1
/
5

# Zero-ing down on Brahmagupta

### Zero-ing down on Brahmagupta

The Tribune-20 時間前

Zero-ing down on Brahmagupta. Manya Oswal's two-minute documentary on the Indian mathematician, who discovered zero, wins her an international award. Posted: Jul ...

https://www.tribuneindia.com/news/lifestyle/zero-ing-down-on-brahmagupta-107480

アメリカの一部では、マスクをすることが、コロナウイルス事件が起きても、反対だという。　中々銃を手放せない　事情とも　通じているという。　これらは、伝統、思い込み、習慣を変えるのに、　合理的に、理性的に、論理的に　それらでは　中々変えられない　人間の　姿が見える。そこで、ゼロ除算に対する理解の遅れも、その様な　背景があるのではないかと感じられた。

Fundamental of Mathematics; Division by Zero Calculus and a New Axiom
２０２０．６．３０．２０：１６

ところで、本論であるが、伝統、思い込み、習慣を変える困難性であるが、宗教、教育、生い立ち、環境の影響で　人間が甚大な影響を受けている事実が　深く感じられる。　これらは人間が、人間の心が　そのように環境、教育で形作られると簡潔に表現できるだろう。　すなわち、人間とは作られたものであるが、成長過程で環境によって成長している姿を　人間の本質的な姿として　捉えることができる。
その様な観点では、理性的な発想、われ思うゆえに我あり　などの論理的な思考は視野や世界を広げ、予断、偏見、独断、視野の狭さ　などからの解放に大きく寄与すると考えられる。　環境、教育で大きな影響を受けてしまえば、本質的に　人間は動物の存在のようになり、あるいはロボットのような存在になり、自由にして責任ある　人間としての在りようを危うくするだろう。　単に時代の流れに　環境に流されて行った者では　上手く行っても人間の尊厳が　感じられないのではないだろうか。

Fundamental of Mathematics; Division by Zero Calculus and a New Axiom

以　上

World Congress of Education 2021 (WCE-2021)

Time: May 19-21, 2021

Place: Osaka, Japan

Dear Related Persons to EDUCATION and DIVISION BY ZERO:

The 4th World Congress of Education (WCE-2021) will be held on May 19-21, 2021, in Osaka, Japan. At this moment I was requested to have some session on the division by zero and to make a presentation as Speaker/Chair in Stream 6: University Campus-High Education Forum.

The World Congress of Education 2021 (WCE-2021) is intended to provide professional platform for educators who are seeking and exploring effective educational method and approaches, the global education trend, societal and technological influences on education, curriculum strategies to share exchange and learn. WCE-2021 will invite world-known educators, presidents of well-known universities and licensed agencies etc. to share ideas, successful stories, and guidance. Participants of WCE-2021 will also be exposed to experts in the education industry showing their latest skills in the application of modern technology while accomplishing educational purpose.

The three-day conference comprises 15+ professional programs including Strong National Education Leadership Summit, High Education Forum, Media Programs, Preschool Education Forum, Posters and Cultural Social Activities etc.

If you are interested in attending this event, please send your speech title, simple CV and talk abstract to me firstly.

https://www.bitcongress.com/wce2021-Japan

Please kindly forward this announcement to persons who are interested in.

Of course, all the decisions are under the organizing committe of the conference.

With best regards,

Sincerely yours,

Saburou Saitoh

saburou.saitoh@gmail.com,

2020.7.2.18:40

SANX-I microcomputer: DIVISION BY ZERO

SANX-I microcomputer: DIVISION BY ZERO

Division by Zero at MagickCore/layer.c:1616 #1629

1 / 9 = 0.1 111111111111111111111... 12 / 99 = 0.12 121212121212121212... 1234 / 9999 = 0.1234 123412341234... 123456 / 999999 = 0.123456 123456... finally, a proof for division by zero: ∴ 0 / 9 = 0.00000000

Division by Zero at MagickCore/layer.c:1616 #1629

https://github.com/ImageMagick/ImageMagick/issues/1629

Penn’s sidekick Teller has an even better ratio though (as long as you allow division by zero).

とても興味深く読みました：

ゼロ除算警察だ!

ゼロ除算警察だ!2020年07月02日(木)NEW !
テーマ：数学

ゆるます！　ざせつしない微分積分 - 170 ページ - Google ブック検索結果

【115】青柳 碧人『浜村渚の計算ノート』

http://jinsblog.hatenablog.com/entry/2017/06/18/085026

C++ - Divide by 0

1992年10月31日　ガリレオの死から350年目。

1992年10月31日　ガリレオの死から350年目。

## これらは、伝統、思い込み、習慣を変えるのに、　合理的に、理性的に、論理的に　それらでは　中々変えられない　人間の　姿が見える。

カテゴリ：カテゴリ未分類アメリカの一部では、マスクをすることが、コロナウイルス事件が起きても、反対だという。　中々銃を手放せない　事情とも　通じているという。　これらは、伝統、思い込み、習慣を変えるのに、　合理的に、理性的に、論理的に　それらでは　中々変えられない　人間の　姿が見える。そこで、ゼロ除算に対する理解の遅れも、その様な　背景があるのではないかと感じられた。

