ヨハン・フリードリッヒ・ヘルバルト（Johann Friedrich Herbart, 1776-1841）は高名な哲学者イマニュエル・カントの後任としてケーニヒスベルク大学で教えた哲学者、心理学者、教育学者です。教育学では、特に、教師個人の経験や価値観にもとづくことの多い教育方法を科学的に体系化した人物として知られています。心理学でも、今日認知的無意識として言及される事柄の先駆けである心理学的な「閾値」の概念で有名です（教育学での知名度に比べるとあまり知られていないようですが）。ここで言う閾値というのは、当面意識にのぼっていないか忘れられているけれども心（記憶）の中には残っている事柄が、意識されるようになる境界線（閾：threshold）のことです。

そして彼もまた、ペスタロッチの影響を受けた人物です。家庭教師 ー と言うと学生のアルバイトのように聞こえますが、当時の学者・知識人にはよくあった職業です ー をしていた子どもたちを連れてペスタロッチの学校を訪れたことがありますし、初の著書は『ペスタロッチの直観のABCの理念』（Pestalozzi’s Idee eines ABC der Anschauung, 1804年：是常正美訳, 1982年）というものです。

このように、理論的にかなり重要な人物で、アメリカでも日本でも、ペスタロッチ主義が教師の技能を基礎づける理論として導入され、流行した後、ヘルバルト主義がそれに代わって導入されています。

教師の技能の基礎というのはこういうことです。教師というのは、昔、読み書きをいくらかできる素人の職業であるとか、農作業のような力仕事や兵役をこなせない、いわゆる使い物にならない男性の職業と見なされていました。その後、19世紀に公教育が普及すると、男性より安上がりな女性の職業とされるようになりましたが、どちらにせよ、専門的知識を要しない職業と考えられていたのです。

（余談ですが、アメリカで教職が女性の職業と見なされるようになる前の時代の一番の有名人教師が、ワシントン・アービングの小説『スリーピー・ホロウ（, 1820）』に出てくるイカボッド・クレイン Ichabod Crane でしょう。Headless Horseman に追っかけられて逃げ帰った人です。下のイラストもご覧ください。）

このような状態にあった教職に専門性を与える知識体系（今日の教職課程で言うと、教科に関する科目ではなく教職に関する科目を思い浮かべてもらうといいです）を提供し、少し大げさな言い方をすると、教師に専門家（プロフェッショナル）としての誇りと自信を与えたのがペスタロッチ主義でありヘルバルト主義です。 

The Headless Horseman Pursuing Ichabod Crane (1858) 

by John Quidor

ヘルバルト主義の内容について主要な点を少し挙げると、教育の目的を倫理学に、方法は心理学に求めるという主張と、「明瞭ー連合ー系統ー方法」として知られる４段階教授法（後にヘルバルトに学んだ人たちによって改良が加えられて、５段階教授法となりました）でしょうか。ちなみに、教育学の授業では、「そろそろお腹が減るバルト」というダジャレも常套句です。

一世を風靡したヘルバルト主義ですが、ペスタロッチ主義のオブジェクト・レッスンが単なる手順のように形式化してしまったのと同様、ヘルバルト主義の４段階教授法ものちに形式主義の批判を受け、衰退しました。ただし、教育の科学的基礎を探求するという部分は継承され、例えばアメリカのヘルバルト学会（the National Herbartian Society）は 教育学会（the National Society for the Study of Education）に発展的に解消されます。ここには例えばジョン・デューイなども所属していました。

さて、以下の部分には、このブログで扱っているアメリカのペスタロッチ主義に関連する限りにおいてですが、ヘルバルト主義についての私のメモを少しだけご紹介します。

まず、教育の目的は倫理学にという点と、閾値の理論に関連する文章です：

“According to Herbart, the chief aim of education is moral character. But instruction cannot be subdivided into intellectual and moral education because the soul itself is not divisible into faculties. New experiences are perceived and assimilated to old ideas, the so-called apperception mass. Since knowledge is not innate, however, the teacher must instill proper interests. These aims can be realized through organizing instruction through according to these [five] steps [of clearness, association, system, method, and correlation]” (Dorothy Rogers, Oswego: Fountainhead of Teacher Education: A century in the Sheldon Tradition, 1961, p.12)

