ここでは「知のパラダイム転換」を概観するために、入手しやすく、かつ面白く読める10冊を選んでみた。
最初に断っておくと、「知のパラダイム転換」は「人文・社会科学が自然科学に侵食され、存在理由を失っていく過程」のことだが、私の造語で、日本のアカデミズムではまったく流通していない。
ダーウィンから「現代の進化論」へ
リチャード・ドーキンスの世界的ベストセラー『利己的な遺伝子』は、生物学のごく一部のイノベーションでしかなかった「現代の進化論」を一般読者に向けてわかりやすく解説した記念碑的著作。その成功の多くは、遺伝子を「利己的（Selfish）」としたネーミングの妙に拠っているが、そのためさまざまな誤解も生んだ。
原著は1976年の発売で、日本では1980年に『生物＝生存機械論』と題されて翻訳された。『利己的な遺伝子』と改題され書店に並んだのは1991年で、それが大きな評判を呼んで第一次の遺伝子＝進化論ブームが起きた。だが当時の日本はまだポストモダン哲学が主流で、「ミトコンドリアが反乱を起こす」というエンタテインメント小説の題材に使われたくらいで、生物学の「革命」がどれほど巨大な衝撃かを（私も含め）ほとんどの日本人は理解できなかった。
社会性昆虫のアルゴリズムの解明から始まった社会生物学は、その後、魚類や鳥類、哺乳類、霊長類などの生態へとその領域を拡大していった。人間（サピエンス）が「現代の進化論」の標的になるのは時間の問題だった。
社会生物学論争という「文化戦争」は1975年、アメリカの生物学者エドワード・Ｏ・ウィルソンが大著『社会生物学』の最終章を「ヒト―社会生物学から社会学へ」として、人間の生態も社会性昆虫などと同様に遺伝的・進化論的に解明できると宣言したことで勃発した。だがアメリカのアカデミズムを激震させたこの大事件は日本のアカデミズムではまったく紹介されず、私がようやくそのことを知ったのは2004年にスティーブン・ピンカーの『人間の本性を考える』を読んだときだ。
「現代の進化論」にもとづいてヒトの生態を解明する科学が進化心理学で、1970年代からアメリカを中心に大きく発展した。ピンカーの本はその集大成で、「肌の色は遺伝しても心（脳）が遺伝することなどあってはならず、知能や性格はすべて環境によって決まる」という「空白の石版」理論を徹底的に批判・論破していく。
「よろこびやかなしみ、愛や憎悪は進化の過程でつくられた心のプログラムだ」という進化心理学のテーゼは、紆余曲折はありながらも、自然科学として膨大な調査・研究が積み重ねられたことで、現代のアカデミズムでは（日本を除いて）広く共有されている。いまではビジネス書ですら、エビデンス（証拠）を示さないものは「非科学的」として相手にされなくなっている。
「氏が半分、育ちが半分」
行動遺伝学は「遺伝決定論」のレッテルを貼られて評判が悪いが、「氏が半分、育ちが半分」という当たり前のことをいっているにすぎない。「遺伝の影響はあってはならない」という「リベラル」なひとたちのドグマが荒唐無稽なのだ。
ここまでは同意するひとも、行動遺伝学のもうひとつの（より重要な）発見については容易に納得しないだろう。それは、「育ちのうち、共有環境の影響はほぼゼロである」というものだ。「共有環境」とは双生児が成長のなかで共有している環境のことで、一般には子育て（家庭環境）をいう。行動遺伝学が正しいとするならば（これには膨大な証拠がある）、子育てには意味がなく、子どもが親に似ているのは遺伝の影響なのだ。
なぜこのようなことになるのか。現在のところもっとも説得力のある仮説を提示したのが在野の発達心理学者ジュディス・リッチ・ハリスで、アメリカで大論争を巻き起こした『子育ての大誤解』において、子どもは遺伝的なちがいをフックにして、友だち集団のなかで自分をできるだけ目立たせようとする複雑なゲームをしているのだと主張した。子どもの〝キャラ（性格）〟がこのようにして決まっていくのなら、「育ち」というのは家庭環境ではなく友だち関係（非共有環境）のことなのだ。――「子どもはなぜいうことをきかないのか？」「子育てはなぜうまくいかないのか？」という多くの親の悩みに、ハリスの集団社会化論だけが、「現代の進化論（行動遺伝学）」にもとづいて明快にこたえることができる。