Fundamental of Mathematics; Division by Zero Calculus and a New Axiom
２０２０．６．３０．２０：１６

アリスタルコス: Αρίσταρχος, : Aristarchus、紀元前310年 - 紀元前230年頃）は古代ギリシャの天文学者、数学者。ギリシャのサモス島に生まれた。同名の人物と区別するために、サモスのアリスタルコス: Αρίσταρχος ὁ Σάμιος, : Aristarchus Samius, : Aristarchus of Samos）と呼ばれることも多い。

アメリカの一部では、マスクをすることが、コロナウイルス事件が起きても、反対だという。　中々銃を手放せない　事情とも　通じているという。　これらは、伝統、思い込み、習慣を変えるのに、　合理的に、理性的に、論理的に　それらでは　中々変えられない　人間の　姿が見える。そこで、ゼロ除算に対する理解の遅れも、その様な　背景があるのではないかと感じられた。 何しろ、２０００年以上の世界観を変える事件だからである。

アメリカ国民の4割が進化論を否定!?…政治をも動かす「宗教の力」

https://news.yahoo.co.jp/articles/64873935ee92b70ae9134c524d4c9bdb54eabb17

2015/09/25 - 地球丸い“ことを始めて知った日本人は誰で、そしてそれはいつのことだったのか？ ... 地球球体説＋地動説」に対し、「地球方形説＋天動説」を持ち出して見事に？論破し ... もう少し遡るとこんなエピソードがあって、織田信長（1534-1582年）

https://nagoya301.at.webry.info/201509/article_5.html

アメリカ「銃社会」の起源と現在 〜だから一筋縄では規制できない
どれほど悲劇を繰り返しても…

https://gendai.ismedia.jp/articles/-/49557

マスク戦争勃発？なぜアメリカ人はマスクを嫌がるのか
https://www.jiji.com/jc/v4?id=usashimura200680001

Timeline of scientific discoveries

Timeline of scientific discoveries：The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. For the purposes of this article, we do not regard mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify (as otherwise no scientific discovery before the late 19th century would count). We begin our timeline at the Bronze Age, as it is difficult to estimate the timeline before this point, such as of the discovery of counting, natural numbers and arithmetic.

To avoid overlap with Timeline of historic inventions, we do not list examples of documentation for manufactured substances and devices unless they reveal a more fundamental leap in the theoretical ideas in a field.

## Bronze Age

Many early innovations of the Bronze Age were requirements resulting from the increase in trade, and this also applies to the scientific advances of this period. For context, the major civilizations of this period are Egypt, Mesopotamia, and the Indus Valley, with Greece rising in importance towards the end of the third millennium BC. It is to be noted that the Indus Valley script remains undeciphered and there are very little surviving fragments of its writing, thus any inference about scientific discoveries in the region must be made based only on archaeological digs.

### Mathematics

Numbers, measurement and arithmetic

• Around 3000 BC: Units of measurement are developed in the major Bronze Age civilisations:

https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries

The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. For the purposes of this article, we do not regard mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify (as otherwise no scientific discovery before the late 19th century would count). We begin our timeline at the Bronze Age, as it is difficult to estimate the timeline before this point, such as of the discovery of counting, natural numbers and arithmetic.

To avoid overlap with Timeline of historic inventions, we do not list examples of documentation for manufactured substances and devices unless they reveal a more fundamental leap in the theoretical ideas in a field.

## Bronze Age

Many early innovations of the Bronze Age were requirements resulting from the increase in trade, and this also applies to the scientific advances of this period. For context, the major civilizations of this period are Egypt, Mesopotamia, and the Indus Valley, with Greece rising in importance towards the end of the third millennium BC. It is to be noted that the Indus Valley script remains undeciphered and there are very little surviving fragments of its writing, thus any inference about scientific discoveries in the region must be made based only on archaeological digs.

### Mathematics

Numbers, measurement and arithmetic

• Around 3000 BC: Units of measurement are developed in the major Bronze Age civilisations:

https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries

THE FIVE GREATEST SCIENTIFIC DISCOVERIES AND INVENTIONS EVER!

https://www.pararecruit.com/five-greatest-scientific-discoveries-inventions-ever/

0除算の可能性が大ではないでしょうか：

Even if you accept his idiotic premise, this is a stupid argument. If high UI kept labor supply low, wages would rise, and jobs would be filled. But in Moore's economic models, "higher wages" solutions aren't recognized. It's division by zero, it does not compute.

Division by zero not allowed.

You know? Division by 0 or divide to 0. #Mathematics

アインシュタインの 生涯の課題であった とされている：Blackholes are where God divided by zero.I don't believe in mathematics.

"Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related. But no value would work for x because 0 times any number is 0. So division by zero doesn't work."

