LESS THAN HUMAN 告白しなかった恋はどこへ行くのだろう。
LESS THAN HUMAN 予想は裏切り、期待は裏切らない。
哲学者たちはなぜ戦争協力したのか？
BOOKウォッチ編集部コメント
先日（京都大学学術出版会）という本を当欄で紹介した。時代によって、さまざまなジャンルの「京都学派」があり、昔のセンセイたちはよく酒を飲んだという内容だったが、「京都学派」の本家本元ともいうべき哲学者たちの戦前、戦中、戦後を検証したのが本書『京都学派』（講談社現代新書）である。
京都学派の祖である西田幾多郎が『善の研究』を独自に著し、弟子の田辺元が後に批判に転ずるものの、西洋哲学と関連づけたことで世界的水準の哲学と見なされるようになった。その後、「京大四天王」と称される教授の西谷啓治、高坂正顕、高山岩男、鈴木成高は東西思想の融合を掲げたことから、「大東亜共栄圏」のスローガンと結びついたとされ、戦後、職を辞した。
著者は「京都学派の哲学者たちの戦争協力から、今日われわれが学ぶべきことは、彼らが主張した、時流に乗った日本精神の正当化の論理は、端から破綻していたということである。彼らの言説は、むしろ西洋哲学的な文脈のなかにおける新たな理論として位置づけ直すべきだろう」と、彼ら一人ひとりの哲学を丹念に分析する。
著者の菅原潤さんは、京都大学とはまったく縁のない哲学研究者である。東北大学大学院で学び、現在、日本大学工学部教授。なぜそんな菅原さんが「京都学派」を取り上げたのか。実は東北大学の理学部の科学哲学概論は田辺元、また西田を真っ向から批判した高橋里美、戦後に京都学派を再建した三宅剛一が教鞭を取った伝統があった。東北大学は京大と哲学にかんして深い縁があったのだ。
戦前の京都学派に変わって戦後は東大教養部の科学史・科学哲学研究室の大森荘蔵、広松渉らが、日本の哲学界をリードした。マルクス主義者であった広松だが、著書『＜近代の超克＞論』で京都学派を再評価したのは興味深い。
本書によると、京大に日本哲学史の講座が開設されたのは2000年だという。戦後、ずっとおひざ元で「京都学派」は封印されていたのだ。戦争と学者についての倫理は、日本の安全保障体制の変更が課題に上がっている今こそ、問われるべきだろう。その材料となる一冊だ。
とても興味深く読みました：ゼロ除算の発見4周年を超えました：
テーマ：
The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.
Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.
It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.
Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.
It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).
Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.
Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.
I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded co
rretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.
ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて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
OUR HUMANITY AND DIVISION BY ZERO
Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/
5000年？？？？？
2017年09月01日(金)NEW !
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0 0 ¼ 0 ) 0 1=1 ¼ 0 ) 0 1 ¼ 0 1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0 0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently
also for physical applications. T
とても興味深く読みました：
10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.
For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s 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.
