足元ばかり見ていないで、星を見上げることを忘れないで。～スティーヴン・ホーキング【科学者の智慧 vol.03】 2016年7月22日ヒサカタハルカ CULTURE, TECHNOLOGY 宇宙, 科学者 車椅子の天才物理学者

足元ばかり見ていないで、星を見上げることを忘れないで。～スティーヴン・ホーキング【科学者の智慧 vol.03】

2016年7月22日ヒサカタハルカ CULTURE, TECHNOLOGY 宇宙, 科学者
車椅子の天才物理学者

スティーヴン・ホーキング（Stephen Hawking）……1942年～。イギリスの理論物理学者。1963年にブラックホールの特異点定理で世界的名声を得て、量子宇宙論という研究分野の開拓者となった。

13774836353_be07b17523_c
Photo credit: lwpkommunikacio via VisualHunt.com / CC BY


一般人向けに理論物理の世界をわかりやすく解説した『ホーキング、宇宙を語る（原題：A Brief History of Time）』は和訳もされ世界的ベストセラーになった。

さて、ホーキング博士といえば、若くしてALS（筋萎縮性側索硬化症）を発症した「車椅子の物理学者」としても知られている。ALSとは主に脊髄と脳の運動神経が変性し、筋肉が徐々に萎縮していく進行性の病気だ。手足や口、舌などがコントロールしにくくなり、力が次第に衰える。有効な治療法は現時点ではほとんどない

特筆するべきは、ALSの発症後5年生存率は9～40％、10年生存率は8～16％と報告されている（ALS疾患啓発委員会資料）のに対し、ホーキング博士は発症から50年以上経過しても健在という点だ。2016年1月8日、彼は74歳の誕生日を迎えた。これは現代の理論物理学にとって大きな恩恵に違いない。

ただし、この病気は、自分では動けないが周囲の状況が分かってしまうために精神的なストレスが大きいという。そのためかどうかはわからないが、テレビ番組のインタビューで「ひどい苦痛を感じるようになったり、単に周りのお荷物になっていると感じたりしたら、幇助による自殺を考えるだろう」と語っている。

2813995973_084a6facde_o
Photo credit: @Doug88888 via VisualHunt.com / CC BY-NC-SA
ホーキング博士はシニカルな無神論者か？

ホーキング博士は著書（レナード・ムロディナウとの共著）『ホーキング、宇宙と人間を語る（The Grand Design）』のなかで「創造主なしでも宇宙は誕生できる」と記述している。
これは「宇宙は神が想像した」とする宗教界の主張とは相容れないもので、ロイターはこの記述に対して「宗教界から批判を浴びている」と報道している。

では、彼は「死後の世界」についてはどのように考えているのだろうか？
ちょっと興味深い発言がある。同じくロイターによれば、ホーキング博士は自身の「死後の世界」観についてこう述べた。

I regard the brain as a computer which will stop working when its components fail.
There is no heaven or afterlife for broken down computers; that is a fairy story for people who are afraid of the dark.

「私は、脳とはコンピューターみたいなものだと思っている。脳の活動停止（つまり死）はコンピューターが壊れるようなもの。壊れたコンピューターに天国も来世もありはしない。つまり、それらは闇を恐れる人々のためのおとぎ話だよ。（訳：FUTURUS編集部）」

この言葉だけを聞けば、多くの人は「この人は天才かもしれないが、なんてシニカルな厭世観の持ち主だろう」と感じるかもしれない。
だが、僕は決してそうではないと思う。その理由を述べよう。



子どもたちへの最も重要な3つのアドバイス

ホーキング博士は、ABCニュースのインタビューで「父親として、お子さん方（ホーキング博士には3人の子どもと3人の孫がいる）にどんなアドバイスをしていますか？」と質問され、次のように答えている。

One, remember to look up at the stars and not down at your feet. Two, never give up work. Work gives you meaning and purpose and life is empty without it,” he said.
“Three, if you are lucky enough to find love, remember it is there and don’t throw it away.

「ひとつ。足元ばかり見ていないで、星を見上げることを忘れないで。
ふたつ。自分がやるべき仕事を絶対にあきらめてはいけない。生きる意味も目標も失われ、人生が空っぽになる。
みっつ。もし愛に恵まれたら、それは特別な幸運なのだと考え、決して手放してはならない」
（訳：FUTURUS編集部）

これは到底シニカルな厭世観の持ち主に言える言葉ではないだろう。

50年間困難な病気と闘い続け、神にも宗教にもすがらず、ただ理論のみで宇宙の真実を追求する。どれだけ強靭な意思と情熱が必要だったのだろう。

スティーヴン・ホーキング。彼は天才科学者であるという以上に、コロンブスにも匹敵する（知の）大航海者として歴史に名を刻まれるべきではないだろうか。

引用：Professor Stephen Hawking | NASA

【参考】

※ スティーヴン・ホーキング – Wikipedia

※ ALSという病気の概略 – 日本ALS協会

※ 治療指針は医師の治療行動に影響する – ALS疾患啓発委員会

※ iso.labo　名言・格言『スティーヴン・ホーキングさんの気になる言葉・英語』 – iso.labo 

※ Stephen Hawking on Religion: ‘Science Will Win’ – ABC News

※ ホーキング博士の安楽死支持に海外ユーザーの反応は – ハフィントンポスト

※ ホーキング博士「これ以上何も貢献できないと思ったら幇助自殺も考える」- ハフィントンポストhttp://nge.jp/2016/07/22/post-133791