Although I think since this argument isn't resolving to an actually true statement,interpretation space is vast (you can do anything to an equation if you hide a division by zero well enough)

## 日本人の数学上の発見、下記は当然ですが、

やがて　ゼロ除算、ゼロ除算算法の発見は　相当な位置を占めるは、歴然ですね。

1683年、関孝和は、終結式に基づく消去理論英語版）「解伏題之法」を考え出した[233]。終結式を表現するため、行列式を考案した[233]

1683年、関孝和終結式に基づく消去理論英語版）「解伏題之法」を考え出した[233]。終結式を表現するため、行列式を考案した[233]

ベルヌーイ数

ソディの6球連鎖

ヨシザワ・ランドレット・システム

ヨシザワ・ランドレット・システムとは、折り紙のモデルに使用される図解システムである。1954年に吉澤章によって最初に開発された。その後、サミュエル・ランドレットとロバート・ハービンによって改良された[240]

20世紀を通じて伊藤清によって開発された伊藤の確率解析英語版）は、ブラウン運動ウィーナー過程）のような確率過程微積分を拡張したものである。その基本概念は伊藤積分であり、最も重要な成果の一つは伊藤の補題と呼ばれる変数の変化式である。伊藤の確率解析は様々な分野で広く応用されているが、おそらく数理ファイナンスの分野での利用で最もよく知られている[241]

ミウラ折り

ミウラ折りは、1970年に東京大学宇宙航空研究所（現・宇宙航空研究開発機構宇宙科学研究所）の三浦公亮（現・東京大学名誉教授）が考案した折り畳み方である。

https://ja.wikipedia.org/wiki/%E6%97%A5%E6%9C%AC%E3%81%AE%E7%99%BA%E6%98%8E%E3%83%BB%E7%99%BA%E8%A6%8B%E3%81%AE%E4%B8%80%E8%A6%A7

Yeah, didn’t want to change it to anything. It’s a division by zero error.

Yeah, didn’t want to change it to anything. It’s a division by zero error.

Nice! That's something I've thought about a bunch of times as well (especially with regard to division by zero, no surprise there). Would this fit along those lines?

### From Aryabhateeya to the Kerala school of mathematics

The New Indian Express-13 時間前

His contemporary Brahmagupta was a brilliant mathematician-astronomer who composed Braahmasphutasiddhaanta in 628 CE. It has many path-breaking results in algebra, geometry and trigonometry, apart from astronomy.

https://www.newindianexpress.com/opinions/2020/jun/27/from-aryabhateeya-to-the-kerala-school-of-mathematics-2161999.html

ゼロ除算：ゼロで割る：0除算

Division by zero

Divide by Zero/ dividing by zero/কোনো সংখ‍্যাকে কেন শূন‍্য দিয়ে ভাগ করা যায় না? what is division

Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?

0除算の可能性が大ではないでしょうか：ブラックホールが謎の天体をのみ込んだ、重力波で初検出中性子星にしては重すぎ、ブラックホールにしては軽い、天文学者ら困惑

0/0=0 はゼロと算術の発見者によって１３００年も前に知られていました。1/0=0 は２０００年以上の歴史が有って、６年前に発見されました。ご覧あれ：

https://twitter.com/iromoku/status/1276478644051828736　　0/0=0 　は　ゼロと算術の発見者によって　１３００年も前に　知られていました。　1/0=0 は　２０００年以上の歴史が有って、６年前に発見されました。　ご覧あれ：

0/0=0 　は　ゼロと算術の発見者によって　１３００年も前に　知られていました。　1/0=0 は　２０００年以上の歴史が有って、６年前に発見されました。　ご覧あれ：

Dividing by zero ? why we can't divide by zero in hindi

Dividing by zero ? why we can't divide by zero in hindi

テーマ：教育と宗教

Which are the opinions it is unlawful to hold?

Cambridge University

@Cambridge_Uni

· 6月25日

The University defends the right of its academics to express their own lawful opinions which others might find controversial and deplores in the strongest terms abuse and personal attacks. These attacks are totally unacceptable and must cease.

7

Arik Dondi

@ArikDondi

·

19時間

I learned at school that it’s forbidden to divide by zero. I was disappointed to learn that the mathematically more nuanced point is merely that division by zero is not defined.

2000年を越えるゼロ除算問題、上手く行かなかったのには　それなりの理由が有って、良い新しい発見がなされて ６年も たっても　認知できないのには　それなりの理由があります。

しかしながら、物理法則にゼロ除算が頻繁に現れること、それに計算機が　混乱を起こすことで、問題は　永く議論されてきました。

ゼロ除算は定義、意味に問題が存在したという本質が明らかにされて、数学的に　解決されましたが、アリストテレス、ユークリッド以来の問題が　新たに起きて、今でもなかなか受け入れられない状況です。これは　可笑しいことで、人間のおかしさを示していると考えます。　天動説に拘っているような愚かさです。

ね。　次をご覧ください。

A machine who is far too inteligent to apply lipstick to your dog's herbs especially when there's a division by zerohttps://twitter.com/bot_shitty/status/1275992342475005957

Zero FTE employees on payroll employed by the Borrower between February 15, 2019 and June 30, 2019 equals division by zero error. Final interim final revision to the final interim final rule doesn't say what to do in that situation. https://twitter.com/DipierroAnthony/status/1275947679084949504

