[広告] 楽天市場

# “Battling the Gods: Atheism in the Ancient World”

How long has atheism been a part of human experience? Most people today regard the sustained, intellectually rigorous adherence to non-religion as an invention of the European Enlightenment — or, more recently, of modernity. But as our guest argues on this edition of ST, atheism is actually — like so many other aspects of Western life and culture — a phenomenon with origins in the societies of the ancient Mediterranean. Our guest is Tim Whitmarsh, the Leventis Professor of Greek Culture at the University of Cambridge; he has published widely on ancient Greek and Roman texts, and he chats with us about his fascinating new book, “Battling the Gods: Atheism in the Ancient World.” Myths, legends, rituals, dramas, and epic poems concerning the gods obviously mattered greatly in — and were fundamental to — ancient Greece and Rome alike, but Whitmarsh has several interesting points to make about the various writers and thinkers who challenged if not dismissed these very gods’ existence. For example: Diagoras of Melos, perhaps the first-ever self-professed atheist; Democritus, the first materialist; Lucretius, author of “On the Nature of Things,” a crucial work of proto-scientific writing; and Socrates, who was famously executed for rejecting the gods of (and thereby corrupting the youth of) the Athenian state. As was noted of Whitmarsh’s book in a starred review in Kirkus: “A seminal work…to be studied, reread, and referenced…. With a non-professorial, relaxed style…Whitmarsh delves deeply into the many philosophers who felt gods were invented by humans or who saw laws, in addition to religion, as merely the imposition of order…. The author’s erudition is impressive.” And further, per The New York Times Book Review: “Excellent…. Whitmarsh argues convincingly that [atheism] isn’t a product of the modern age but rather reaches back to early Western intellectual tradition in the ancient Greek world…. The best part of ‘Battling the Gods’ is the Greek chorus of atheists themselves…. If you’ve been paying attention to contemporary atheists you might be startled by the familiarity of the ancient positions.”

“Battling the Gods: Atheism in the Ancient World” | Public Radio Tulsa publicradiotulsa.org/post/battling-gods-atheism-ancient-world このページを訳す 2015/11/25 – For example: Diagoras of Melos, perhaps the first-ever self-professed atheist; Democritus, the first materialist; Lucretius, author of “On the Nature of Things,” a crucial work of proto-scientific writing; and Socrates, who was famously … In part two of our look at the ancient Greek philosopher, we ask students at a California school about the Socratic teaching method and the questions it inspires. …  Asked To Divide Zero By Zero, Siri Waxes Philosophical (And Personal).

とても興味深く読みました：ゼロ除算の発見4周年を超えました：

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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

W = \frac{1}{z},

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、
[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) .

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

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.

# 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

# Newton, Brahmagupta and the Law of Gravity

We need more ministers like Shri Devnani to let our countrymen, women and children know what a great nation we are.

Of course, everyone knows by now that the Zero was invented in India by Aryabhata, though even here the ubiquitous Brahmagupta stakes a claim.

Sir Isaac Newton (1643 – 1727), move over. Your days as the pre-eminent holder of the exalted title ‘Discoverer of the Law of Gravity’ is in grave peril. Enter stage left, Brahmagupta who saw the apple fall from a tree in his garden over 1,000 years prior to Newton’s rip-off discovery and went, ‘Eureka, the apple fell from the tree in a straight, perpendicular line, drawn by the earth’s core.  I have discovered Gravity’. Now the exclamatory ‘Eureka’, of course, has been credited to Archimedes (287 BC – 212 BC), his bathtub, and the subsequent displacement of water, known as the Archimedes principle of buoyancy.

In his uncontrollable excitement, Archimedes is said to have jumped out of his bathtub, running naked all over the house yelling the magic words, ‘Eureka, Eureka’ . Yes, he said it twice over, and who can blame him. There are those who aver that he only exclaimed those words when he actually got into his bath. But honestly, his running around in his birthday suit makes for damn sight more exciting copy. One last thing about Archimedes. Born 287 BC and died 212 BC, the years reducing with the passage of time? How cool is that?

I digress. Let’s get back to Brahmagupta. A mathematician and an astronomer, he would have had to expound his revolutionary theories in Sanskrit or whatever language they spoke all those millenniums ago.  We have all this from an unimpeachable source, namely, the esteemed Rajasthan Education Minister, Vasudev Devnani, the same gentleman who once spectacularly claimed that cows inhaled and exhaled oxygen!  The well-informed Minister has doubtless done his homework, unlike those shameless copycats from the west, and we Indians can hold our heads high at the minister’s stunning revelation. About Brahmagupta I mean, not the cows.