行動遺伝学や分子遺伝学などによって、近年、遺伝子（ゲノム）の仕組みが急速に解明されてきた。がん研究者（がんもいまでは〝遺伝子の病〟と見なされている）シッダールタ・ムカジーの『遺伝子』は、ダーウィンやメンデルの時代から、科学者たちが遺伝の謎を解明し、ときに優生学のような悲劇を引き起こしつつも、それを病気の治療や社会の改良に役立てようとしてきた歴史を描いている。
遺伝の科学はいまや、ヒトゲノム（遺伝地図）を解読しただけでなく、「クリスパー・キャス9」などのテクノロジーを使って遺伝情報を1文字単位で編集することを可能にした。これによって、乳がんを引き起こす遺伝的変異を生殖細胞の段階で修正するような治療が期待されるが、その一方で子どもの肌や髪、目の色をあらかじめ設計したり（理論的にはいまでも可能）、発達障害や精神疾患のリスクを低めつつ知能を高める（これは将来の課題）デザイナーベイビーの誕生が現実味を帯びてきた。こうした技術が資本市場で販売されるようになれば、人類の未来にとてつもない影響を及ぼすことになるだろう。
遺伝の科学とならんで「現代の進化論」を支えるのが脳科学の急速な発展だ。fMRI（機能的核磁気共鳴画像法）などの新しいテクノロジーによって、感情や行動と脳の活動の関係を詳細に調べることができるようになったことで、これまで哲学が独占的に扱ってきた「意識」は脳科学の研究領域になった。
脳については膨大な本が書かれているが、幻肢の研究で知られるラマチャンドランの『脳のなかの幽霊』を挙げた。幻肢とは事故で手足を失っても「指先」などが痛むことで、神経科医のラマチャンドランは鏡を巧妙に使って腕（足）があるかのように錯覚させることで治療に成功した。こうした脳の錯覚にも進化論的な基礎があり、生き物の長大な歴史のなかで、利己的な遺伝子によって「設計」されてきたのだ。
複雑系が牽引する因果論の転換
「現代の進化論」とならんで、知のパラダイム転換を牽引するのが複雑系だ。その立役者の一人が「フラクタル」で知られる数学者のベノワ・マンデルブロ。
古来、ひとびとは世界を因果律で理解してきた。なんらかの結果（洪水）には必ず原因（大雨による河川の増水）があり、ときに日食のように因果関係が判然としないことが起きると、それはすべて超自然的なもの（神）の仕業とされた。ニュートン力学は因果論（決定論）の頂点で、啓蒙主義時代の知識人はこれによって世界をあますことなく記述し、「神の設計図」を読み解けると信じていた。
だが19世紀になると、従来の力学ではうまく説明できない現象が見つかるようになった。水を入れたコップに花粉を落としたときに起こるブラウン運動もそのひとつで、物理学者はどうやってもその法則性を解明できなかった。
この問題を解決したのがアインシュタインで、花粉の動きが統計的に予測できることから水の分子の存在を証明した。その後、微細な世界の研究が進むにつれて、原子や電子に因果論は役に立たず、確率的にしか記述できないことがわかってきた。これが量子力学で、いまでは古典物理学（ニュートン力学）は確率的世界の特殊なケースとして扱われている。
マンデルブロはこれをさらに拡張し、確率的世界の外側に広大な「複雑系世界」があると考えた。確率的世界はベルカーブ（正規分布）で予測できるが、複雑系世界はロングテール（べき分布）なので、正規分布で表すことはできない。だがそこにも法則性はあり、フラクタル（複雑系の図形）は単純なルールの繰り返しでつくることができる。
複雑系の世界は、身長1メートルの大群衆のあいだに、身長10メートルや100メートルの巨人がいるような奇妙な世界だ。その典型はインターネットで、ほとんどのホームページはわずかなアクセスしかないが、そのなかにGoogleやFacebook、Yahoo!のような膨大なアクセスのあるハブが存在する。こうした構造は飛行機の路線図（ハブ空港でつながるネットワーク）から宇宙（真空のなかに銀河というハブが点在する）までいたるところに見られ、生態系や脳のシナプス、遺伝の発現の仕方も複雑系であることがわかってきた。複雑系こそが世界の根本法則で、量子力学のような確率的世界はその特殊ケースなのだ。