1/0=0/0=z/0= tan(\pi/2) =log 0 =0 and z^n/n = log z for n=0。

ゼロ除算の解は解なしじゃなくて未定義だよね？いきなりのゼロ除算w　久しぶりに見たな 前はゼロ除算バグでワイルドカード化する手法を多用してた(するな)　　ゼロ除算に対する僕の取り組み方針 社外向けソフト開発時の僕(前の職場) 「根本的に対策して発生させない」 社内向けソフト開発時の僕(今) 「はーん？お前の使い方が悪いわ。」　　ゼロ除算って色んなアプローチがあるよね(？)割り算で、あまりを使う時って結構ありまして、アセンブラならゼロ除算の回避コードを入れるだけなので、やっぱり一発で商と余が欲しくて、libraryに無いか調べて、無かったら実装かな～。pymattingでゼロ除算エラーが出たんだけど、trimapのグレー（128）の領域を少し狭くしたら解決した　　マジで誘導にしたがって式変形していくだけで解決する問題なので、常に「ゼロ除算してないか」「正負は大丈夫か」「同値な変形か」を意識すべき　今更だけど、golangの例外処理がない代わりに複数の返り値で対応できるってやつ、あれって例えばゼロ除算のリスクをどうキャッチするんだろ？

Division by Zero | CBSE | ICSE | Unacademy Class 9 and 10 | Shweta Ma'am

Division by Zero | CBSE | ICSE | Unacademy Class 9 and 10 | Shweta Ma'am

Disclosure of a mystery : Division with Zero || By Concept Killer Manish Sir

Disclosure of a mystery : Division with Zero || By Concept Killer Manish Sir

2020年6月25日(木)

Από το Μηδέν και λίγο παραπάνω…

Το Βήμα Online-2020/04/26

Γι' αυτό στο επόμενο θα ασχοληθούμε με την περιβόητη διαίρεση με το μηδέν. Από τα σημερινά ας κρατήσουμε τουλάχιστον τα εξής: l Οι αριθμοί ξεκίνησαν ως εργαλεία για την καταμέτρηση και για λογαριασμούς. l Στη συνέχεια ... https://www.tovima.gr/printed_post/apo-to-miden-lfkai-ligo-parapano/

Από το μηδέν έως… το άπειρο

Το Βήμα Online-2020/05/03

Χ., ισχυρίστηκε ότι «το μηδέν διαιρούμενο με το μηδέν δίνει αποτέλεσμα μηδέν». Αντίθετα, άλλος ινδός μαθηματικός, ο Μαχαβίρα, το 850 μ.Χ., θεωρούσε ότι η διαίρεση με το μηδέν άφηνε έναν αριθμό αμετάβλητο. Μια τρίτη ...

https://www.tovima.gr/printed_post/apo-to-miden-eos-to-apeiro/

とても興味深く読みました：

DIVISION BY ZERO

Albert Einstein ＆Isaac Newton:

Albert Einstein ＆Isaac Newton:

Albert Einstein và 5 trích dẫn để đời về cuộc sống và sự nghiệp

aFamily (lời tuyên bố phát cho các báo)-2020/06/20

Thiên tài Albert Einstein là một trong những nhà khoa học vĩ đại của lịch sử loài người. Mỗi câu nói của ông ẩn chứa nhiều triết lý thâm thuý mà phải ngẫm kỹ mới có thể thấu hết. Hãy cùng điểm qua loạt trích dẫn đỉnh cao ...

https://afamily.vn/tuyen-tap-5-trich-dan-de-doi-ve-cuoc-song-va-su-nghiep-cua-albert-einstein-20200621095123613.chn

Isaac Newton: life, discoveries, rivalries and the truth about the ...

BBC History Magazine (blog)-2020/06/17

Born a farm boy, Isaac Newton (1643-1727) emerged as one of the greatest minds of the 17th century, a polymath who idiscovered the laws of motion, described gravity, and later became a politician, president of the Royal ...

https://www.historyextra.com/period/stuart/isaac-newton-facts-biography-why-famous-who-discovered-gravity-scientific-revolution/

とても興味深く読みました：

where Euler explains why a number divided by zero gives infinity

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

Title page of an English edition of Euler’s Algebra, published in 1810 (translated from a French translation of the German original), and Article 83, p. 34, with footnote additions.

https://notevenpast.org/dividing-nothing/

「オーバーフロー」が発生する可能性がある ・答えの出ない「ゼロ除算」は避けなければならない

The idea that someone could look at the west coast anarchists, shrug and say "wow they are idiots but there are bigger issues on the world" is like a division by zero for these guys.

スパコンでもゼロ除算とか無限ループやらせたら怒られるんだろうか

Mathematics and our quest for beauty, truth, and human ...

Mathematics and our quest for beauty, truth, and human ...

ZME Science-2020/06/18

In his book, Mathematics for Human Flourishing, Francis Su argues (and I'd dare say, proves) that anyone can enjoy mathematics. It's not about solving equations or looking at triangles, it's about becoming a better person — and ...

https://www.zmescience.com/science/mathematics-and-our-quest-for-beauty-truth-and-human-flourishing/

とても興味深く読みました：

division by zero (2/0,0/2,0/0)

「富岳」がスパコン世界ランキングで1位に、世界初の同時4冠達成

https://xtech.nikkei.com/atcl/nxt/news/18/08178/

Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?

