札幌市中央区南3条西8丁目八光ビル１Ｆ

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     AM 11:00～PM 8:00    定休日　木曜日　　第3週水曜日

 

 

        

　　　　　

 

 

 

　駐車場のご案内　　　　8丁目近辺のタイムズ（やわらぎ斎場さん、タイムズ駐車場除く）

　　　　　　　　　　　　　　　 詳しくは、スタッフまでお問合せください

 

　　　　　　　　　　　　　　　　狸小路8丁目　アップルパーク　

　　　　　　　　　　　　　　　　比較的すいていて、止めやすいです。

 

 

 

 

 

 

 

 

宇宙はなぜ、どのように生まれたのか。ホーキング氏はこの根源的な問いに挑み、重力や時空に関する一般相対性理論や極微の世界で起きる現象を説明する量子力学を駆使して、アインシュタイン以後の宇宙論の発展に大きく貢献した。

宇宙には大きさがゼロで密度が無限大の「特異点」が存在するという特異点定理を１９６０年代に発表。相対論では説明できず、量子力学と合わせて理解する必要性を示し衝撃を与えた。これが宇宙の始まりやブラックホールの仕組みの解明につながると主張した。

７４年には「ホーキング放射」と呼ばれる理論を提唱。ブラックホールは非常に強い重力を持ち、あらゆる物をのみ込むと考えられているが、周囲にのみ込む物がない状態では、逆にエネルギーを放出して蒸発するという仮説だ。

名古屋大の杉山直教授は「いずれも常識を超える理論で宇宙の根本に迫るだけに検証が難しいが、間違いなくノーベル賞に匹敵する仕事をした」と話す。

米航空宇宙局（ＮＡＳＡ）はツイッターで「数々の理論は膨大な可能性への扉を開いてくれた。われわれ、そして世界はその可能性を探検し続けていく」と悼んだ。

 

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

2017年11月15日(水)
テーマ：

The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.

Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.

It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.

Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.

It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).

Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.

Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.

 

 I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.

 

 

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインド�
��初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

An Early Reference to Division by Zero C. B. Boyer

 

OUR HUMANITY AND DIVISION BY ZERO

Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/

 

5000年？？？？？

2017年09月01日(金)NEW ! 
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0
0 ¼ 0 ) 0
1=1 ¼ 0 ) 0
1 ¼ 0
1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0
0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T

とても興味深く読みました：

 

 

10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s goi
ng to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.

Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…

Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.

RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?

PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.

RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.

PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.

RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?

PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.

RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.

PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.

RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?

PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.

 

再生核研究所声明 424(2018.3.29): 　レオナルド・ダ・ヴィンチとゼロ除算

次のダ・ヴィンチの言葉を発見して、驚かされた：

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

我々の周りにある偉大なことの中でも、無の存在が最も素晴らしい。その基本は時間的には過去と未来の間にあり、現在の何ものをも所有しないというところにある。この無は、全体に等しい部分、部分に等しい全体を持つ。分割できないものと割り切ることができるし、割っても掛けても、足しても引いても、同じ量になるのだ。

レオナルド・ダ・ヴィンチ。ルネッサンス期を代表する芸術家、画家、彫刻家、建築技師、設計士、兵器開発者、科学者、哲学者、解剖学者、動物学者、ファッションデザイナーその他広い分野で活躍し「万能の人（uomo universale：ウォモ・ウニヴェルサーレ）」と称えられる人物

そもそも西欧諸国が、アリストテレス以来、無や真空、ゼロを嫌い、ゼロの西欧諸国への導入は相当に遅れ、西欧へのアラビヤ数字の導入は　レオナルド・フィボナッチ（1179年頃～1250年頃
）によるとされているから、その遅れの大きさに驚かされる：

フィボナッチはイタリアのピサの数学者です。正確には「レオナルド・フィリオ・ボナッチ」といいますが、これがなまって「フィボナッチ」と呼ばれるようになったとされています。
彼は少年時代に父親について現在のアルジェリアに渡り、そこでアラビア数字を学びました。当時の神聖ローマ皇帝・フリードリヒ2世は科学と数学を重んじていて、フィボナッチは宮殿に呼ばれ皇帝にも謁見しました。後にはピサ共和国から表彰もされました。

ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大きな数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（

historicalmathematicians.blogspot.com/2012/03/blog-post.html　　02/03/2012 -）

ゼロや無に対する恐怖心、嫌疑観は現在でも欧米諸国の自然な心情と考えられる。ところが上記ダ・ヴィンチの言葉は　如何であろう。無について好ましいものとして真正面から捉えていることが分かる。ゼロ除算の研究をここ４年間して来て、驚嘆すべきこととして驚かされた。ゼロの意味、ゼロ除算の心を知っていたかのような言明である。

まず、上記で、無を、時間的に未来と過去の間に存在すると言っているので、無とはゼロのことであると解釈できる。ゼロとの捉え方は四則演算を考えているので、その解釈の適切性を述べている。足しても引いても変わらない。これはゼロの本質ではないか。さらに、凄いこと、掛けても割っても、ゼロと言っていると解釈でき、それはゼロ除算の最近の発見を意味している:  0/1 =1/0=0。－　ゼロ除算を感覚的に捉えていたと解釈できる。ところが更に、凄いことを述べている。

この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：

{\bf Fruitful world}\index{fruitful world}

\medskip

 

For example, in very and very general partial differential equations, if the coefficients or terms are zero, we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we see the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall \index{Yamane phenomena}Yamane phenomena, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.

\medskip

 

{\bf From $0$ to $0$; $0$ means all and all are $0$}

\medskip

 

As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.

\medskip

 

その意味は深い。我々はゼロの意味をいろいろと捉え考え、ゼロとはさらに　基準を表すとか、不可能性を示すとか、無限遠点の反映であるとか、ゼロの2重性とかを述べている。ゼロと無限の関係をも述べている。ダ・ヴィンチの鋭い世界観に対する境地に驚嘆している。

以　上

 

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. 
 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. 

 

 ハルマゲドンへのカウントダウン

Countdown to Armageddon

我々の世界的な金融システムが劇的に変化しており、現金は急速に過去のものになってきています。私達はデジタルの世界に住んでいるし、各国政府や大手銀行は、紙幣や硬貨の両方から離れての移行を奨励しています。しかし、キャッシュレス現金無しの社会は私達の将来の為に何を意味するのでしょうか？このようなシステムへの危険性はありますか？

Our worldwide financial system is changing dramatically, and cash is rapidly becoming a thing of the past. We live in a digital world, and national governments and big banks are both encouraging the move away from paper currency and coins. But what would a cashless society mean for our future? Are there any dangers to such a system?

New technology for a cashless society is marching right in step with other moves toward the coming Antichrist world government. We often hear about the “New World Order” and “Global Governance”?buzzwords that are helping to prepare the world for a new international financial and political system, a society controlled by networked computers containing a database of information on nearly everyone?as Revelation chapter 13 appears to have predicted nearly 2,000 years ago!

キャッシュレス現金無しの社会の新技術は、今ちょうど来るべき反キリストの世界政府に向かって他の動きと調和［一致］して進行しています。

私達はしばしば、新しい国際金融と政治システムの世界を準備する為に支援している「新世界秩序」と「グローバル・ガバナンス統治,管理」の専門用語,宣伝文句の、ほぼ全員に関する情報のデータベースを含むネットワークに接続されたコンピューターによってコントロールされる社会について聞いています。

黙示録 第13章は、それについてほぼ2000年前に、はっきりと予告しています！

I wrote the above two paragraphs about twelve years ago for a Magazine & by keeping in tune with the signs of the times you can see how this message is continuing to develop and accelerate on a worldwide scale.

あなたがこのメッセージを理解し進展させ,全世界規模で加速し続けているのを確認する事ができ、時の徴シルシとかみ合うように、私は約12年前に上記の二つの段落を雑誌の為に書きました。

Each day that we move a day closer to the beginning of ‘the new’ system, we see more stories from both the alternative media and the mainstream media that show we’re rapidly entering a day and age of people being microchipped ‘en masse’.