このとてつもない発見をしたマンデルブロには主著『フラクタル幾何学』（ちくま学芸文庫）があるが、かなりの数学的素養がないと読みこなせない。一般読者向けに『フラクタリスト―マンデルブロ自伝』（早川書房）があるものの、ここではマンデルブロに師事したヘッジファンドマネージャー、ナシーム・タレブの『ブラック・スワン』を挙げた。2008年のリーマンショックに端を発した金融市場の大混乱を複雑系で読み解き、世界的なベストセラーになった。
マンデルブロによれば市場も典型的な複雑系で、ベルカーブは当てはまらない。これはすなわち、加減乗除と微積分に正規分布を加えたマクロ経済学の数式では市場を記述できないということだ。この批判は経済学の世界ではずっと無視されてきたが、どれほど精緻なマクロモデルもリーマンショックをまったく予測できなかったことで見事に証明され、いまやマクロ経済学は「科学」から脱落しつつある。
ビッグデータ解析、結果に価値
従来型のマクロ経済学に代わって登場したのが、市場を数式に還元するのではなく、ビッグデータを解析して因果関係を見つける手法だ。その先駆者はアメリカの経済学者スティーヴン・レヴィットで、『ヤバい経済学』は「アメリカで犯罪が減ったのは、中絶の合法化で若く貧しい女性が出産しなくなったから」などの大胆な分析で話題を呼んだ。
〝ビッグデータ経済学〟が可能になったのは大量のデータをコンピュータで高速処理できるようになったからだが、いまではデータ解析自体も人力ではなく、深層学習させたAI（人工知能）が行なうようになっている。ビジネスの世界では因果関係はブラックボックスでもかまわず、収益を最大化する方法（結果）さえわかればいいのだ。
マクロ経済学が「科学」から脱落しつつあるのとは対照的に、ミクロ経済学はゲーム理論と一体化して「科学」として精緻化されていった。相互作用が限定された（ミクロの）世界では、私的利益を最大化しようとするひとびとの行動をアルゴリズムとして記述できるのだ。
経済学が前提とする「合理的経済人（エコン）」に異議を唱えたのが心理学者のエイモス・トベルスキーとダニエル・カーネマンで、さまざまな独創的な実験によって、人間がおうおうにして不合理な選択をする「ヒューマン」であることを示した。
二人が創始した行動経済学の成果は、ダニエル・カーネマンの『ファスト＆スロー』にまとめられている。ヒトは直観的な「ファスト（速い）思考」と理性的な「スロー（遅い）思考」のふたつの思考回路を使い分けているとの行動経済学の主張は、いまでは脳科学的にも裏づけられている。
「ヒューマン」がファスト思考で不合理な選択をするからといって、ミクロ経済学が否定されたわけではない。「限定合理的な経済人」をモデル化したより現実的なゲーム理論が登場すると同時に、進化の過程で生じたバイアスを利用して効率的な社会制度を設計しようとする試みも行なわれている。その成果は政策にも採用され、いまや経済学でもっとも活気のある分野になった。――詳しくはリチャード・セイラー、キャス・サンスティーン『実践 行動経済学』（日経BP社）などを読まれたい。
強大なテクノロジーが導く先は
ここまで述べてきたように、知のパラダイム転換の背景にはコンピュータやICT（情報通信技術）、遺伝子工学、AIなど急速なテクノロジーの発達がある。この驚くべき進歩がつづけば、2045年にはコンピュータの知能が人間を超えるシンギュラリティ（技術的特異点）に達し、超人類（ポストヒューマン）が誕生するとの予測もある（レイ・カーツワイル『ポスト・ヒューマン誕生』NHK出版）。
強大なテクノロジーは、いったいわれわれをどこに連れていくのか。それにこたえるのが『WIRED』誌創刊編集長であるケヴィン・ケリーの『テクニウム』だ。
私たちはごく当たり前のように、人間が科学やテクノロジーを「道具」として使っていると考えている。だがケリーはこれを逆転させ、テクニウム（テクノロジー生態系）が、倫理的・数学的知能のきわめて高い天才（ギフテッド）たちを〝ヴィークル〟として自らの可能性を最大化しようとしているのだという。人間は生き物として「利己的な遺伝子」の道具であると同時に、知性をもったことで「利己的なテクノロジー」の道具にもなったのだ。そうとうに大胆な説だが、このように考えればイーロン・マスクやピーター・ティールなどシリコンバレーの成功者たちが「テクノロジー至上主義者（サイバーリバタリアン）」である理由がわかる。