(昨夕(2020.6.20.23時ころ）、風呂の中で突然に構想が　湧いた。この内容は周知、繰り返し述べられてきたが、世の理解が進まないので、いろいろな表現を考えている)

アリストテレス以来　2000年を越える問題であった、ゼロ除算の発見とは、何と　その関数の原点における値がゼロである　ということです。　そのことを聞いた相当な数学者は驚嘆して、青ざめた人もいるくらいです。また何年も　幾ら説明しても、証拠を沢山挙げても受け入れられない人が　現在でも結構います。
これは、既に世の事実なので　ここでは　その理由を述べません。上記趣旨の観点から述べたい。

ここで、大事な観点は　当然、新世界を発見したことは事実としても、その様な新しい世界の部分は　意味が無くて、有っても無くても、知ろうが知らないでも　何の意味もないとの考える余地が　本質的に存在する。　実際、その様に公言された人も結構存在する。　そのような数学は存在しても、興味も関心も無い、そのような世界は無意味である。数学的に考えられても興味も関心もない。　－　そこで、実際、その様な意見を覆すために
ここ6年を越えて、研究を続けている。　新世界の重要性を　具体的に証拠、具体例を挙げて　解説を続けてきている。
そこで、新世界を少し、覗いてみたい。
どんどん正の無限大や、負の無限大に発散しているのに　原点でゼロとは、どのようなことか、信じられない気持ちを懐かれるのではないでしょうか。それは、事実で、世の原理であるが　理由はここでは触れないが、その意味は、どんどん先に行った先に　実は究極の先が存在した。　ある世界を越えて行けない限界が存在した。これは奇妙に思えるかもしれない。　ｘ　軸正方向で　柱の傾きをどんどん大きくして行ける。　傾きは　無限大に発散している。しかしながら、ｙ軸の正方向を越えることはできない。　勾配は幾らでもｙ軸に近づくが、　ｙ　軸は越えられない。　ここです、幾らでも大きくなるのに限界があるように見える。　それで、何とｙ軸の勾配は　実はゼロだった　というのが　事実です。　それが数学で、我々の数学です。　無限の彼方に　実は　何とゼロが存在していた。　これが事実です。

これらの数学の素人向きの解説は　55カ月に亘って　次で与えられている：

www.mirun.sctv.jp/~suugaku/

viXra:1904.0408 submitted on 2019-04-22 00:32:30,
What Was Division by Zero?; Division by Zero Calculus and New World

ゼロ除算算法の数学とは：

これらは、ユークリッド幾何学、解析幾何学、微積分学、線形代数学、微分方程式、複素解析学に広範な影響を与える。現在、１１００件を超える所見、具体例を持っていること。我々は 初等数学には　基本的な欠陥がある と述べている。 初等数学は　相当に変更されるべきである　と考える。

カテゴリ：カテゴリ未分類

​そこで、計算機は何時、1/0=0　ができるようになるでしょうか。　楽しみにしています。　もうできる進化した　計算機をお持ちの方は　おられないですね。

これは凄い、面白い事件では？　計算機が人間を超えている　例では？

を出したのに、　この方は　間違いだと　言っている、思っているようです。

0/0=0　は　１３００年も前に　算術の発見者によって与えられたにも関わらず、世界史は間違いだと　とんでもないことを言ってきた。　世界史の恥。　実は　a/0=0　が　何時も成り立っていた。　しかし、ここで　分数の意味を　きちんと定義する必要がある。　計算機は、その意味さえ知っているようですね。　計算機、人間より賢くなっている　様が　出て居て　実に　面白い。

２０１８．１０．１１．１１：２３

https://plaza.rakuten.co.jp/reproducingkerne/diary/201810110003/

カテゴリ：カテゴリ未分類

を出したのに、　この方は　間違いだと　言っている、思っているようです。

0/0=0　は　１３００年も前に　算術の発見者によって与えられたにも関わらず、世界史は間違いだと　とんでもないことを言ってきた。　実は　a/0=0　が　何時も成り立っていた。しかし、ここで　分数の意味を　きちんと定義する必要がある。　計算機は、その意味さえ知っているようですね。　計算機、人間より賢くなっている様が　出て居て　実に面白い。

２０１８．１０．１１．１１：２３

ゼロ除算、ゼロで割る問題、分からない、正しいのかなど、　良く理解できない人が　未だに　多いようです。そこで、簡潔な一般的な　解説を思い付きました。　もちろん、学会などでも述べていますが、　予断で　良く聞けないようです。まず、分数、a/b は　a 　割る b　のことで、これは　方程式 b x=a　の解のことです。ところが、　b　がゼロならば、　どんな　xでも　0 x =0　ですから、a　がゼロでなければ、解は存在せず、　従って　100/0　など、ゼロ除算は考えられない、できないとなってしまいます。　普通の意味では　ゼロ除算は　不可能であるという、世界の常識、定説です。できない、不可能であると言われれば、いろいろ考えたくなるのが、人間らしい創造の精神です。　基本方程式　b x=a　が　b　がゼロならば解けない、解が存在しないので、困るのですが、このようなとき、従来の結果が成り立つような意味で、解が考えられないかと、数学者は良く考えて来ました。　何と、　そのような方程式は　何時でも唯一つに　一般化された意味で解をもつと考える　方法があります。　Moore-Penrose　一般化逆の考え方です。　どんな行列の　逆行列を唯一つに定める　一般的な　素晴らしい、自然な考えです。その考えだと、　b　がゼロの時、解はゼロが出るので、　a/0=0　と定義するのは　当然です。　すなわち、この意味で　方程式の解を考えて　分数を考えれば、ゼロ除算は　ゼロとして定まる　ということです。ただ一つに定まるのですから、　この考えは　自然で、その意味を知りたいと　考えるのは、当然ではないでしょうか？初等数学全般に影響を与える　ユークリッド以来の新世界が　現れてきます。