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
ゼロ除算に 興味を抱いている方の 率直な 疑念です。大きな国際会議で、感情的になって 現代の数学を破壊するもので 全く認められないと発言
れた方がいる。現代初等数学には基本的な欠陥があって、我々の空間の認識は ユークリッド以来の修正が求められ、初等数学全般の再構成が要求されていると述べている。それで、もちろん、慎重に 慎重に対応しているのは当然である。
本来 数学者は 論理に厳格で 数学の世界ほど 間違えの無い世界は無いと言えるのではないだろうか。 実際、一人前の数学者とは、独自の価値観を有し、論理的な間違いはしない者である と考えられているのではないだろうか。２０００年を越える超古典的な数学に反した 新しい世界が現れたので、異常に慎重になり、大丈夫か大丈夫かと４年間を越えて反芻して来た（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）。 そこで、ゼロ除算の成果における信頼性を客観的に 疑念に対する回答として纏めて置こう。これらは、貴重な記録になると考えられる。
まず、研究成果は 3年半を越えて、広く公開している：
数学基礎学力研究会 サイトで解説が続けられている：
また、o に 関連情報を公開している。
ゼロ除算の研究は、内外の研究者に意見を求められながら共同で進め、１２編を越える論文を出版確定にしている。日本数学会では６期３年間を越えて関係講演を行い、成果を発表して来た。 またその際、ゼロ除算の解説冊子（2015.1.14付け）を１０００部以上広く配布して意見を求めてきたが、論理的な不備などはどこからも指摘されていない。ここ４年間海外の関係専門家と２５０以上のメールで議論してきた（ある人がそう述べてきた：2018年2月27日 18:45 Since then I have received about 250 messages from you about it. Unbelievable! :2018年2月27日 18:45）が 論理的な不備は指摘されなく、関係者の諒解（理解）が付いていると判断されている。逆に他の理論については 全て具体的に批判し、良くないと述べている。50カ国２００名以上参加の大きな国際会議に 全体講演者として招待され、講演を行い、かつ論文がその会議禄に２編Springer社から出版される。公開していたゼロ除算の総合的な研究著書原案154ページに対して、イギリスの出版社が出版を勧め、外部審査、社内審査を終えて、著書の出版を決定している。
ゼロ除算を裏付ける知見は 初等数学全般から７００件を超え、公開している。共著者として論文執筆に参加している人は、代表者以外内外８名である。
以上の状況は ゼロ除算の数学的な信用性を裏付けていると考えるが、如何であろうか。
以 上
2018.3.18．午前中 最後の講演： 日本数学会 東大駒場、函数方程式論分科会 講演書画カメラ用 原稿
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.
より
なぜ、LESS THAN HUMANは問題なのか？
哲学と政治
哲学と政治
哲学は人間存在や人生の意義を説き明かすことに取り組む。古代ギリシャの哲学者プラトンは、良き国家統治と正義を実現できるのは哲学者だけと説いた。フランス革命を導いた啓蒙思想や、戦後の学生運動に影響した実存主義など、哲学は近現代の政治や社会に影響を及ぼす一方、今年生誕２００年を迎えたマルクスの思想は、社会主義独裁国家などにもつながった。
ゼロ除算の発見は日本です：
∞？？？
∞は定まった数ではない・・・
人工知能はゼロ除算ができるでしょうか：
とても興味深く読みました：
ゼロ除算の発見と重要性を指摘した：日本、再生核研究所
ゼロ除算関係論文・本
テーマ：
The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.
Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.
It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.
Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.
It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).
Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.
Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.
I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.
ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて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
OUR HUMANITY AND DIVISION BY ZERO
Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While
this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/
5000年？？？？？
2017年09月01日(金)NEW !
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0 0 ¼ 0 ) 0 1=1 ¼ 0 ) 0 1 ¼ 0 1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0 0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T
とても興味深く読みました：
10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.
For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s 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, an
d 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.
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
1/0=0、0/0=0、z/0=0
1/0=0、0/0=0、z/0=0
1/0=0、0/0=0、z/0=0
ソクラテス・プラトン・アリストテレス その他
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
&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
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか
再生核研究所声明 411(2018.02.02): ゼロ除算発見4周年を迎えて
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.
より
*057 Pi
nelas,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
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？
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don’t believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。1423793753.460.341866474681。
Einstein’s Only Mistake: Division by Zero
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#divide by zero
TOP DEFINITION
A super-smart math teacher that teaches at HTHS and can divide by zero.
Hey look, that genius’s IQ is over 9000!
by October 21, 2009
Dividing by zero is the biggest 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
3
by is undefined.
Divide by zero is undefined.
by October 28, 2006
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 on 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
by September 08, 2006
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.
:
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 withbecause of dividing by zero:
Let’s say there are THREE apples, and ZERO people. How many apples does each person get? Friggin… How the 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.by February 15, 2010
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東大教授がこっそり教えてくれるLESS THAN HUMANの真実
The following is also from 2 pages of yesterday’s Sankei Shimbun.
It is an unexpected fact that Japan has been criticized as being a servile diplomacy of the United States, from the malicious peripheral nations and the leftist activists, and it is scattered.
A truly ridiculous recommendation like this time … no recommendation to China etc. which is the world’s largest and the worst human rights violation nation,
It is impossible to keep silent about the form of CERD that is no longer tolerable, repeatedly attacking repeatedly, targeting Japan.