この引用、四角カッコ内はロジャースの本の記述にしたがって私が補いました。ヘルバルトの４段階教授法とは「明瞭ー連合ー系統ー方法」です。後に弟子のツィラーやラインといった人たちによって５段階に改良され、「予備ー提示ー比較ー総括ー応用」となっていますが、ロジャースの説明ではこれがちょっとごっちゃになっているような気もします（大した問題ではないかもしれませんが）。５段階の英訳は通常、 ① preparation, ② presentation, ③ association and comparison, ④ generalization or abstraction, ⑤ practical application です。

スタンフォードのオンライン哲学辞典には、こんな風にまとめられています：

“Herbart writes:

The sole and entire task of education [Erziehung] is encompassed by the concept, “morality” [Moralität]. 

If virtue is the realization of human freedom, then the goal of Herbartian education is to make the child capable of living virtuously, viz., by forming the pupil’s character. For reasons that will become clearer below, Herbart identifies moral character with a “many-sided” character. Many-sidedness is a regulative ideal guiding one’s striving towards full individuality: the teacher helps the pupil develop all his unique talents and interests as far and as coherently as possible. That is, the teacher helps the pupil systematically connect his interests around the central principle that is his self.”

＊引用元の情報や注は消してあるので、上のリンクでご確認ください（ちなみに、このStanford Encyclopedia of Philosophy というのはかなり役に立つ、よくまとめられている資料です）。

ヘルバルト主義が教授学の科学的基礎を提供したという点について、アメリカの教師教育（教員養成校）の歴史を書いたオグレンは、こう言っています：

“…Herbartianism systematized psychological theories into concrete approaches to teaching based on engaging and fostering children’s interests” (Christine A. Ogren, The Am
erican State Normal School, 2005, p.131).

なぜオスウィーゴの校史にこれが書かれているかというと、オスウィーゴはペスタロッチ主義だけでなく、フレーベルの幼稚園やヘルバルト主義を導入するのについても先駆的だったからです。なので、上に引用したロジャースはこういっています：

“Oswego, therefore, became one of the first schools to emancipate itself from the movement it had started.” (Rogers, pp.12-3)

けれど、以下の引用にあるように、ヘルバルト主義のアメリカの中心地はイリノイ師範学校です：

“The “Oswego Method” dominated normal schools until 1880 and was replaced by Herbartianism, which emanated from the Illinois Normal University, for the remainder of the century.” (Richard J. Altenbaugh and Kathleen Underwood, “The Evolution of Normal Schools,” in John I. Goodlad et al. Eds., Places Where Teachers Are Taught, 1990, p.140)

そしてイリノイには校長の John W. Cook、さらに教員として Charles McMurry、 Frank McMurry、 Charles DeGarmo がいました。いずれもアメリカのヘルバルト主義の大物です。

オスウィーゴの創設者シェルドンなどは、ペスタロッチ主義からヘルバルト主義への転換を特に問題とはしなかったようです。同じくロジャースはちょっと皮肉な口調でこう言っています：

“As far as Sheldon was concerned, the only heresy to any chosen doctrine was to follow it simply because it was chosen. Anyway, the problem of reorganization was less severe than it seemed. It was easy to switch from the formal procedures of Pestalozzianism to the equally formal Herbartian steps in teaching a lesson.” (Rogers, p.13)

ただし、村山英雄の指摘によれば、ヘルバルト教育学はペスタロッチほどの影響はオスウィーゴに与えなかったようです。（『オスウィーゴー運動の研究』, 1978, p.333）

上のような評価もしているロジャースですが、ヘルバルト主義は教授法の科学的基礎に目を向け、学習（学問）についての最新の知見を学校教育に適用した功績はあるものの、オスウェーゴのオブジェクト・レッスンに好意的な見方をすれば、児童の興味を刺激し開発するという意味では後退で、児童を見落としてしまったと評しています(Rogers, p.80)。上のオグレンとは評価がわかれていますね。

ヘルバルト主義が形骸化したという点については、オグレンはこう言っています：

“Like object teaching, Herbartianism ran the risk of becoming overly formulaic. Normal’s Cook reflected, “That Herbartianism becomes dogmatic is the real danger.” But he asserted, “If we start with the determination that the child shall have a clear intellectual life all of the time and that he shall not be sacrificed to the gods of stupidity by immersing him in formal work, the whole trouble will end.” Although the trouble did not end as normal schools at times oversimplified the five formal steps, Herbartianism helped to infuse teaching methods with an element of psychological theory. While these developments had a huge impact on practical preparation for teaching, they also encouraged further empirical research in educational psychology.” (Ogren, pp.131-2)