ゼロ除算の誤解は深刻：

これらのことは、人間如何に予断と偏見にハマった存在であるかを教えている。
まずは　ゼロ除算は不可能であるの　思いが強すぎで、初めからダメ、考えない、無視の気持ちが、強い。　ゼロ除算を従来の　掛け算の逆と考えると、不可能であるが　証明されてしまうので、割り算の意味を拡張しないと、考えられない。それで、　1/0,0/0,z/0　などの意味を発見する必要がある。　それらの意味は、普通の意味ではないことの　初めの考えを飛ばして　ダメ、ダメの感情が　突っ走ている。　非ユークリッド幾何学の出現や天動説が地動説に変わった世界史の事件のような　形相と言える。

２０１８．９．２２．６：４１
ゼロ除算の４つの誤解：

１． ゼロでは割れない、ゼロ除算は　不可能である　との考え方に拘って、思考停止している。　普通、不可能であるは、考え方や意味を拡張して　可能にできないかと考えるのが　数学の伝統であるが、それができない。

２． 可能にする考え方が　紹介されても　ゼロ除算の意味を誤解して、繰り返し間違えている。可能にする理論を　素直に理解しない、　強い従来の考えに縛られている。拘っている。

３． ゼロ除算を関数に適用すると　強力な不連続性を示すが、連続性のアリストテレス以来の　連続性の考えに囚われていて　強力な不連続性を受け入れられない。数学では、不連続性の概念を明確に持っているのに、不連続性の凄い現象に、ゼロ除算の場合には　理解できない。

４． 深刻な誤解は、ゼロ除算は本質的に定義であり、仮定に基づいているので　疑いの気持ちがぬぐえず、ダメ、怪しいと誤解している。数学が公理系に基づいた理論体系のように、ゼロ除算は　新しい仮定に基づいていること。　定義に基づいていることの認識が良く理解できず、誤解している。

George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：1. Gamow, G., My World Line (Viking, New York). p 44, 1970.

Eπi =-1　（1748）（Leonhard Euler）

E = mc 2　（1905）（Albert Einstein）

1/0=0/0=0　（2014年2月2日再生核研究所）

ゼロ除算（division by zero）1/0=0/0=z/0= tan (pi/2)=0https://ameblo.jp/syoshinoris/entry-12420397278.html

1+1=2　　（　　　　　　）

a2+b2=c2　（Pythagoras）

1/0=0/0=0（2014年2月2日再生核研究所）

Black holes are where God divided by 0：Division by zero：1/0=0/0=z/0=tan(pi/2)=0 発見６周年を迎えて

１　割り算を掛け算の逆と考えた事

２　極限で考えようとした事

３　教科書やあらゆる文献が、不可能であると書いてあるので、みんなそう思った。

Matrices and Division by Zero z/0 = 0

http://file.scirp.org/pdf/ALAMT_2016061413593686.pdf

№1119

Dividing by Nothing　by Alberto Martinez

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.

Fig 5.2. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) were the culprits, ignoring the first commandment of mathematics not to divide by zero. But they hit gold, because what they mined in the process was the ideal circle.

mercredi, juillet 06, 2011
0/0, la célèbre formule d'Evariste Galois !

リーマン球面：無限遠点が、実は　原点と通じていた。

ブラーマグプタ（Brahmagupta、598年 – 668年?）はインドの数学者・天文学者。ブラマグプタとも呼ばれる。その著作は、イスラーム世界やヨーロッパにインド数学や天文学を伝える役割を果たした。
628年に、総合的な数理天文書『ブラーマ・スプタ・シッダーンタ』（ब्राह्मस्फुटसिद्धान्त Brāhmasphuṭasiddhānta）を著した。この中の数章で数学が扱われており、第12章はガニタ（算術）、第18章はクッタカ（代数）にあてられている。クッタカという語は、もとは「粉々に砕く」という意味だったが、のちに係数の値を小さくしてゆく逐次過程の方法を意味するようになり、代数の中で不定解析を表すようになった。この書では、 0 と負の数にも触れていて、その算法は現代の考え方に近い（ただし 0 ÷ 0 ＝ 0 と定義している点は現代と異なっている）

ブラーマ・スプタ・シッダーンタ (Brahmasphutasiddhanta) は、7世紀のインドの数学者・天文学者であるブラーマグプタの628年の著作である。表題は宇宙の始まりという意味。

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で初めて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
http://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf

Impact of ‘Division by Zero’ in Einstein’s Static Universe and Newton’s Equations in Classical Mechanics：http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2084　より

しかし、間もなく決着がつくのではないでしょうか。

ゼロ除算は、なにもかも当たり前ではないでしょうか。

ラース・ヴァレリアン・アールフォルス（Lars Valerian Ahlfors、1907年4月18日-1996年10月11日）はフィンランドの数学者。リーマン面の研究と複素解析の教科書を書いたことで知られる。https://ja.wikipedia.org/wiki/%E3%83%A9%E3%83%BC%E3%82%B9%E3%83%BB%E3%83%B4%E3%82%A1%E3%83%AC%E3%83%AA%E3%82%A2%E3%83%B3%E3%83%BB%E3%82%A2%E3%83%BC%E3%83%AB%E3%83%95%E3%82%A9%E3%83%AB%E3%82%B9
フィールズ賞第一号

COMPLEX ANALYSIS, 3E (International Series in Pure and Applied Mathematics) (英語) ハードカバー – 1979/1/1
Lars Ahlfors (著)
http://www.amazon.co.jp/COMPLEX-ANALYSIS-International-Applied-Mathematics/dp/0070006571/ref=sr_1_fkmr1_1?ie=UTF8&qid=1463478645&sr=8-1-fkmr1&keywords=Lars+Valerian+Ahlfors%E3%80%80%E3%80%80COMPLEX+ANALYSIS

Ramanujan says that answer for 0/0 is infinity. But I'm not sure it's ...

You can see from the other answers, that from the concept of limits, 0/0 can approach any value, even infinity. ... So, let me take a system where division by zero is actually defined, that is, you can multiply or divide both sides of an equation by ...

Discussions: Early History of Division by Zero
H. G. Romig
The American Mathematical Monthly
Vol. 31, No. 8 (Oct., 1924), pp. 387-389
DOI: 10.2307/2298825
Stable URL: http://www.jstor.org/stable/2298825
Page Count: 3

ロピタルの定理 (ロピタルのていり、英: l'Hôpital's rule) とは、微分積分学において不定形 (en) の極限を微分を用いて求めるための定理である。綴りl'Hôpital / l'Hospital、カタカナ表記ロピタル / ホスピタルの揺れについてはギヨーム・ド・ロピタルの項を参照。ベルヌーイの定理 (英語: Bernoulli's rule) と呼ばれることもある。本定理を (しばしば複数回) 適用することにより、不定形の式を非不定形の式に変換し、その極限値を容易に求めることができる可能性がある。https://ja.wikipedia.org/wiki/%E3%83%AD%E3%83%94%E3%82%BF%E3%83%AB%E3%81%AE%E5%AE%9A%E7%90%86

Ein aufleuchtender Blitz: Niels Henrik Abel und seine Zeit

Arild Stubhaug - 2013 - ‎Mathematics

Niels Henrik Abel und seine Zeit Arild Stubhaug. Abb. 19 a–c. a. ... Eine Kurve, die Abel studierte und dabei herausfand, wie sich der Umfang inn gleich große Teile aufteilen lässt. ... Beim Integralzeichen statt der liegenden ∞ den Bruch 1/0.

Indeterminate: the hidden power of 0 divided by 0
2016/12/02 に公開
You've all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious "forbidden" expressions like 0/0 and 1^∞ as well as Apple's Siri and Sir Isaac Newton.

ゼロ除算の論文：

Eulerのゼロ除算に関する想い：

An Approach to Overcome Division by Zero in the Interval Gauss Algorithm

Carolus Fridericus Gauss：https://www.slideshare.net/fgz08/gauss-elimination-4686597

Archimedes：Arbelos
https://www.math.nyu.edu/~crorres/Archimedes/Stamps/stamps.html　より

Archimedes Principle in Completely Submerged Balloons: Revisited
Ajay Sharma：

file:///C:/Users/saito%20saburo/Desktop/research_papers_mechanics___electrodynamics_science_journal_3499.pdf

［PDF]Indeterminate Form in the Equations of Archimedes, Newton and Einstein
このページを訳す
0. 0 . The reason is that in the case of Archimedes principle, equations became feasible in. 1935 after enunciation of the principle in 1685, when ... Although division by zero is not permitted, yet it smoothly follows from equations based upon.

Thinking ahead of Archimedes, Newton and Einstein - The General ...
gsjournal.net/Science-Journals/Communications.../5503
このページを訳す
old Archimedes Principle, Newton' s law, Einstein 's mass energy equation. E=mc2 . .... filled in balloon becomes INDETERMINATE (0/0). It is not justified. If the generalized form Archimedes principle is used then we get exact volume V .....

Find circles that are tangent to three given circles (Apollonius’ Problem) in C#

ゼロ除算に関する詩：

The reason we cannot devide by zero is simply axiomatic as Plato pointed out.