We must suspend support only in the UN budget that is spent on CERD.
Ultimately, Japan and the US led the time to notice that there is no way to rectify the world besides making a coalition of countries of true freedom and democracy, as well.
US suspension of Palestinian support
US paper news refugee definition change request
WASHINGTON – Hiroyuki Kano, The Washington Post reported on Thursday that the Trump regime decided to stop the contribution to the United Nations Relief and Works Agency for Palestine Refugees in the Near East (UNRWA).
It is expected to announce it within a few weeks, saying that neighboring countries are asking for a substitution.
The United States is the largest contributor to UNRWA, and in fact it is concerned that the deterioration of the situation in Gaza in Palestine Autonomous Region will cause further violence against Israel.
The U.S. government is calling for reforms such as the definition of refugees to be supported by UNRWA and the use of support money and excluding their descendants with only about 5 million Palestinian refugee status qualified as refugees at the time of Israel’s founding in 1948 It is also a policy to encourage people to reduce it to less than 1/10.
According to the newspaper, the budget of UNRWA is $ 1.1 billion (about 122 billion yen), and the U.S. was burdened with this about 1/3.
The U.S. government has also decided to cancel the $ 200 million assistance targeting the Gaza Strip and the West Bank, separately. The Trump regime aims to respond to the Palestinian autonomous government’s pressure to resume peace negotiations with Israel.
However, the Palestinian side has strongly repulsed because refugee definition change involves the problem of ‘returning right’.
噂の「LESS THAN HUMAN」を体験せよ！
こんにちは。鈴木真奈美です。
熱い想いと涙がこみあげてきました。
すべてが歴史的瞬間。
７１年前に起きた人類史上最大の悲劇は、私たちの想像をはるかに超えたものだったことでしょう。
７１年前に、被爆し、
愛する家族や知人をなくし、
壮絶な苦痛を味わい、
最も憎いはずの国の大統領とも、笑顔で握手を交わし、抱き合える。
最も悲惨な出来事が起きても、人は許しあえ、未来を共に歩いていけるのだという、希望と可能性を感じました。
平和を願うたくさんの方が待ち望み、
実現に向けて、たくさんの方が奔走され、努力を積み重ねたからこそ、実現したこの日。
歴史的に残る一日だったと思います。
（お写真は、朝日新聞Webより引用）
叶うなら、原爆資料館の滞在時間がもう少しあれば・・・・という想いもないわけではありません。
長崎の被爆された方たちの想いも、いかばかりかと思います。
でも、「広島訪問」という実績だけが目的なら、さっさとスピーチと献花をし、立ち去ることも選択肢としてあったでしょう。
それでもオバマ大統領は、最初に原爆資料館を訪れ、自らが折った折り鶴を、小中学生に手渡されたそう。
原爆慰霊碑に花輪を捧げた時は、10秒ほど目を閉じられた。
５分という予定をはるかにこえた１７分のスピーチ。
さらに被爆者の方にも挨拶された。
短い時間で、できる限りを尽くしてくださったのだと思います。「謝罪」という形はなくとも、大統領の「心」が伝わってきました。
∵‥∴‥∵‥∴‥∴‥∵‥∴‥∵‥∴‥∴‥∵‥
●私たちは、変わることができる。
核保有国は、恐怖の論理からぬけ出す勇気をもち、核兵器のない世界を目指すべきです。
●すべての人命は、かけがえのないものです。
私たちは「一つの家族の一部である」という考え方です。
これこそが、私たちが伝えていかなくてはならない物語です。
●広島と長崎が核戦争の始まりとしてではなく、我々の道義的な目覚めの始まりだったといえる未来にしよう。
（大統領スピーチより、一部引用）
∵‥∴‥∵‥∴‥∴‥∵‥∴‥∵‥∴‥∴‥∵