アメリカでは進化論を否定する保守派が「インテリジェント・デザイン」を唱え、生命は超知性体＝神によって創造されたと主張している。シリコンバレーのイデオローグたちはそれを、高い知能を持つ者たち（インテリジェント）がコンピュータをプログラムするように功利的・合理的に世界をデザインすることで、人類のよりよい未来を創造していくのだと読み換える。人類がテクニウムに支配されているとするならば、シンギュラリティが来るかどうかは別として、私たちは行きつくところまで行くしかないということなのだろう。
最後に、ユヴァル・ハラリの『サピエンス全史』を挙げておく。ハラリは「現代の進化論」を歴史学に適用し、進化心理学的な知見を大胆に取り入れて、ヒト（サピエンス）の来歴と未来を一挙に書き直す野心的な試みを見事に成功させ、著書は世界じゅうでベストセラーになった。だがより興味深いのは、『サピエンス全史』が日本で「ビジネス書大賞2017」を受賞したことだ。
ここまで述べてきたように、政治学・経済学・社会学・心理学から哲学にいたるまで、従来、人文・社会科学とされてきた分野を自然科学が侵食する「知のパラダイム転換」が1960年代から始まり、強大なテクノロジーによって加速度的にその領域を拡大しているが、日本の「文系アカデミズム」は一貫してこの世界的潮流を無視してきた。
その結果、より現実的で知的なビジネスパーソンが、世界基準から脱落しガラパゴス化した日本のアカデミズムを見捨てつつあるという現状がここに象徴されているのだろう。
◇
※本論考は朝日新聞の専門誌『Journalism』10月号から収録しています。同号の特集は「現在地を知る100冊」です。https://webronza.asahi.com/journalism/articles/2018090500006.html
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：2014年2月2日 4周年を超えました：
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 454: The International Conference on Applied Physics and Mathematics, Tokyo, Japan, October 22-23}
\author{{\it Institute of Reproducing Kernels}\\
kbdmm360@yahoo.co.jp
}
\date{2018.9.29}
\maketitle
{\Large \bf
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 based on the new concept of division by zero calculus: for the function $f(z) = 1/z$
$$
f(0) = 0
$$
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 site: http://okmr.yamatoblog.net/
\medskip
In the above international conference:
\medskip
\medskip
John Martin, Program Coordinator\\
http://www.meetingsint.com/conferences/\\appliedphysics-mathematics\\Applied Physics and Mathematics Conference 2018\\
appliedphysics@annualmeetings.net\\
appliedphysics@meetingseries.org
\medskip
\medskip
we will present our results while 11:00-12:00, October 23 and we will accept all the related questions and comments while 13:00-15:00 around.