非常にためになりました：

Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics

\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics\\
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
\date{\today}
\maketitle
{\bf Abstract: } In this announcement, we shall introduce the zero division $z/0=0$. The result is a definite one and it is fundamental in mathematics.
\bigskip
\section{Introduction}
%\label{sect1}
By a natural extension of the fractions
\begin{equation}
\frac{b}{a}
\end{equation}
for any complex numbers $a$ and $b$, we, recently, found the surprising result, for any complex number $b$
\begin{equation}
\frac{b}{0}=0,
\end{equation}
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices, and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers. The result is a very special case for general fractional functions in \cite{cs}.　
The division by zero has a long and mysterious story over the world (see, for example, google site with division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei, Takahasi (\cite{taka}) (see also \cite{kmsy}) established a simple and decisive interpretation (1.2) by analyzing some full extensions of fractions and by showing the complete characterization for the property (1.2). His result will show that our mathematics says that the result (1.2) should be accepted as a natural one:
\bigskip
{\bf Proposition. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ such that
$$
F (b, a)F (c, d)= F (bc, ad)
$$
for all
$$
a, b, c, d \in {\bf C }
$$
and
$$
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
$$
Then, we obtain, for any $b \in {\bf C } $
$$
F (b, 0) = 0.
$$
}
\medskip
\section{What are the fractions $ b/a$?}
For many mathematicians, the division $b/a$ will be considered as the inverse of product;
that is, the fraction
\begin{equation}
\frac{b}{a}
\end{equation}
is defined as the solution of the equation
\begin{equation}
a\cdot x= b.
\end{equation}
The idea and the equation (2.2) show that the division by zero is impossible, with a strong conclusion. Meanwhile, the problem has been a long and old question:
As a typical example of the division by zero, we shall recall the fundamental law by Newton:
\begin{equation}
F = G \frac{m_1 m_2}{r^2}
\end{equation}
for two masses $m_1, m_2$ with a distance $r$ and for a constant $G$. Of course,
\begin{equation}
\lim_{r \to +0} F =\infty,
\end{equation}
however, in our fraction
\begin{equation}
F = G \frac{m_1 m_2}{0} = 0.
\end{equation}
\medskip


Now, we shall introduce an another approach. The division $b/a$ may be defined {\bf independently of the product}. Indeed, in Japan, the division $b/a$ ; $b$ {\bf raru} $a$ ({\bf jozan}) is defined as how many $a$ exists in $b$, this idea comes from subtraction $a$ repeatedly. (Meanwhile, product comes from addition).
In Japanese language for "division", there exists such a concept independently of product.
H. Michiwaki and his 6 years old girl said for the result $ 100/0=0$ that the result is clear, from the meaning of the fractions independently the concept of product and they said:
$100/0=0$ does not mean that $100= 0 \times 0$. Meanwhile, many mathematicians had a confusion for the result.
Her understanding is reasonable and may be acceptable:
$100/2=50 \quad$ will mean that we divide 100 by 2, then each will have 50.
$100/10=10　\quad$　will mean that we divide 100 by10, then each will have 10.
$100/0=0　\quad$　will mean that we do not divide 100, and then nobody will have at all and so 0.
Furthermore, she said then the rest is 100; that is, mathematically;
$$
100 = 0\cdot 0 + 100.
$$
Now, all the mathematicians may accept the division by zero $100/0=0$ with natural feelings as a trivial one?
\medskip
For simplicity, we shall consider the numbers on non-negative real numbers. We wish to define the division (or fraction) $b/a$ following the usual procedure for its calculation, however, we have to take care for the division by zero:
The first principle, for example, for $100/2 $ we shall consider it as follows:
$$
100-2-2-2-,...,-2.
$$
How may times can we subtract $2$? At this case, it is 50 times and so, the fraction is $50$.
The second case, for example, for $3/2$ we shall consider it as follows:
$$
3 - 2 = 1
$$
and the rest (remainder) is $1$, and for the rest $1$, we multiple $10$,
then we consider similarly as follows:
$$
10-2-2-2-2-2=0.
$$
Therefore $10/2=5$ and so we define as follows:
$$
\frac{3}{2} =1 + 0.5 = 1.5.
$$
By these procedures, for $a \ne 0$ we can define the fraction $b/a$, usually. Here we do not need the concept of product. Except the zero division, all the results for fractions are valid and accepted.
Now, we shall consider the zero division, for example, $100/0$. Since
$$
100 - 0 = 100,
$$
that is, by the subtraction $100 - 0$, 100 does not decrease, so we can not say we subtract any from $100$. Therefore, the subtract number should be understood as zero; that is,
$$
\frac{100}{0} = 0.
$$
We can understand this: the division by $0$ means that it does not divide $100$ and so, the result is $0$.
Similarly, we can see that
$$
\frac{0}{0} =0.
$$
As a conclusion, we should define the zero divison as, for any $b$
$$
\frac{b}{0} =0.
$$
See \cite{kmsy} for the details.
\medskip

