2016年8月29日/生物谷BIOON/--根据非常知名的物理学家Lawrence Krauss在《科学美国人》杂志上的一篇帖子，它潜在地是“半个世纪内粒子物理学最为重要的发现”，“一种未预料到的新的基本粒子，比最近发现的希格斯粒子（Higgs particle）重6倍”。
只可惜，经证实，它根本就不是什么发现。使用大型强子对撞机（Large Hadron Collider, LHC）的科学家们承认它是统计噪声。
因此，物理学标准模型仍然保持完好。我坦白有些如释重负：在这个令人眼花缭乱的一年，关于我们世界的一些广泛接受的情形仍然成立。科学家们（和很多科学作家）当然对这个不是新闻的新闻感到失望。正如John Timmer在美国知名科技博客Ars Technica上观察到的那样，“对一种新粒子（自从发现希格斯粒子以来）的这种最为有希望的提示最终经证实是一场泡沫很难不让人感到失望。”
天文物理学家Ethan Siegel在Starts with a Bang（开始于大爆炸）网站上发表的令人绝望的帖子中，问道物理学家如何自我欺骗相信这种新的粒子。Siegel在统计上详细地解答他自己的问题。
但是猜测物理学家自我欺骗的原因是他们与我们一样也是人是非常容易的。他们想要相信。他们也需要相信，就像我们想要看到的那样。Siegel引用已故的伟大物理学家Richard Feinman的名言来作出结论：“不要欺骗自己，你自己正是最容易被欺骗的人。”
并不是每个人都感到失望。在“智能”设计网站Uncommon Descent上，针对“物理打开大大的裂口？”话题，Rob Sheldon引用物理学家Sabine Hossenfelder所说的物理学上的“噩梦般结局”。Sheldon补充道，“他们的理论所缺乏的就是迫使在政府资助的学校中教导它的法庭裁决，就达尔文学说那样。”
噩梦般结局是什么？Hossenfelder在她的博客BackRe（Action）上解释道，对LHC而言，“我们已进入被称作噩梦般结局的境地：希格斯粒子和没有别的粒子。很多粒子物理学家认为这是最坏的结果。这让他们缺乏指导，迷失在快速增加的模型中。没有一些新的物理发现，他们就没有什么要去研究，他们已经50年没有新的东西去研究了，而且没有新的物理发现能够告诉他们在哪个方向探究终极的统一目标和/或量子引力。”
古人类学家John Hawks关于人类进化的研究当然与“智能”设计网站的这个话题相差甚远。然而，他也赞同地引用Hossenfelder所说的话，“我希望这个最新的无效结果将传递一种明晰的信息：你不能够相信科学家们的判断，这是因为他们未来的资金资助依赖于他们持续的乐观。”
Hawks补充道，“我的反应是在人类起源上投资几十亿美元将产生比LHC更多的发现。”
在《科学美国人》杂志的Cross-Check博客上，John Horgan并没有提到LHC中的这种销声匿迹的新粒子，但是他也引用Hawks之前引用的Hossenfelder关于物理学资金资助前景方面的相同评论。Horgan发表帖子的时机是他的引起轰动效应的书籍《科学的终结（The End of Science）》发表20周年。当时，他声称研究人员已经揭示出宇宙的最为基本的事实，剩下的就是填补空白。 Horgan承认这些空白是许许多多琐碎的东西，而不是诸如大爆炸和自然选择进化论之类的基本内容。他也承认他的理论依赖于你如何定义“基本的（fundamental）”。其他的基础问题，如为何宇宙中并非无物存在，可能是无法解答的。“关于我的科学的终结理论的奇特之处在于它从未被说是正确的。它仅是说迄今为止是正确的。我认为它迄今为止是对的，而且一些科学家似乎谨慎地表示赞同。”
与此同时，遗传学：NgAgo基因编辑工具真地发挥作用吗？
与此同时，科学家们正在在实验室中填空这些空白。在2000年，Craig Venter预测破解基因组学需要这个世纪大多数时间。因此，从事遗传研究的人们开展大量的研究---和获得人们所希望的资金资助。（很可能包括，Hawks---和我们当中的许多人---如此迫切想要的关于人类起源方面的研究。）
这周，针对利用源自格氏嗜盐碱杆菌（Natronobacterium gregoryi）的被称作NgAgo的蛋白进行基因编辑的新工具的争论甚嚣尘上。今年5月，这种方法表在Nature Biotechnology期刊上，但是其他的研究人员愤怒地报道不能够重复它。
寻找除CRISPR/Cas9之外的基因编辑方法一直在进行，这是因为尽管CRISPR/Cas9得到广泛的使用，它也有不足之处。Heidi Ledford本周早些时候在Nature News上评论了一些其他的备选方法。作为NgAgo的开发者，中国河北科技大学生物科学与工程学院韩春雨（Chunyu Han）副教授声称NgAgo只切割靶基因。根据David Cyranoski针对这一争论在Nature News上发表的帖子，CRISPR/Cas9有时会在错误的基因上进行基因编辑。
Cyranoski报道尽管韩春雨副教授仍然坚信他的NgAgo发现是正确的，但是他每天收到几十次不堪其扰的电话和短信。NgAgo令人失望的表现也在推特（Twitter）和Google网上论坛上引发风暴。
我认为NgAgo看起来并不好。这是因为发表这篇论文的Nature Biotechnology期刊已发起一项调查。
干细胞研究员Paul Knoepfler在他的博客The Niche上从一开始就在追踪NgAgo。他观察到，“关于NgAgo的情形，有希望很快就会变得更加清楚。一些人将NgAgo与STAP相提并论，但是我认为就目前而言，下这样的结论仍然为时过早。”
你可能回想起，STAP（stimulus-triggered acquisition of pluripotency, 刺激触发的多能性获得）是2014～2015最大的论文撤回新闻，涉及一名日本研究员在两篇Nature论文（已撤回）中声称通过让已分化的小鼠细胞遭受应激而制造出多能性干细胞。这名日本研究员随后被剥夺她的博士学位。去年二月，Shannon Palus在《撤稿观察（Retraction Watch）》中对STAP来龙去脉进行了总结。（生物谷 Bioon.com）http://mt.sohu.com/20160829/n466505791.shtml
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
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\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}
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}
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。
1423793753.460.341866474681。
Einstein's Only Mistake: Division by Zero
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