Now the obvious question to ask is, why was this kept a closely guarded secret all these years? When the charlatan Newton claimed the gravity discovery as his own, why did not a phalanx of Indian scientists and politicians jump down Sir Issac’s throat and expose him for his chicanery? Couldn’t we have engaged a battery of legal eagles and nailed him on some patent infringement case? That’s what I would like to know, as would millions of other patriotic Indians. Now that we know all this, thanks in large measure to Minister Devnani, one must perforce cast doubts on the aforementioned Archimedes’ claim as well. Except that I can’t, for the life of me, work out how a man can be born on a certain date and died on another date well before he was born! Which puts me in an awful quandary in trying to determine whether Brahmagupta was born before or after Archimedes.

I am now inclined to believe all those fables my grandmother used to tell us gaggle of grandchildren sitting round her in our village home, while she gently placed blobs of curd rice in our palms in circular motion. ‘If you know your Ramayana, you will know that India invented the aeroplane, Pushpaka Vimana, piloted by Rama, after that dramatic rescue mission of Sita from Lanka’. So that’s why India’s first indigenously made aeroplane was named Pushpak. If you are still sceptical, and have three and a half hours to spare, go to YouTube and watch the 1958 epic film, Sampoorna Ramayanam where there’s a scene of the flying chariot with our icons cruising through fluffy, cotton wool clouds. That should silence the Doubting Thomases.

Of course, everyone knows by now that the Zero was invented in India by Aryabhata, though even here the ubiquitous Brahmagupta stakes a claim. Just can’t keep him out. Again, a host of Europeans, most notably the Italian Fibonacci puts his hand up as another discoverer of the Zero. Much ado about nothing, literally!  However, I think we are all satisfied that everything worth discovering or inventing has been done so, right here in India. The rest of the bearded and whiskered scientists from the west are all merely glory hunters, with an eye to the main chance. Sadly, Indians are known to be modest to a fault, and hence this strange reluctance to take credit where it is clearly due. Any wonder the westerners hogged all the limelight?

We need more ministers like Shri Devnani to let our countrymen, women and children know what a great nation we are. More power to your shoulders, Devnani old chap. If you can’t find anything good to suit your political discourse over the past 100 years, better go back a thousand years! Just mind those confusing BCs and ADs. We await more headline grabbing pronouncements from you in the coming months. Directly inspired by you, a bunch of us have done some ferreting around and have come up with a few startling discoveries of our own. I would like to share this with you Devnani Sir, and you can go ahead and spread the good word.

They say Alexander Fleming discovered penicillin in 1928 in London. Bunkum! Fact: a very bright Malayali nurse in Calicut, Sister Miriam, while treating an English sailor afflicted with venereal disease, came upon the discovery when she was idly experimenting with some antibiotic drugs and their effects on leeches, worms, rabbits and the like. The modest Sister Miriam thought no more about it, but the clever, now cured, licentious sailor made off with a few vials of the drug and handed it over to a hospital in London to which the good Dr. Fleming was attached. The rest is history. Of course, this will be dismissed by the English as mere claptrap, so we are leaving this in the capable hands of our minister to take up with Westminster.

I can go on and on, but the point has been adequately made. Even now, there are strong rumours of a cure having been found in India for the two undefeated Cs – Common Cold and Cancer. May I humbly enjoin upon our Government to act swiftly and patent this before some bright NRI from Sloan Kettering pinches it?

(The author is a brand consultant with an interest in music, cricket, humour and satire)

##### Tags: , , ,
とても興味深く読みました：

Blackholes are where God divided by zero. I don’t believe in mathematics. George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist re-

marked that “it is well known to students of high school algebra” that division by zero is not valid; and Einstein admitted it as the biggest blunder of his life [1] 1. Gamow, G., My World Line (Viking, New York). p 44, 1970.

·         愛別離苦（あいべつりく） – 愛する者と別離すること

·         怨憎会苦（おんぞうえく） – 怨み憎んでいる者に会うこと

·         求不得苦（ぐふとくく） – 求める物が得られないこと

·         （ごうんじょうく） – (人間の肉体と精神）が思うがままにならないこと

の四つの苦に対する人間の在り様の根本を問うた仏教の教えは人類普遍の教えであり、命あるものの共生、共感、共鳴の精神を諭されたと理解される。人生の意義と生きることの基本を真摯に追求された教えと考えられる。アラブや西欧の神の概念に直接基づく宗教とは違った求道者、修行者の昇華された世界を見ることができ、お釈迦様は人類普遍の教えを諭されていると考える。