このた「私たちは一つの家族の一部である」という言葉は、まさに地球ファミリーだなぁと感じました。
この表現が、特別なものではなく、当たり前のものなってほしい。
政治的背景はあると思いつつも、今回、日本側が謝罪を求めなかったことも、価値ある尊い選択だったと思います。
共同通信が事前に、広島・長崎で被爆された方に実施したアンケートでも、７８・３％が原爆投下への謝罪を求めないと回答されたのだそう。
日本という民族の懐の深さと品格を感じました。
執拗に、声高に、いつまでも謝罪を求めるより、無言で、静かに迎えたほうが、品位が感じられる。
そして、「知る」ことから始まると思うのです。
世界中の多くの方が、広島や長崎を訪問してくださることを願わずには、いられません。
『あなたが生きている今日は、
誰かが生きたくても生きられなかった一日。
かけがえのない今日という日を、大事に生きたい。』
この重みを、あたらめて、実感しました。
今日という平和な日は、
先人たちの尊い犠牲の上に成り立った奇跡の日。
未来の平和につなげていけるよう、７０億分の１から始めていこう。
最後に、昨年から何度もお伝えしているように、今年は「始まり」と「終わり」という節目が、いたるところで起こります。
日本の神域、伊勢でのサミットに続き、今回の広島も、日本のひとつの「終わり」と「始まり」なのでしょう。
この辺りのお話も、夏至の瞑想会でお届けしたいと思っています。
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私も私のできることを、私の居場所で、心をこめて。
お会いできる皆様、楽しみにしています。
鈴木真奈美
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PS：和訳と原文を引用させていただきます。
和文は若干、誤訳もありな気がしますが、響きます。
それ以上に原文は、一言一言に圧倒的な力を感じます。
（和文は、Huffingpostさん、英文はニューヨーク・タイムズ紙さんからの引用です。下部にリンクもはっていますので、よかったら）
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71年前の明るく晴れ渡った朝、空から死神が舞い降り、世界は一変しました。閃光と火の玉がこの街を破壊し、人類が自らを破滅に導く手段を手にしたことがはっきりと示されたのです。
なぜ私たちはここ、広島に来たのでしょうか？
私たちは、それほど遠くないある過去に恐ろしい力が解き放たれたことに思いをはせるため、ここにやって来ました。
私たちは、10万人を超える日本の男性、女性、そして子供、数多くの朝鮮の人々、10人ほどのアメリカ人捕虜を含む死者を悼むため、ここにやって来ました。
彼らの魂が、私たちに語りかけています。彼らは、自分たちが一体何者なのか、そして自分たちがどうなったのかを振り返るため、本質を見るように求めています。
広島だけが際立って戦争を象徴するものではありません。遺物を見れば、暴力的な衝突は人類の歴史が始まった頃からあったことがわかります。フリント（編注・岩石の一種）から刃を、木から槍を作るようになった私たちの初期の祖先は、それらの道具を狩りのためだけでなく、自分たちの同類に対して使ったのです。
富をもとめ、また民族主義や宗教的な理由からも悲惨な戦争が起こってきました。帝国が台頭し、また衰退しました。人々が奴隷になり、また解放の道もたどってきました。それぞれの歴史の転換点において、罪のない多くの人たちが犠牲になりました。その犠牲となった人たちの名前は、時が経つと忘れられました。それが人類の歴史であります。
第二次世界大戦は、広島と長崎で、とても残虐な終わりを迎えました。これまで人類の文明は、素晴らしい芸術を生み出してきました。そして偉大な思想や、正義、調和、真実の考えを生み出してきました。しかし、同じところから戦争も出てきました。征服をしたいという思いも出てきました。古いパターンが、新しい能力によってさらに増幅されました。そこには制約が働きませんでした。
ほんの数年の間に6000万もの人たちが亡く
りました。男性、女性、子供達。私たちと全く変わらない人たちです。撃たれ、殴られ、あるいは行進させられ、飢えさせられ、拘束され、またはガス室に送られて亡くなりました。
世界中には、この戦争の歴史を刻む場所が沢山あります。慰霊碑が、英雄的な行いなども含めて、色々なことを示しています。空っぽな収容所などが、そういうことを物語っています。
しかし、空に上がったキノコ雲の中で、私たちは人類の非常に大きな矛盾を強く突きつけられます。私たちの考え、想像、言語、道具の製作、私たちが自然とは違うということを示す能力、そういったものが大きな破壊の力を生み出しました。
いかにして物質的な進歩が、こういったことから目をくらませるのでしょうか。どれだけ容易く私たちの暴力を、より高邁な理由のために正当化してきたでしょうか。
私たちの偉大な宗教は、愛や慈しみを説いています。しかし、それが決して人を殺す理由になってはいけません。国が台頭し、色々な犠牲が生まれます。様々な偉業が行われましたが、そういったことが人類を抑圧する理由に使われてきました。
科学によって私たちはいろいろなコミュニケーションをとります。空を飛び、病気を治し、科学によって宇宙を理解しようとします。そのような科学が、効率的な殺人の道具となってしまうこともあります。
現代の社会は、私たちに真理を教えています。広島は私たちにこの真理を伝えています。技術の進歩が、人類の制度と一緒に発展しなければならないということを。科学的な革命によって色々な文明が生まれ、そして消えてゆきました。だからこそいま、私たちはここに立っているのです。
私たちは今、この広島の真ん中に立ち、原爆が落とされた時に思いを馳せています。子供たちの苦しみを思い起こします。子供たちが目にしたこと、そして声なき叫び声に耳を傾けます。私たちたちは罪のない人々が、むごい戦争によって殺されたことを記憶します。これまでの戦争、そしてこれからの戦争の犠牲者に思いを馳せます。