教授法に対する貢献だけではなく、当時勃興しつつあった教育心理学や児童研究（child study：クラーク大学のスタンレー・ホールなどが有名です）にもつながったということです。

ヘルバルトの書いたものはカントの系列に連なる人のものらしく難解で、特に数学的な話が出てくると私の手には負えないところがあるのですが、それでも、教育理論を学ぶのであれば、ある程度は避けて通れない重要な思想家です。ペスタロッチ主義の研究をするにしても同じで、ここに書いたメモだけでも、このことはある程度は伝わるのではないでしょうか。

主な内容（予定）

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

再生核研究所声明 427(2018.5.8): 神の数式、神の意志　そしてゼロ除算

NHKスペシャル　神の数式番組を繰り返し拝見して感銘を受けている。素晴らしい映像ばかりではなく、内容の的確さ、正確さに、ただただ驚嘆している。素晴らしい。

ある物理学の本質的な流れを理解し易く表現していて、物理学の着実な発展が良く分かる。

原爆を作ったり、素粒子を追求していたり、宇宙の生成を研究したり、物理学者はまるで、現代の神官のように感じられる。素粒子の世界と宇宙を記述するアインシュタインの方程式を融合させるなど、正に神の数式と呼ぶにふさわしいものと考えられる。流れを拝見すると物理学は適切な方向で着実に進化していると感じられる。神の数式に近づいているのに　野蛮なことを繰り返している国際政治社会には残念な気持ちが湧いて来る。ロシアの天才物理学者の終末などあまりにも酷いのではないだろうか。世界史の進化を願わざるを得ない。

アインシュタインの相対性理論は世界観の変更をもたらしたが、それに比べられるオイラーの公式は数学全般に大きな変革をもたらした：　

With this estimation, we stated that the Euler formula

$$

e^{\pi i} = -1

$$

is the best result in mathematics in details in：　No.81, May 2012 (pdf 432kb)

余りにも神秘的な数式のために、アインシュタインの公式 E= mc^2　と並べて考えられる　神の意志　が感じられるだろう。　ところで、素粒子を記述する方程式とアインシュタインの方程式を融合したら、　至る所に1/0 が現れて　至る所無限大が現れて計算できないと繰り返して述べられている。しかしながら、数学は既に進化して、1/0=0　で無限大は　実はゼロだった。　驚嘆すべき世界が現れた。しかしながら、数学でも依然として、rがゼロに近づくと　無限大に発散する事実が有るので、弦の理論は否定できず、問題が存在する。さらに、形式的に発散している場合でも、ゼロ除算算法で、有限値を与え、特異点でも微分方程式を満たすという新しい概念が現れ、局面が拓かれたので、数学者ばかりではなく、物理学者の注意を喚起して置きたい。

物理学者は、素粒子の世界と巨大宇宙空間の方程式を融合させて神の方程式を目指して研究を進めている。数学者はユークリッド以来現れたゼロ除算1/0と空間の新しい構造の中から、神の意志を追求して　新しい世界の究明に乗り出して欲しいと願っている。いみじくもゼロ除算は、ゼロと無限大の関係を述べていて、素粒子と宇宙論の類似を思わせる。

人の生きるは、真智への愛にある、すなわち、事実を知りたい、本当のことを知りたい、高級に言えば　神の意志　を知りたいということである。　そこで、我々のゼロ除算についての考えは真実か否か、広く内外の関係者に意見を求めている。関係情報はどんどん公開している。　ゼロ除算の研究状況は、

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　関連情報がある。

以　上

ゼロ除算の論文が２編、出版になりました：

ICDDEA: International Conference on Differential & Difference Equations and Applications
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
• Editors

• (view affiliations)
• Sandra Pinelas
• Tomás Caraballo
• Peter Kloeden
• John R. Graef
Conference proceedingsICDDEA 2017

log0=log∞=0log⁡0=log⁡∞=0 and Applications
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305

Division by Zero Calculus and Differential Equations
Sandra Pinelas, Saburou Saitoh
Pages 399-418

2017年11月15日(水)
テーマ：

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

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

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

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

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

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

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

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

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて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 v
alues 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.