私達は「新しい」システムの初めに日々近づく毎日を送り、（既成の社会的基準に基づかず）新しい、型にはまらないメディアと、急速に（未来における一定の）時代に入っていく主流メディアの両方からのより多くの記事,報告を見ていて、この時代の人々は「一括に,ひとまとめに」されマイクロチップ化されています。

Nearly 10 years ago, reporter Brian Williams and NBC news did a story about what the year 2017 would look like. Predicting that most to all human beings would have a microchip with which they could be positively identified by 2017, and we see NBC’s ‘prediction’ getting closer each day that we move closer to the death of the old system, that could be brought about with the coming economic collapse that we have long been warned of. We’re also seeing more signs we’re getting closer to that moment every day.?

10年近く前(その時点で)、記者ブライアン・ウィリアムズとNBCニュースは、2017年はどのように見えるかについて話をしました。全ての人間のほとんどは、2017年までに識別する事ができるマイクロチップを持っているだろうと積極的に(その時点で)予測し、そして我々は、NBCの「予測」は、我々が近づくに連れて持たらされる可能性があり、古いシステムの死からの移行が毎日近づいているのを見ています。

私達が長い間 警告されてた来たるべき経済の崩壊です。我々はまた、毎日その瞬間に近づいているより多くの※●兆候を見ています。

※●【兆候・徴候】ちょうこう

物事が起こる前ぶれ。きざし。

Of course, we can’t predict with 100% accuracy that by 2017, this chip implant technology will be in place worldwide for most or all people. But one thing is certain a cashless society is coming sometime in the future with a microchip or some sort of electronic tattoo in the right hand or forehead to buy & sell. Some economists suggest sometime between 2017 to 2030 we may see this new economic micro chipping system in place & mandatory?

Note ※● In 2017, 500 thousand people in the United States are implant microchips!

もちろん、我々は2017年までに、このチップのインプラント〔体の組織などに〕挿入,埋め込む技術は、世界中のほとんどまたは全ての人の為の適した当を得た事を100％の精度で予測する事はできません。

注●※2017年では、アメリカで約50万人がマイクロチップを埋め込んでいるそうです！

As in 2017 it is said that 500,000 people are embedding microchips in the USA.

しかし、一つのことは、キャッシュレス現金無しの社会が●購入と●売却する為のマイクロチップを●額かまたは●右手の電子タトゥー入れ墨のようなものが、将来的にいつか来る事は確実です。

一部のエコノミストは、我々は〈法律・政策などが〉機能を果たしている場合、強制的なこの新しい経済マイクロチッピング･システムを見る事ができるであろうと、●2017年から2030年の間のいつかを示唆しています。

As we move into 2016, all over the world, we are seeing a relentless march toward a cashless society, and nowhere is this truer?than in northern Europe.

2016年になると(その時点で)、私達はヨーロッパ北部よりも、世界中どこでもキャッシュレス現金無しの社会への絶え間のない行進を見るようになる事は、真実で（より現実的）です。

In Sweden, hundreds of bank branches no longer accept or dispense cash, and thousands of ATM machines have been permanently removed. At this point, bills and coins only account for just 2 percent of the Swedish economy, and many stores no longer take cash at all.

スウェーデンでは、銀行の支店の数百店は現金をもはや受け入れないか、または現金を供給しないし、ATM機を何千台も永久に廃止しました。この時点で、紙幣、硬貨はスウェーデン経済のわずか2％を占めていて、多くの店は、もはや全ての現金を取り扱いません。

The notion of a truly “cashless society” was once considered to be science
fiction, but now we are being told that it is “inevitable”, and authorities insist that it will enable them to thwart criminals, terrorists, drug runners, money launderers and tax evaders.

真に「キャッシュレス現金無しの社会」の概念は、一度は SFサイエンス・フィクションであると考えられたが、今我々はそれが「避けられない」事であると言われており、当局はそれが犯罪者、テロリスト、麻薬密輸業者、マネー ロンダリングと脱税者を阻止するのを可能にする事を主張します。

Cash transactions of more than 2,500 euros have already been banned in Spain, and France and Italy have both banned all cash transactions of more than 1,000 euros.

2500ユーロ以上の現金取引は、すでにスペインで禁止されており、フランスとイタリアの両方は1000ユーロ以上の全ての現金取引を禁止しています。

Little by little, cash is being eradicated.