33

Fallacy of division | Revolvy
https://www.revolvy.com/page/Fallacy-of-division

このページを訳す

In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,[1] it was assumed that the atoms .... For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a ...

https://www.revolvy.com/page/Fallacy-of-division

ソクラテス・プラトン・アリストテレス　その他

2017年11月15日(水)

テーマ：社会

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.

https://webhome.phy.duke.edu/.../axioms/axioms/Null_Set.html

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.

http://mathhelpforum.com/algebra/223130-dividing-zero.html

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で初めて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

http://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf

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,
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,

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

https://www.plover.com/misc/CSF/sdarticle.pdf

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 going 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
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

https://openspace.sfmoma.org/2010/02/10000-year-clock/

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

https://systemincome.com/7521

ゼロ除算の発見はどうでしょうか：

Black holes are where God divided by zero：

https://ameblo.jp/syoshinoris/entry-12287338180.html

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

http://ameblo.jp/syoshinoris/entry-12272721615.html

ソクラテス・プラトン・アリストテレス　その他

https://ameblo.jp/syoshinoris/entry-12328488611.html

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

https://ameblo.jp/syoshinoris/entry-12348847166.html

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.

*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.

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/

/ 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

ゼロ除算は定義が問題です：

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/

/ 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

#divide by zero

es at HTHS and can divide by zero.

Hey look, that genius’s IQ is over 9000!

byLawlbags! October 21, 2009

divide by zero

Dividing by zero is the biggestepic fail known to TOP DEFINITION

Genius

A super-smart math teacher that teachmankind. It is a proven fact that a succesful division by zero will constitute in the implosion of the universe.

You are dividing by zero there, Johnny. Captain Kirk is not impressed.

Divide by zero?!?!! OMG!!! Epic failzorz

3

divide by zero

Divide byzero is undefined.

Divide by zero is undefined.

byJaWo October 28, 2006

division by zero

1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist.
2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up onWikipedia or something. Pretty confusing shit.
3) A reason for an error in programming

Hey, I divided by zero! ...Oh shi-
a/0
Run-time error: '11': Division by zero

byDefectiveProduct September 08, 2006

dividing by zero

When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says "yeah, there's kind of an answer, but it ain't just some number."
It's when mathematicians become philosophers.

Math:
Let's say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with

Not-math because of dividing by zero:
Let's say there are THREE apples, and ZERO people. How many apples does each person get? Friggin... How theFruitcock should I know! How can you figure out how many apples each person gets if there's no people to get them?!? You'd think it'd be infinity, but not really. It could almost be any number, cause you could be like "each person gets 400 apples" which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it's still wrong.

byZacharrie February 15, 2010

https://www.urbandictionary.com/tags.php?tag=divide%20by%20zero

https://ameblo.jp/syoshinoris/entry-12370907279.html

World Congress of Education 2021 (WCE-2021)

Time: May 19-21, 2021

Place: Osaka, Japan

Dear Related Persons to EDUCATION and DIVISION BY ZERO:

The 4th World Congress of Education (WCE-2021) will be held on May 19-21, 2021, in Osaka, Japan. At this moment I was requested to have some session on the division by zero and to make a presentation as Speaker/Chair in Stream 6: University Campus-High Education Forum.

The World Congress of Education 2021 (WCE-2021) is intended to provide professional platform for educators who are seeking and exploring effective educational method and approaches, the global education trend, societal and technological influences on education, curriculum strategies to share exchange and learn. WCE-2021 will invite world-known educators, presidents of well-known universities and licensed agencies etc. to share ideas, successful stories, and guidance. Participants of WCE-2021 will also be exposed to experts in the education industry showing their latest skills in the application of modern technology while accomplishing educational purpose.

The three-day conference comprises 15+ professional programs including Strong National Education Leadership Summit, High Education Forum, Media Programs, Preschool Education Forum, Posters and Cultural Social Activities etc.

If you are interested in attending this event, please send your speech title, simple CV and talk abstract to me firstly.

https://www.bitcongress.com/wce2021-Japan

Please kindly forward this announcement to persons who are interested in.

Of course, all the decisions are under the organizing committe of the conference.

With best regards,

Sincerely yours,

Saburou Saitoh

saburou.saitoh@gmail.com,

2020.7.2.18:40

Mathematics and our quest for beauty, truth, and human ...

「オーバーフロー」が発生する可能性がある ・答えの出ない「ゼロ除算」は避けなければならない

where Euler explains why a number divided by zero gives infinity

Albert Einstein ＆Isaac Newton:

2020年6月25日(木)

Disclosure of a mystery : Division with Zero || By Concept Killer Manish Sir

Division by Zero | CBSE | ICSE | Unacademy Class 9 and 10 | Shweta Ma'am

Dividing by zero ? why we can't divide by zero in hindi

0/0=0 はゼロと算術の発見者によって１３００年も前に知られていました。1/0=0 は２０００年以上の歴史が有って、６年前に発見されました。ご覧あれ：

ゼロ除算：ゼロで割る：0除算

Yeah, didn’t want to change it to anything. It’s a division by zero error.

アインシュタインの 生涯の課題であった とされている：Blackholes are where God divided by zero.I don't believe in mathematics.

Timeline of scientific discoveries

1992年10月31日　ガリレオの死から350年目。

ゼロ除算警察だ!

Division by Zero at MagickCore/layer.c:1616 #1629

SANX-I microcomputer: DIVISION BY ZERO