これら２点は、インドの誠に偉大なる、世界史、人類における文化遺産である。我々はそれらの偉大な文化を尊崇し、数理科学にも世界の問題にも大いに活かして行くべきであると考える。　数理科学においては、十分に発展し、生かされているので、仏教の教えの方は、今後世界的に広められるべきであると考える。仏教はアラブや欧米で考えられるような意味での宗教ではなく、　哲学的、学術的、修行的であり、上記宗教とは対立するものではなく、広く活かせる教えであると考える。世界の世相が悪くなっている折り、仏教は世界を救い、世界に活かせる基本的な精神を有していると考える。

ちなみに、ゼロは　空や無の概念と通じ、仏教の思想とも深く関わっていることに言及して置きたい。　いみじくも高度に発展した物理学はそのようなレベルに達していると報じられている。この観点で、歴史的に永い間、ゼロ自身の西欧社会への導入が異常に遅れていた事実と経過は　大いに気になるところである。

The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world:
http://www.scirp.org/journal/alamt
http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html

Announcement 326: The division by zero z/0=0/0=0 – its impact to human beings through education and research

そもそも、ニュートン、ダーウィンの時代とは　中世の名残を多く残し、宗教の存在は世界観そのものの基礎に有ったと言える。それで、アリストテレスの世界観や聖書に反して　天動説に対して地動説を唱えるには　それこそ命を掛けなければ主張できないような時代背景が　存在していた。

そのような時に世の運動、地上も、天空も、万有を支配する法則が存在するとの考えは　それこそ、世界観の大きな変更であり、人類に与えた影響は計り知れない。進化論　人類も動物や生物の進化によるものであるとの考えは、　人間そのものの考え方、捉え方の基本的な変更であり、運動法則とともに科学的な思考、捉え方が世界観を根本的に変えてきたと考えられる。勿論、自然科学などの基礎として果たしている役割の大きさを考えると、驚嘆すべきことである。

その上に　存在している。如何に行くべきか、在るべきかの基本は　その法則と作られた存在の元、原理を探し、それに従わざるを得ないとなるだろう。しかしながら、狭く捉えて　唯物史観などの思想も生んだが、それらは、心の問題、生命の神秘的な面を過小評価しておかしな世相も一時は蔓延ったが、自然消滅に向かっているように見える。

ニュートンの作用、反作用の運動法則などは、人間社会でも、人間の精神、心の世界でも成り立つ原理であり、公正の原則の基礎（再生核研究所声明 1　(2007/1/27)：　美しい社会はどうしたら、できるか、美しい社会とは）にもなる。　自国の安全を願って軍備を強化すれば相手国がより、軍備を強化するのは道理、法則のようなものである。慣性の法則、急には何事でも変えられない、移行処置や時間的な猶予が必要なのも法則のようなものである。力の法則　変化には情熱、エネルギー，力が必要であり、変化は人間の本質的な要求である。それらはみな、社会や心の世界でも成り立つ原理であり、掘り下げて学ぶべきことが多い。ダーウィンの進化論については、人間はどのように作られ、どのような進化を目指しているのかと追求すべきであり、人間とは何者かと絶えず問うて行くべきである。根本を見失い、個別の結果の追求に明け暮れているのが、現在における科学の現状と言えるのではないだろうか。単に盲目的に夢中で進んでいる蟻の大群のような生態である。広い視点で見れば、経済の成長、成長と叫んでいるが、地球規模で生態系を環境の面から見れば、癌細胞の増殖のような様ではないだろうか。人間の心の喪失、哲学的精神の欠落している時代であると言える。

ニュートン、ダーウィンの大きな影響を纏めたので（声明３１４）今回はユークリッド幾何学の影響について触れたい。

ユークリッド幾何学の建設について、ユークリッド自身（アレクサンドリアのエウクレイデス（: Εὐκλείδης, Eukleídēs、: Euclīdēs、: Euclid（ユークリッド）、? – ）は、の、とされる。上最も重要な著作の1つ『原論』（）の著者であり、「の父」と称される。治世下（紀元前323年-283年）ので活動した。）が絶対的な幾何学の建設に努力した様は、『新しい幾何学の発見―ガウス ボヤイ ロバチェフスキー』リワノワ 著松野武 訳1961　東京図書　に見事に描かれており、ここでの考えはその著書に負うところが大きい。

