The Eternal Quest for Aether, the Cosmic Stuff That Never Was
“We’ve Been Wrong Before” is Popular Mechanics' encyclopedia of scientific ideas that sounded good at the time but didn't quite pan out. Today: The hunt for aether, which Aristotle, alchemists, and even Isaac Newton used to explain gaps in our understanding of the universe.
One of the most important science experiments of all time was a complete and utter failure.
In 1887, Albert Michelson and Edward Morley set up their project in the dormitory basement at a university in Cleveland, Ohio. The idea was to bounce light beams off mirrors in different directions and measure their speeds. The two researchers thought their hoped-for result-capturing light moving at different velocity-would help to prove the existence of aether.
The aether was the invisible material thought to permeate all the empty space in the universe, used by famous thinkers from Aristotle to Isaac Newton to explain the mysteries of the natural world. The much-heralded Michelson-Morley experiment, as the 1887 event would go down in history, sought to detect the existence of this undetectable substance.
Instead, it found nothing.
The experiment would go down as a faceplant, a failure that marked the end for a theory that had dominated physics for 2,000 years. But the fallout of the Michelson-Morley experiment led to the idea of the universal speed of light, inspired Einstein’s breakthroughs in relativity, and opened the door to much of modern physics. Sometimes it takes failure to move forward.
The Stuff of Gods
Aether meant many things to many people. Ancient Greeks saw aether as the god of light and the fifth element of the universe. To the medieval alchemists, it was the fabled philosopher’s stone that could turn lead into gold and prolong life. Centuries later, early modern scientists like René Descartes and Nikola Tesla were still pointing to aether to explain fundamental natural phenomena like gravity and light. Yet aether does not exist, and it never did. It may be the most enduring imaginary concept in scientific history.
Aether was invented by the ancients. In Greek mythology it described the pure air that the gods breathed in the heavens as opposed to the normal air breathed by mortals on Earth.
The word “aether” comes from the Greek aithêr, meaning “upper air.” The Greeks’ mythology described the pure air that the gods breathed in the heavens as opposed to the normal air breathed by mortals on Earth, and went further than that. Aether was also a Greek god, one of the first-born deities in the pantheon, the primordial god of light and the sky. This bright, divine Aether was the classical philosophers’ version of our upper atmosphere. In Plato’s theory of the cosmos, he writes that there are different kinds of air and “the brightest part is called the aether.”https://finance.yahoo.com/news/eternal-quest-aether-cosmic-stuff-120000091.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：2014年2月2日 4周年を超えました：
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
\documentclass[12pt]{article}
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\begin{document}
\title{\bf Announcement 412: The 4th birthday of the division by zero $z/0=0$ \\
(2018.2.2)}
\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 in the preface and last section of the manuscript as follows:
\bigskip
{\bf Preface}
\medskip
The division by zero has a long and mysterious story over the world (see, for example, H. G. Romig \cite{romig} and Google site with the division by zero) with its physical viewpoints since the document of zero in India on AD 628. In particular, note that Brahmagupta (598 -668 ?) established the four arithmetic operations by introducing $0$ and at the same time he defined as $0/0=0$ in
Brhmasphuasiddhnta. Our world history, however, stated that his definition $0/0=0$ is wrong over 1300 years, but, we will see that his definition is right and suitable.
The division by zero $1/0=0/0=z/0$ itself will be quite clear and trivial with several natural extensions of the fractions against the mysterously long history, as we can see from the concepts of the Moore-Penrose generalized inverses or the Tikhonov regularization method to the fundamental equation $az=b$, whose solution leads to the definition $z =b/a$.
However, the result (definition) will show that
for the elementary mapping
\begin{equation}
W = \frac{1}{z},
\end{equation}
the image of $z=0$ is $W=0$ ({\bf should be defined from the form}). This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere (\cite{ahlfors}). �As the representation of the point at infinity of the Riemann sphere by the
zero $z = 0$, we will see some delicate relations between $0$ and $\infty$ which show a strong
discontinuity at the point of infinity on the Riemann sphere. We did not consider any value of the elementary function $W =1/ z $ at the origin $z = 0$, because we did not consider the division by zero
$1/ 0$ in a good way. Many and many people consider its value by the limiting like $+\infty $ and $- \infty$ or the
point at infinity as $\infty$. However, their basic idea comes from {\bf continuity} with the common sense or
based on the basic idea of Aristotle. --
For the related Greece philosophy, see \cite{a,b,c}. However, as the division by zero we will consider its value of
the function $W =1 /z$ as zero at $z = 0$. We will see that this new definition is valid widely in
mathematics and mathematical sciences, see (\cite{mos,osm}) for example. Therefore, the division by zero will give great impacts to calculus, Euclidean geometry, analytic geometry, differential equations, complex analysis in the undergraduate level and to our basic ideas for the space and universe.