少しずつ、現金が根絶されています。

Most of us just seem to accept that this change is “inevitable”, and we are being assured that it will be for the better.

私達のほとんどは、ちょうどこの変更は「不可避」である事を受け入れているようで、そして我々にはそれが良い方向になる事が保証されています。

Starting in 2016 is a year in which Australia will accelerate towards becoming a genuine cashless society.

2016年が開始すると、オーストラリアは本物のキャッシュレス現金無しの社会になる方向に向かって加速する年になります。(過去形)

The cashless society will be a new world free of $1 and $2 coins, or $5 or $10 bank notes.

キャッシュレス現金無しの社会は 無料の1ドルと 2ドルコイン、 または 5ドルまたは 10ドル紙幣の新しい世界になります。

A new world in which all commercial transactions, from buying an i-pad or a hamburger to, purchasing a newspaper, paying household bills or picking up the dry-cleaning, will be paid for electronically.

全ての商取引内の新しい世界は、新聞の購入、i-padやハンバーガーの購入、家庭の請求書の支払い、ドライクリーニングを取りに行ってから、電子的に支払われます。

It’s been reported that Australia will likely be “a fully cashless society” by 2022.

オーストラリアはおそらく●2022年までに「完全なキャッシュレス現金無しの社会」になる事が報告されています。

?In 2015, banks in India made major progress on this front, and income tax rebates are being considered by the government as an incentive “to encourage people to move away from cash transactions”.

2015年に(その時点で)インドの銀行は、この前面的に大きな進歩を遂げて、所得税の還付は、政府が「現金取引から離れて移行する人々を奨励する」 奨励策,奨励金制度として検討されています。

In the America the debate is on to eliminate the $100 bills. Stating it’s all about taxes & not crime or terrorism.

アメリカでの議論は、100ドル紙幣を排除する事にあります。それは税金に関するものであり、犯罪やテロリズムに関するものではありません。

One of the main problems is that the $100 bill circulates predominantly?outside the USA. They will take a step closer to eliminating the dollar as the reserve currency, and eventually we will end up with a new one-world currency as early as 2018 but probably by 2020?

主な問題の1つは100ドル紙幣が米国の外側,外部で（力・数・影響力などの点で）より優位を占め,顕著であり,圧倒的に多く循環している事です。彼らは近い将来に準備通貨としてのドルを排除するステップ段階を取るだろうし、最終的に我々は、早ければ2018年というよりは、おそらく2020年までに新たな統一世界通貨〔の状態に〕なるでしょうか？

Americans, developing countries, and even Germany and Japan have less trust in their government, and will likely put up a fight against attempt to disarm cash.

アメリカ人、発展途上国、さらにはドイツと●日本は自国政府にあまり信頼を持っていないし、おそらく現金を解除,［制限, 撤廃］しようとする試みと戦います。

However, this new cashless financial system will probably come in through wars, civil disorders, and fears of such things as terrorism and epidemics of new, incurable diseases. All these happenings will make people desperate for change. Eventually they will be ready to toss out the old and embrace the new. It’s already happened in a big way in the area of technology, and is now happening with commerce.

しかし、この新しいキャッシュレス現金無しの金融システムは、おそらく戦争、市民の（政治的）無秩序, 不穏,騒動, 暴動、テロ、と新しい難病の伝染病のようなものの恐怖を通ってやって来ます。

これら全ての出来事は、人々を変革の為に必死にさせます。結局、彼らは古いものを放り出すと、新しい事を受け入れるようになります。それは既に技術の分野で大々的に起こっていて、そして今（大規模な）通商,貿易で起こっています。

Those who want to be a part of his new economy and society will be eventually compelled to receive the “mark of the Beast” in their right hand or forehead?probably in the form of a tiny computerized chip bearing all their personal, financial, and medical information. Big Brother and the New World Order will thereby be able to monitor everyone’s every move.

彼の新しい経済・社会の一部になりたい人は、最終的に自分の●右手または●額に「●獣の刻印」を受けるように強要され、おそらく全ての彼らの個人的、金融、および医療情報を含んだ小さなコンピュータ化されたチップの形でなされるでしょう。●ビッグブラザー 全体主義国家, 独裁政権, 独裁者と新世界秩序は、それによって誰でもの全ての行動をモニターする事ができるようになります。

Without “cash”, the public will be at the mercy of those pushing and pulling the levers. If someone had “control” over the availability to your money through a cashless society, they have control over your food and ultimately you and your family!