言葉だけで、そのような苦しみに声を与えるものではありません。しかし私たちには共有の責任があります。私たちは、歴史を真っ向から見据えなけれなりません。そして、尋ねるのです。我々は、一体これから何を変えなければならないのか。そのような苦しみを繰り返さないためにはどうしたらいいのかを自問しなくてはなりません。
いつの日か、被爆者の声も消えていくことになるでしょう。しかし「1945年8月6日の苦しみ」というものは、決して消えるものではありません。その記憶に拠って、私たちは慢心と戦わなければなりません。私たちの道徳的な想像力をかきたてるものとなるでしょう。そして、私たちに変化を促すものとなります。
あの運命の日以来、私たちは希望を与える選択をしてきました。
アメリカ合衆国そして日本は、同盟を作っただけではなく友情も育んできました。欧州では連合（EU）ができました。国々は、商業や民主主義で結ばれています。
国、または国民が解放を求めています。そして戦争を避けるための様々な制度や条約もできました。
制約をかけ、交代させ、ひいては核兵器を廃絶へと導くためのものであります。それにもかかわらず、世界中で目にする国家間の攻撃的な行動、テロ、腐敗、残虐行為、抑圧は、「私たちのやることに終わりはないのだ」ということを示しています。
私たちは、人類が悪事をおこなう能力を廃絶することはできないかもしれません。私たちは、自分自身を守るための道具を持たなければならないからです。しかし我が国を含む核保有国は、（他国から攻撃を受けるから核を持たなければいけないという）「恐怖の論理」から逃れる勇気を持つべきです。
私が生きている間にこの目的は達成できないかもしれません。しかし、その可能性を追い求めていきたいと思います。このような破壊をもたらすような核兵器の保有を減らし、この「死の道具」が狂信的な者たちに渡らないようにしなくてはなりません。
それだけでは十分ではありません。世界では、原始的な道具であっても、非常に大きな破壊をもたらすことがあります。私たちの心を変えなくてはなりません。戦争に対する考え方を変える必要があります。紛争を外交的手段で解決することが必要です。紛争を終わらせる努力をしなければなりません。
平和的な協力をしていくことが重要です。暴力的な競争をするべきではありません。私たちは、築きあげていかなければなりません。破壊をしてはならないのです。なによりも、私たちは互いのつながりを再び認識する必要があります。同じ人類の一員としての繋がりを再び確認する必要があります。つながりこそが人類を独自のものにしています。
私たち人類は、過去で過ちを犯しましたが、その過去から学ぶことができます。選択をすることができます。子供達に対して、別の道もあるのだと語ることができます。
人類の共通性、戦争が起こらない世界、残虐性を容易く受け入れない世界を作っていくことができます。物語は、被爆者の方たちが語ってくださっています。原爆を落としたパイロットに会った女性がいました。殺されたそのアメリカ人の家族に会った人たちもいました。アメリカの犠牲も、日本の犠牲も、同じ意味を持っています
アメリカという国の物語は、簡単な言葉で始まります。すべての人類は平等である。そして、生まれもった権利がある。生命の自由、幸福を希求する権利です。しかし、それを現実のものとするのはアメリカ国内であっても、アメリカ人であっても決して簡単ではありません。
しかしその物語は、真実であるということが非常に重要です。努力を怠ってはならない理想であり、すべての国に必要なものです。すべての人がやっていくべきことです。すべての人命は、かけがえのないものです。私たちは「一つの家族の一部である」という考え方です。これこそが、私たちが伝えていかなくてはならない物語です。
だからこそ私たちは、広島に来たのです。そして、私たちが愛している人たちのことを考えます。たとえば、朝起きてすぐの子供達の笑顔、愛する人とのキッチンテーブルを挟んだ優しい触れ合い、両親からの優しい抱擁、そういった素晴らしい瞬間が71年前のこの場所にもあったのだということを考えることができます。
亡くなった方々は、私たちとの全く変わらない人たちです。多くの人々がそういったことが理解できると思います。もはやこれ以上、私たちは戦争は望んでいません。科学をもっと、人生を充実させることに使ってほ
いと考えています。
国家や国家のリーダーが選択をするとき、また反省するとき、そのための知恵が広島から得られるでしょう。
世界はこの広島によって一変しました。しかし今日、広島の子供達は平和な日々を生きています。なんと貴重なことでしょうか。この生活は、守る価値があります。それを全ての子供達に広げていく必要があります。この未来こそ、私たちが選択する未来です。この未来こそ、核戦争の夜明けではないということを、そして私たちの道義的な目覚めであることを、広島と長崎が教えてくれたのです。
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The following is a transcript of President Obama’s speech in Hiroshima, Japan, as recorded by The New York Times.
Seventy-one years ago, on a bright cloudless morning, death fell from the sky and the world was changed. A flash of light and a wall of fire destroyed a city and demonstrated that mankind possessed the means to destroy itself.
Why do we come to this place, to Hiroshima? We come to ponder a terrible force unleashed in a not-so-distant past. We come to mourn the dead, including over 100,000 Japanese men, women and children, thousands of Koreans, a dozen Americans held prisoner.