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 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 

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.

Einstein’s Only Mistake: Division by Zero

 

#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

 

Institute of Economics for Humans

The 《 Renaissance of Economics 》by reassessing ” An Inquiry into the Nature and Causes of the Wealth of Nations ” and “The Theory of Moral Sentiments”

<The 1^st report> (Total three reports)

<The first half>

＜Dark Ages of Economics after the death of Adam Smith＞

Adam Smith’s works had a quite large influence over the modern society.

In fact, most self-professed “economists” and “economic experts” have called themselves Adam Smith’s successor.

However, those so-called successors did not understand properly what Adam Smith meant. They interpreted it to suit their purpose distorting the true meaning and spread their theories around the world.

Not to mention the Marxian economics the theory of which was already “over”, the modern economics overuses meaningless mathematical formulae to confuse people.

No need to argue the uselessness of Marxian economics, when we look at the miserable situation of many countries around the world controlled by the Communist Party with Marxist theory. There isn’t any single successful case.

As to capitalist countries (developed countries), we have never heard that “the modern economics made conspicuous contribution to the development of a national economy”. Rather, “economic forecasts” or “policy proposals” are no different than oracles delivered by a shaman.”  They are like fortune-telling, far less accurate than predictions of earthquake.

Economics after Adam Smith was in a miserable situation comparable to that of the Dark Ages absolutely ruled by the Church (Catholic Church and its factions) after the great prosperity of Greece and Rome.

In the Dark Ages, the great scientific and rational spirit in Greece and Rome was lost and the cult-like Christianity dominated and brainwashed people with violence (including burnings and tortures).

＜Freed by Renaissance＞

Fortunately the “Renaissance” that started from Italy in the 14th century and continued until about the 16th century gave us a clue to get out of the dark era.

But, even in the 18th century when Smith lived, inquisitions were often held, and the victims of cruel torture by the Church, dismemberment and burning existed.

At such a time, it was a very courageous act that Smith wrote and published this book based on rational and scientific spirit. Although we should succeed this valuable property properly, its contents were distorted and passed down to us, as I mentioned above.

It was just like people was forced to believe “the Ptolemaic system” by the Church in Europe in the Middle Ages, although the “Copernican theory” was a matter of course in the Greek Roman age.

In the economics after Adam Smith, just like “the Ptolemaic system “, the belief that “godlike scholars and politicians” will make the economy in good shape prevailed. Of course such idea is wrong.

They are no different from ordinary human beings. The correct “Copernican theory of economics” is that “no one can arbitrarily control complicated events (Complexity) such as an economy or society”

Fortunately, recent developments in natural science, the development of communication means such as the Internet has made it possible to check the correctness of the “Copernican theories of economics and society” by experiments.

Research on Self-similarity, Phase transition, Criticality, Fluctuation, Delay, evolution theory, biology, behavioral economics , etc., not to mention Complex system are greatly contributing to prove the correctness of the “Copernican theories of economics”

Also, the development of the Internet has enabled to record “connections among people” as communication data, which have been invisible to date, and to play a very important role in scientific verification.

We can now perform quite easily social experiments which used to require a large amount of money and labor at low cost.

<Economy and society which should be understood as “movies” rather than “still pictures”>

”An Inquiry into the Nature and Causes of the Wealth of Nations” (Hereinafter referred to as “The Wealth of Nations”) is famous for Adam Smith’s book, today. But, “The theory of Moral Sentiments” had far more influence on the world then.

Before the details of “connection among people, i.e. “network”, are revealed by the Internet, Smith recognized the importance of “network” with his unique observing eyes. In other words, he explained clearly the mechanism and functions of a society and economy by the word “sympathy” in the “The Theory of Moral Sentiments”

“Sympathy” is a quite ingenious means of network connecting the human brains, and society moves in the direction that this network points by itself.

For example, snow or sand grains accumulate to a certain “critical point” beyond which they cause avalanches. In human society, too, when “sympathy through the network of brains exceeds a critical point, suddenly (social) change will happen. In other words, social and economic movements are caused by transmission of “sympathy”, a network system of human brains. They are not controlled by a specific social policy or by a great person.

If it looks so, it is just a coincidence.

From Sir Isaac Newton to Albert Einstein and Niels Henrik David Bohr (the quantum theory), natural scientists have studied the nature as if they take snap shots of phenomena in the world. But it is only a moment of constantly changing real world like a movie, just like a “frozen world” in a SF movie in which time is halted.