「現金」がなければ、国民はレバーを押し引きされ、彼らのなすがままになります。誰かがキャッシュレス現金無しの社会を通して、あなたのお金の「コントロール」（入手の）可能性,利用できる有効［有用］性を持っていた場合、彼らはあなたの食べ物と、最終的にあなたとあなたの家族を管理しています！

?For the first time, the hi-tech means of fulfilling the chilling vision the apostle John received nearly 2000 years ago is in the making!

使徒ヨハネが、ほぼ2000年前に受けた、ぞっとする幻ビジョン（預言）の成就である、初めてのハイテク手段は発達［進行］中の状態で用意されています！

If Earth Were a Novel, Would the Historical Sciences Be Reliable Narrators?

Historical methods are crucial in arriving at the proper results in the historical sciences, which include geology, evolutionary biology, cosmology and anthropology.

The idea is that geology or even cosmology is imprecise because it deals with incompleteness, poor data resolution and lack of experimental control. Credit: skeeze/pixabay

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20 HOURS AGO

 

Stephen Jay Gould (1941-2002), the American palaeontologist and writer, delivered a memorable extemporaneous speech upon receiving the ‘History of Geology Division’ award during the 100th Annual Meeting of the Geological Society of America (GSA), Denver, 1988. A copy of its transcription had been sitting quietly among some paper clippings in my possession, having followed me around all these years, and I recently rediscovered it by accident.

While rereading his long-forgotten speech, which touches upon the importance of the history of science and the social context in the creation of ideas in academe, I was struck by some of his statements. At one point, he says, “We know that science is inevitably socially embedded, that social context could actually aid the growth of natural knowledge, can be illuminating. Darwin’s mature theory of natural selection really is laissez-faire economics translated into nature, where it works better than it does in economics.” Through this example, Gould emphasises the point that social context aids in the growth of science.

He further says that the methods of history are more appropriate in geology than elsewhere: “We are charged as geologists with explaining what happens after it happens, not before it occurs. The inordinately complex and unique geological events that occur but once, such as the extinction of dinosaurs, are not the material of the conventional, stereotypical history of science. You are dealing with complex contingency of events that happened once.” In other words, the stereotypical science deals with prediction, wherein experimental methods rule the roost and the Popperian diktat of falsifiability by repetition is the primary criterion of success. This is very different from the pluralist way of approximating the truth in the historical sciences.

The belief that scientific knowledge is obtained by breaking it down into its simplest parts originated possibly with René Descartes, elevated to the status of a creed in later years by Karl Popper. Conversely, the idea is that geology or even cosmology is imprecise because it deals with incompleteness, poor data resolution and lack of experimental control. It was Thomas Kuhn who shook the foundations of the analytical philosophy of science, questioning the assumption that knowledge cannot be value-free. Robert Frodeman, however, defines the research pathways followed in geology as hermeneutic, i.e. based on the theory of interpretation. This is a method followed when apparent truths have to be deciphered from a given text. Here, objectivity is slightly compromised because the reader also brings in her presuppositions and expectations.

In the same vein, a geologist is trying to read the history of Earth like she would a text from various outcrops by giving categorising clues as significant and insignificant. The observer’s presuppositions in fact influence the outcome of the observation, somewhat comparable to the paradox that exists in quantum mechanics: wherein observation itself changes what is being observed. Erwin Schrödinger labours on just this point in his book What is Life? (1944). As long as this mysterious boundary exists between the object and the subject, Schrödinger wonders whether we will ever be able to get a “complete, gapless description of physical objects” and sighs along with Immanuel Kant that “never to know anything at all about thing-in-itself”.

However, this does not mean that the accounts of science are not purely subjective, just that the “truths of science, as with most things, fall somewhere in the middle.”