ユークリッドは絶対的な幾何学を建設するためには、絶対的に正しい基礎、公準、公理に基づき、厳格な論理によって如何なる隙や曖昧さを残さず、打ち立てられなければならないとして、来る日も来る日も、の海岸を散歩しながら　ユークリッド幾何学を建設した（『原論』は19世紀末から20世紀初頭まで数学（特に）の教科書として使われ続けた。線の定義について、「線は幅のない長さである」、「線の端は点である」など述べられている。基本的にその中で今日と呼ばれている体系が少数の系から構築されている。エウクレイデスは他に、、、、誤謬推理論、図形分割論、などについても著述を残したとされている。）。

ユークリッド幾何学、原論は２０００年以上も越えて多くの人に学ばれ、あらゆる論理的な学術書の記述の模範、範として、現在でもその精神は少しも変わっていない、人類の超古典である。―　少し、厳密に述べると、ユークリッド幾何学の基礎、いわゆる第５公準、いわゆる平行線の公理は徹底的に検討され、２０００年を経て公理系の考えについての考えは改められ―　公理系とは絶対的な真理という概念ではなく、矛盾のない仮定系である　―　、非ユークリッド幾何学が出現した。論理的な厳密性も徹底的に検討がなされ、ヒルベルトによってユークリッド幾何学は再構成されることになった。非ユークリッド幾何学の出現過程についても上記の著書に詳しい。

しかしながら、ユークリッド幾何学の実態は少しも変わらず、世に絶対的なものがあるとすれば、それは数学くらいではないだろうかと人類は考えているのではないだろうか。

19/03/2012

ここでは、数学とは何かについて考えながら、数学と人間に絡む問題などについて、幅.広く面白く触れたい。

）。

―　数学は公理系によって定まり、そこから、論理的に導かれる関係の全体が一つの数学の様 にみえる。いま予想されている関係は、そもそも人間には無関係に確定しているようにみえる。その数学の全体はすべて人間には無関係に存在して、確定しているようにみえる。すなわち、われわれが捉えた数学は、人間の要求や好みで発見された部分で、その全貌は分か らない。抽象的な関係の世界、それはものにも、時間にも、エネルギーにも無関係で、存在 している。それではどうして、存在して、数学は美しいと感動させるのであろうか。現代物理学は宇宙全体の存在した時を述べているが、それでは数学はどうして存在しているのであろうか。宇宙と数学は何か関係が有るのだろうか。不思議で 不思議で仕方がない。数学は絶対で、不変の様にみえる。時間にも無関係であるようにみえる。数学と人間の関係は何だ ろうか。―

（ゼロ除算の研究に専念してきた物理学者と興味深い議論をしてきた。　それで気づかされた視点である。）

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

から、最近でも数学についていろいろな意見を表明してきている：

ゼロ除算の研究者は我々の研究グループを除いて世界で大体１５名くらいいて、彼らの研究は今でも混乱していると言える。大きく分けると数学の基礎が無くて、論理が通じず、混乱している数学の愛好者たち、ゼロ除算不可能性に満足できず　―　この元は多くは計算機がゼロ除算に会うと計算機障害を起こすが、それを回避することに動機がある　―　公理論的に独自の数学を建設している者、そして物理学上の立場からゼロ除算の研究に取り組んでいる者である。この最後のグループとの相当な議論をして感じたことを述べたい。―　尚、我々の研究グループは、内外大体８名である。ゼロ除算は本質的に解明され、基本は既に確定していると考えている。―　我々の存念を繰り返し内外に広く送っているが、上記グループからも批判が寄せられず、我々の主張を相当理解され、認めてきていると判断している。

そこで、数学についてそのような視点から考えさせられることがある。いろいろな理論が提起されて、いろいろな結果が導かれる。何をもってそれらを評価し、価値あるものと判断できるかという視点である。公理系や論理も、仮定もいろいろ存在して、様々な研究成果が得られている。ここで、評価をどのようにするかである。ある純粋数学者は人類の名誉のためにこの問題を解いたと表現するが、他の人はそんなことは分からず、また興味も関心もないという。興味、関心の前に　結果そのものが分からないは　今や純粋数学ではほとんどであると言えよう。

そして

オイラーの公式が数学上の最高の結果であると表現した：

No.81, May 2012(pdf 432kb)

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

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.

それで、結局は世界史に貢献できる結果こそが良い結果であると言えよう。

そこで、ゼロ除算の重要性を示すために多角的な取り組みを始め、いろいろな表現を考え、意見表明を行っている。数学者の名誉のために、人類の名誉ためにである。―　実際、数学には恥ずかしい初歩的な欠陥があると主張している。さらに、人はゼロ除算の真相から、人間の愚かさを自覚することが出来るから、人間の精神の開放に　ゼロ除算は大きく貢献できると考えている。

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