitoh and M.Yamada,

Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. 6(2015), 1--8. http://www.ijapm.org/show-63-504-1.html

H. Michiwaki, H. Okumura and S. Saitoh,

Division by Zero $z/0 = 0$ in Euclidean Spaces,

International Journal of Mathematics and Computation, 28(2017); Issue 1, 2017), 1-16.

H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,

Journal of Technology and Social Science (JTSS), 1(2017), 70-77.

S. Pinelas and S. Saitoh,

Division by zero calculus and differential equations. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics).

S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/

S. Saitoh, A reproducing kernel theory with some general applications,

2018.3.18．午前中　最後の講演：　日本数学会　東大駒場、函数方程式論分科会　講演書画カメラ用　原稿
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.
https://ameblo.jp/syoshinoris/entry-12361744016.html より

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.):

Differential and Difference Equations with Applications:

ICDDEA, Amadora, 2017.

(Springer Proceedings in Mathematics and Statistics, Vol. 230)

May 2018 587 pp.

ゼロ除算の論文が２編、出版になりました：

ICDDEA: International Conference on Differential & Difference Equations and Applications
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
• Editors

• (view affiliations)
• Sandra Pinelas
• Tomás Caraballo
• Peter Kloeden
• John R. Graef
Conference proceedingsICDDEA 2017

log0=log∞=0log⁡0=log⁡∞=0 and Applications
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305

Division by Zero Calculus and Differential Equations
Sandra Pinelas, Saburou Saitoh
Pages 399-418