We have to arrange globally our modern mathematics in our undergraduate level. Our common sense on the division by zero will be wrong, with our basic idea on the space and the universe since Aristotle and Euclid. We would like to show clearly these facts in this book. The content is in the undergraduate level.
\bigskip
\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.
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{ahlfors}
L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.
\bibitem{cs}
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\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{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.
\bibitem{a}
https://philosophy.kent.edu/OPA2/sites/default/files/012001.pdf
\bibitem{b}
http://publish.uwo.ca/~jbell/The 20Continuous.pdf
\bibitem{c}
http://www.mathpages.com/home/kmath526/kmath526.htm
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature - an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann281}
Announcement 281 (2016.2.1): The importance of the division by zero $z/0=0$.
\bibitem{ann282}
Announcement 282 (2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.
\bibitem{ann293}
Announcement 293 (2016.3.27): Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.
\bibitem{ann300}
Announcement 300 (2016.05.22): New challenges on the division by zero z/0=0.
\bibitem{ann326}
Announcement 326 (2016.10.17): The division by zero z/0=0 - its impact to human beings through education and research.
\bibitem{ann352}
Announcement 352(2017.2.2): On the third birthday of the division by zero z/0=0.
\bibitem{ann354}
Announcement 354(2017.2.8): What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.
\bibitem{362}
Announcement 362(2017.5.5): Discovery of the division by zero as $0/0=1/0=z/0=0$
\bibitem{380}
Announcement 380 (2017.8.21): What is the zero?
\bibitem{388}
Announcement 388(2017.10.29): Information and ideas on zero and division by zero (a project).
\bibitem{409}
Announcement 409 (2018.1.29.): Various Publication Projects on the Division by Zero.
\bibitem{410}
Announcement 410 (2018.1 30.): What is mathematics? -- beyond logic; for great challengers on the division by zero.
\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]
arXiv:1712.09467 [math.GM]
Hiroshi Okumura and Saburou Saitoh
The Descartes circles theorem and division by zero calculus. ２０１７．１１．１４
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,
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) .
再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12276045402.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12263708422.html
1/0=0、0/0=0、z/0=0
ソクラテス・プラトン・アリストテレス その他
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか
〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか
〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか
再生核研究所声明 411(2018.02.02): ゼロ除算発見4周年を迎えて
ゼロ除算の論文
Mysterious Properties of the Point at Infinity
Mysterious Properties of the Point at Infinity
Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
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
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∞=0log0=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
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∞=0log0=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
ゼロ除算（division by zero）1/0=0、0/0=0、z/0=0
2018年05月28日(月)
テーマ：数学
テーマ：数学
これは最も簡単な 典型的なゼロ除算の結果と言えます。 ユークリッド以来の驚嘆する、誰にも分る結果では ないでしょうか？
Hiroshi O. Is It Really Impossible To Divide By Zero?. Biostat Biometrics Open Acc J. 2018; 7(1): 555703. DOI: 10.19080/BBOJ.2018.07.555703
ゼロで分裂するのは本当に不可能ですか？ - Juniper Publishers
再生核研究所 ゼロ除算の発見と重要性を指摘した：2014年2月2日
神の数式：
神の数式が解析関数でかけて居れば、 特異点でローラン展開して、正則部の第1項を取れば、 何時でも有限値を得るので、 形式的に無限が出ても 実は問題なく 意味を有します。
物理学者如何でしょうか。
割り算のできる人には、どんなことも難しくない
世の中には多くのむずかしいものがあるが、加減乗除の四則演算ほどむずかしいものはほかにない。
ベーダ・ヴェネラビリス（アイルランドの神学者）
数学名言集：ヴィルチェンコ編：松野武 山崎昇 訳大竹出版1989年
P199より
Please look the papers:
Reality of the Division by Zero z/0=0
DOI:
10.12732/ijam.v27i2.9.
地球平面説→地球球体説
天動説→地動説
1/0=∞若しくは未定義 →1/0=0（628年→2014年2月2日）
リーマン球面における無限遠点は、実は、原点０に一致していました。
地球人はどうして、ゼロ除算1300年以上もできなかったのか？
２０１５．７．２４．９：１０
意外に地球人は知能が低いのでは？ 仲間争いや、公害で自滅するかも。
生態系では、人類が がん細胞であった とならないとも 限らないのでは？
Einstein's Only Mistake: Division by Zero
何故ゼロ除算が不可能であったか理由
１ 割り算を掛け算の逆と考えた事
２ 極限で考えようとした事
３ 教科書やあらゆる文献が、不可能であると書いてあるので、みんなそう思った。
Matrices and Division by Zero z/0 = 0
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