What Gould says, however, is that the historical methods are crucial in arriving at the proper results in the historical sciences such as geology, evolutionary biology, cosmology and anthropology. In the course of his speech at the GSA annual meeting, he moves over to his favourite topic: viewing the story of the universe as a never-ending sequence of contingencies and the string of what-ifs that they prompt. An interesting parallel can be seen in the philosophy of Kuhn. He introduced the idea that science does not progress through the linear accumulation of knowledge but through intermittent succession of stasis and revolution – a.k.a. paradigm shifts. Gould’s theory of contingency, or what may be called punctuated equilibrium, in evolutionary mechanics closely resembles these paradigm shifts as expounded by Kuhn.

Contingency is used as a creative tool in the hands of novelists like Leo Tolstoy. More recently, Kurt Vonnegut used contingency and the evolutionary theme in his novel Galápagos (1985). It is a story of a group of people marooned on the imaginary island of Santa Rosalina, within the Galápagos archipelago. The world is in the throes of a financial meltdown, followed shortly after by a disease outbreak that made the humans infertile (à la AIDS), leaving the Santa Rosalina people the only humans in the world capable of reproduction.

After several million years, they have evolved into a physical form resembling a furry seal with a snout and flipper like hands and able to walk upright. The narrator blames the unusual size of the human brain as the source of all problems of humanity. In Vonnegut’s novel, it is natural selection that ultimately finds a way to develop a narrow, pointed head for the descendants of Santa Rosalina suited for swimming, by reducing the size of the brain and making them less intelligent.

Few would have known if Gould read Galápagos before he developed the idea of contingency in his scientific writings, which subsequently appear in his famous book Wonderful Life (1989). He had admitted his debt to the Hollywood film It’s a Wonderful Life (1946). In the last part of his book, Gould writes, “… we are an improbable and fragile entity, fortunately successful after precarious beginnings as a small population in Africa, not the predictable end result of a global tendency. We are a thing, an item of history, not an embodiment of general principles.”

This is why he says the Pikaia is an icon. The Pikaia was a small annelid-like worm, the world’s first known soft-body fossil chordate from the Burgess shale, a 500-million-year-old oceanic deposit in Canada containing numerous weird fossilised soft-bodied marine organisms. The worm was from the Cambrian age and probably a predecessor of fish and an ancestor of vertebrates. Now, play the tape of life again, as the guardian angel does in It’s a Wonderful Life and imagine if the Pikaia had not survived the Cambrian decimation. This time, the contingency requires that we humans do not appear in history, as well as creatures ranging from the shark to the orang utan.

What single natural law can predict the Pikaia’s chances of survival through the evolutionary net? What law can describe the eventual emergence of man on the African Pleistocene steppes after billions of years? Gould does not say that this is a random event to be explained away by historical antecedents. Like in physics, we see the primacy of initial conditions: change one of them and you get a
different result. What is more important is how long-term behaviour is sensitive on the values of the initial conditions, resulting in the generation of an evolving variable called the strange attractor.

Does it mean that past experience can always be counted on to predict the future? For example, in 2018, the pace of anthropogenic activities and the rate at which they impact the global climate has no antecedence. We also presume that the scale of human activities is unprecedented in Earth’s history and therefore that we have no clues in the rock archives to predict what will happen next. The lack of historical precedence makes Gould’s contingencies relevant here.

In 2002, John Harte  several questions that have no answers in the chapters of nature’s textbook. They included ‘how will climate warming alter life’, ‘what is the role of biodiversity in maintaining essential Earth system processes’ and how do we reach the goal of a sustainable future’. Harte’s view is that many of the models in Earth system science are extremely complex with many adjustable parameters, making them unfalsifiable. But falsifiability, according to Popper, is an inherent component of research that helps test any scientific hypothesis.

To tide over this difficulty, some advocate a unification of methodologies, of the natural sciences and the physical sciences. Such studies, by default, incorporate a methodological pluralism, a best of both worlds. Indeed, newer scientific questions posed by Earth system processes demand a paradigm shift towards the integration of both approaches.

 is a professor of geodynamics at the Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru.

 

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

\documentclass[12pt]{article}

\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}

\numberwithin{equation}{section}

\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.

&nbsp
;

 

 

 

 

 

\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) .

 

 

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

 

 

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

 

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

 

2018年05月28日(月)
テーマ：

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

 

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

       &nbs
p;