Their souls speak to us. They ask us to look inward, to take stock of who we are and what we might become.
It is not the fact of war that sets Hiroshima apart. Artifacts tell us that violent conflict appeared with the very first man. Our early ancestors having learned to make blades from flint and spears from wood used these tools not just for hunting but against their own kind. On every continent, the history of civilization is filled with war, whether driven by scarcity of grain or hunger for gold, compelled by nationalist fervor or religious zeal. Empires have risen and fallen. Peoples have been subjugated and liberated. And at each juncture, innocents have suffered, a countless toll, their names forgotten by time.
The world war that reached its brutal end in Hiroshima and Nagasaki was fought among the wealthiest and most powerful of nations. Their civilizations had given the world great cities and magnificent art. Their thinkers had advanced ideas of justice and harmony and truth. And yet the war grew out of the same base instinct for domination or conquest that had caused conflicts among the simplest tribes, an old pattern amplified by new capabilities and without new constraints.
In the span of a few years, some 60 million people would die. Men, women, children, no different than us. Shot, beaten, marched, bombed, jailed, starved, gassed to death. There are many sites around the world that chronicle this war, memorials that tell stories of courage and heroism, graves and empty camps that echo of unspeakable depravity.
Continue reading the main story
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Yet in the image of a mushroom cloud that rose into these skies, we are most starkly reminded of humanity’s core contradiction. How the very spark that marks us as a species, our thoughts, our imagination, our language, our toolmaking, our ability to set ourselves apart from nature and bend it to our will — those very things also give us the capacity for unmatched destruction.
How often does material advancement or social innovation blind us to this truth? How easily we learn to justify violence in the name of some higher cause.
Every great religion promises a pathway to love and peace and righteousness, and yet no religion has been spared from believers who have claimed their faith as a license to kill.
Nations arise telling a story that binds people together in sacrifice and cooperation, allowing for remarkable feats. But those same stories have so often been used to oppress and dehumanize those who are different.