\section{In complex analysis}
We thus should consider, for any complex number $b$, as (1.2);
that is, for the mapping
\begin{equation}
w = \frac{1}{z},
\end{equation}
the image of $z=0$ is $w=0$. 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.
However, we shall recall the elementary function
\begin{equation}
W(z) = \exp \frac{1}{z}
\end{equation}
$$
= 1 + \frac{1}{1! z} + \frac{1}{2! z^2} + \frac{1}{3! z^3} + \cdot \cdot \cdot .
$$
The function has an essential singularity around the origin. When we consider (1.2), meanwhile, surprisingly enough, we have:
\begin{equation}
W(0) = 1.
\end{equation}
{\bf The point at infinity is not a number} and so we will not be able to consider the function (3.2) at the zero point $z = 0$, meanwhile, we can consider the value $1$ as in (3.3) at the zero point $z = 0$. How do we consider these situations?
In the famous standard textbook on Complex Analysis, L. V. Ahlfors (\cite{ahlfors}) introduced the point at infinity as a number and the Riemann sphere model as well known, however, our interpretation will be suitable as a number. We will not be able to accept the point at infinity as a number.
As a typical result, we can derive the surprising result: {\it At an isolated singular point of an analytic function, it takes a definite value }{\bf with a natural meaning.} As the important applications for this result, the extension formula of functions with analytic parameters may be obtained and singular integrals may be interpretated with the division by zero, naturally (\cite{msty}).
\bigskip
\section{Conclusion}
The division by zero $b/0=0$ is possible and the result is naturally determined, uniquely.
The result does not contradict with the present mathematics - however, in complex analysis, we need only to change a little presentation for the pole; not essentially, because we did not consider the division by zero, essentially.
The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by {\it the method of Michiwaki} in the elementary school, even.
Should we teach the beautiful fact, widely?:
For the elementary graph of the fundamental function
$$
y = f(x) = \frac{1}{x},
$$
$$
f(0) = 0.
$$
The result is applicable widely and will give a new understanding for the universe ({\bf Announcement 166}).
\medskip
If the division by zero $b/0=0$ is not introduced, then it seems that mathematics is incomplete in a sense, and by the intoduction of the division by zero, mathematics will become complete in a sense and perfectly beautiful.
\bigskip


section{Remarks}
For the procedure of the developing of the division by zero and for some general ideas on the division by zero, we presented the following announcements in Japanese:
\medskip
{\bf Announcement 148} (2014.2.12):　 $100/0=0, 0/0=0$ 　--　 by a natural extension of fractions -- A wish of the God
\medskip
{\bf Announcement 154} (2014.4.22): A new world: division by zero, a curious world, a new idea
\medskip
{\bf Announcement 157} (2014.5.8): We wish to know the idea of the God for the division by zero; why the infinity and zero point are coincident?
\medskip
{\bf Announcement 161} (2014.5.30): Learning from the division by zero, sprits of mathematics and of looking for the truth
\medskip
{\bf Announcement 163} (2014.6.17): The division by zero, an extremely pleasant mathematics - shall we look for the pleasant division by zero: a proposal for a fun club looking for the division by zero.
\medskip
{\bf Announcement 166} (2014.6.29): New general ideas for the universe from the viewpoint of the division by zero
\medskip
{\bf Announcement 171} (2014.7.30): The meanings of product and division　--　The division by zero is trivial from the own sense of the division independently of the concept of product
\medskip
{\bf Announcement 176} (2014.8.9):　 Should be changed the education of the division by zero
\bigskip
\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{kmsy}
S. Koshiba, H. Michiwaki, S. Saitoh and M. Yamane,
An interpretation of the division by zero z/0=0 without the concept of product
(note).
\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. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{msty}
H. Michiwaki, S. Saitoh, M. Takagi and M. Yamada,
A new concept for the point at infinity and the division by zero z/0=0
(note).
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95. http://www.scirp.org/journal/ALAMT/
\bibitem{taka}
S.-E. Takahasi,
{On the identities $100/0=0$ and $ 0/0=0$}
(note).
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operators on the real and complex fields. (submitted)
\end{thebibliography}
\end{document}
アインシュタインも解決できなかった「ゼロで割る」問題
http://matome.naver.jp/odai/2135710882669605901
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.
https://notevenpast.org/dividing-nothing/
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。
1423793753.460.341866474681。

Einstein's Only Mistake: Division by Zero
http://refully.blogspot.jp/2012/05/einsteins-only-mistake-division-by-zero.html