For the details, please see the below:
\medskip
(If a person participates in our session around the morning and afternoon free discussions, he should pay euro 250. If the person registers in a group of 5 or more, the amount will be reduced to euro 180 per person. The morning session is very valuable and has the potential to bring change in the education system.
For one night stay on 22nd October, he needs to pay euro 150.
I hope everything is clear.
Kindly let me know if any query.
Thanks!
Regards,
John)
}
\bigskip
\bigskip
{\Huge \bf
Close the mysterious and long history of division by zero and \\ open the new world since Aristoteles-Euclid: $1/0=0/0=z/0= \tan (\pi/2)=0.$
}
\bigskip
\bigskip
{\large \bf
For a triangle ABC with side length $a,b,c$.
We have the formula
$$
\frac{a^2 + b^2 - c^2}{a^2 - b^2 + c^2} = \frac{\tan B}{\tan C}.
$$
If $ a^2 + b^2 - c^2 =0$, then $C = \pi/2$. Then,
$$
0 = \frac{\tan B}{\tan \frac{\pi}{2}} = \frac{\tan B}{0}.
$$
Meanwhile, for the case
$
a^2 - b^2 + c^2 =0,
$
then $B = \pi/2$, and we have
$$
\frac{a^2 + b^2 - c^2}{0}= \frac{\tan \frac{\pi}{2}}{\tan C}=0.
$$
\end{document}
ソクラテス・プラトン・アリストテレス その他
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
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
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
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, 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
https://adarvetranslations.com/…/our-humanity-and-division…/
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
https://adarvetranslations.com/…/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
https://www.plover.com/misc/CSF/sdarticle.pdf
とても興味深く読みました：
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 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.
https://openspace.sfmoma.org/2010/02/10000-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 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.
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
ゼロ除算の発見はどうでしょうか：
Black holes are where God divided by zero：
再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議
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
https://www.youtube.com/watch?v=iQld9cnDli4
〔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
https://www.youtube.com/watch?v=DvyAB8yTSjs&t=3318s
〔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
https://www.youtube.com/watch?v=KjvFdzhn7Dc
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://www.youtube.com/watch?v=fWVv9puoTSs
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
https://ameblo.jp/syoshinoris/entry-12348847166.html
再生核研究所声明 416(2018.2.20): ゼロ除算をやってどういう意味が有りますか。何か意味が有りますか。何になるのですか － 回答
再生核研究所声明 417(2018.2.23): ゼロ除算って何ですか － 中学生、高校生向き 回答
再生核研究所声明 418(2018.2.24): 割り算とは何ですか？ ゼロ除算って何ですか － 小学生、中学生向き 回答
再生核研究所声明 420(2018.3.2): ゼロ除算は正しいですか，合っていますか、信用できますか － 回答
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.
https://ameblo.jp/syoshinoris/entry-12361744016.html 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.
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
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
1423793753.460.341866474681。
Einstein's Only Mistake: Division by Zero
ゼロ除算は定義が問題です：
再生核研究所声明 １４８（2014.2.12） 100/0=0, 0/0=0 － 割り算の考えを自然に拡張すると ― 神の意志 https://blogs.yahoo.co.jp/kbdmm360/69056435.html
再生核研究所声明１７１（2014.7.30）掛け算の意味と割り算の意味 ― ゼロ除算100/0=0は自明である？http://reproducingkernel.blogspot.jp/2014/07/201473010000.html
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
1423793753.460.341866474681。
Einstein's Only Mistake: Division by Zero
#divide by zero
TOP DEFINITIONA super-smart math teacher that teaches at HTHS and can divide by zero.Hey look, that genius’s IQ is over 9000!by Lawlbags! October 21, 2009Dividing by zero is the biggest epic fail known to mankind. 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
0 件のコメント:
コメントを投稿