Science allows us to communicate across the seas and fly above the clouds, to cure disease and understand the cosmos, but those same discoveries can be turned into ever more efficient killing machines.
The wars of the modern age teach us this truth. Hiroshima teaches this truth. Technological progress without an equivalent progress in human institutions can doom us. The scientific revolution that led to the splitting of an atom requires a moral revolution as well.
That is why we come to this place. We stand here in the middle of this city and force ourselves to imagine the moment the bomb fell. We force ourselves to feel the dread of children confused by what they see. We listen to a silent cry. We remember all the innocents killed across the arc of that terrible war and the wars that came before and the wars that would follow.
Mere words cannot give voice to such suffering. But we have a shared responsibility to look directly into the eye of history and ask what we must do differently to curb such suffering again.
Some day, the voices of the hibakusha will no longer be with us to bear witness. But the memory of the morning of Aug. 6, 1945, must never fade. That memory allows us to fight complacency. It fuels our moral imagination. It allows us to change.
And since that fateful day, we have made choices that give us hope. The United States and Japan have forged not only an alliance but a friendship that has won far more for our people than we could ever claim through war. The nations of Europe built a union that replaced battlefields with bonds of commerce and democracy. Oppressed people and nations won liberation. An international community established institutions and treaties that work to avoid war and aspire to restrict and roll back and ultimately eliminate the existence of nuclear weapons.
Still, every act of aggression between nations, every act of terror and corruption and cruelty and oppression that we see around the world shows our work is never done. We may not be able to eliminate man’s capacity to do evil, so nations and the alliances that we form must possess the means to defend ourselves. But among those nations like my own that hold nuclear stockpiles, we must have the courage to escape the logic of fear and pursue a world without them.
We may not realize this goal in my lifetime, but persistent effort can roll back the possibility of catastrophe. We can chart a course that leads to the destruction of these stockpiles. We can stop the spread to new nations and secure deadly materials from fanatics.
And yet that is not enough. For we see around the world today how even the crudest rifles and barrel bombs can serve up violence on a terrible scale. We must change our mind-set about war itself. To prevent conflict through diplomacy and strive to end conflicts after they’ve begun. To see our growing interdependence as a cause for peaceful cooperation and not violent competition. To define our nations not by our capacity to destroy but by what we build. And perhaps, above all, we must reimagine our connection to one another as members of one human race.
For this, too, is what makes our species unique. We’re not bound by genetic code to repeat the mistakes of the past. We can learn. We can choose. We can tell our children a different story, one that describes a common humanity, one that makes war less likely and cruelty less easily accepted.
We see these stories in the hibakusha. The woman who forgave a pilot who flew the plane that dropped the atomic bomb because she recognized that what she really hated was war itself. The man who sought out families of Americans killed here because he believed their loss was equal to his own.
My own nation’s story began with simple words: All men are created equal and endowed by our creator with certain unalienable rights including life, liberty and the pursu
it of happiness. Realizing that ideal has never been easy, even within our own borders, even among our own citizens. But staying true to that story is worth the effort. It is an ideal to be strived for, an ideal that extends across continents and across oceans. The irreducible worth of every person, the insistence that every life is precious, the radical and necessary notion that we are part of a single human family — that is the story that we all must tell.
That is why we come to Hiroshima. So that we might think of people we love. The first smile from our children in the morning. The gentle touch from a spouse over the kitchen table. The comforting embrace of a parent. We can think of those things and know that those same precious moments took place here, 71 years ago.
Those who died, they are like us. Ordinary people understand this, I think. They do not want more war. They would rather that the wonders of science be focused on improving life and not eliminating it. When the choices made by nations, when the choices made by leaders, reflect this simple wisdom, then the lesson of Hiroshima is done.
The world was forever changed here, but today the children of this city will go through their day in peace. What a precious thing that is. It is worth protecting, and then extending to every child. That is a future we can choose, a future in which Hiroshima and Nagasaki are known not as the dawn of atomic warfare but as the start of our own moral awakening.
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生きとし生けるものが幸せにありますように。
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※恐れ入りますが、メルマガは届かなくても、個別に配信することはできかねますが、マグマグさんでも同様の内容を配信しています。
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