It’s necessary to watch “movies “to understa
nd the real moving world. In other words, “flow of time”, i.e. “history”, is an important part of this Renaissance.of Economics.

Today’s science, such as Complex system Similarity, the birth and growth of living creatures, evolution and genetic alternation are now stepping into the theme of “flow of time”, i.e. “history”. And that is also the tailwind for the “Renaissance of Economics”.

I will discuss here the “true meaning” of two voluminous work of Adam Smith, i.e. “The Wealth of Nations” and “The Theory of Moral Sentiments” which are the origin of the “Renaissance of Economics”, taking into account of its actual situation.  .

First of all, we will discuss “The Wealth of Nations” below.

(End of the first half  To be continued to the latter part)

(Responsibility for the wording of this article lies with : Hiroshi Ohara)

こんにちは。今日はkritikと呼ばれる議論がそもそもどういうものなのかを、自分なりの理解とともにここに記します。

初っぱなから注意書なのですが、kritikという言葉は、アメリカにおいてad/da,cp,Tのどれにも当てはまらない議論を総称して言っている感じがすると証言する方もいる程度に曖昧な使われ方をすることがあり、今回解説するkritikは主に否定側がーー肯定側も多少論点を追加する必要があるにせよ、強力な武器として使うことができると私は考えていますがーー使う、メタディベート的な視点を含んだ議論であるとここで断っておきます。当然、ここでのべられる”kritik”が全てではないことを承知の上で読んでください。ただ、最近のNDTのブリーフをネットで入手して眺めていると、kritikと称されるものはだいたい以下で解説するような議論であることが多いです。

なお、アメリカアカデミックディベートの原稿や資料、情報の入手は以下のサイトがおすすめです。

:原稿などが検索できます

:原稿や資料が検索でき、ディベーターの意見交換掲示板も閲覧/書き込みできる。

:あっちの代表的なディベートブログらしい。たしかに色々おもしろいことが書いてありそう。

Google検索:見てみたい原稿に入っていそうな語句とfiletype:docという呪文とをセットで検索にかければ、わりとブリーフがでてきて研究材料を集められる。また、著名なディベート理論家の名前でpdf検索をするとセオリーの文献にもあたれる。

Roger Solt “Demystifying the Critique” より

The judgments we come to at the end of debate rounds may only be provisional, based on the evidence and arguments in that round, but overtime the sum of our provisional judgments is what ultimately constitutes our moral and
political belief system. 
Policy debates are important. As citizens in a democracy, we have individually small but collectively large inputs into the policies our government chooses. As future decision makers or opinion leaders, the judgments about policy which debaters come to may be especially important.
試合の最後にたどりつく判定は試合中の資料と議論に基づく仮初めのものでしかないだろうが、時を重ねるにつれて積み重なったジャッジングは最終的に、道徳や政治の信条を構成することになる。政策ディベートは大事なのだ。民主主義に生きる市民として、我々一人ひとりは小さな存在だが、それが集まれば政府の選ぶ政策に大きな影響を与える。ディベーターがたどり着く政策についての判定は、将来の政策決定者もしくはオピニオンリーダーとしてのことを考えると、特に大切だろう。

Gordon Mitchell “Pedagogical possibilities for argumentative agency in academic debate” より
While an isolated academic space that affords students an opportunity to learn in a protected environment has significant pedagogical value (see e.g. Coverstone 1995, p. 8-9), the notion of the academic debate tournament as a sterile laboratory carries with it some disturbing implications, when the metaphor is extended to its limit. To the extent that the academic space begins to take on characteristics of a laboratory, the barriers demarcating such a space from other spheres of deliberation beyond the school grow taller and less permeable. When such barriers reach insurmountable dimensions, argumentation in the academic setting unfolds on a purely simulated plane, with students practicing critical thinking and advocacy skills in strictly hypothetical thought-spaces.
保護された環境下で学ぶ機会を学生に与えられる、隔離されたアカデミックな空間は重大な教育的価値を持つ。しかしその一方で、滅菌された実験室としてのアカデミックディベート大会という概念は、その考え方が限界に達したときにいくらかの混乱をもたらす。学術的な空間が実験室としての特性を持てばその分、そのような空間を学校外の他の討論スペースから区別する壁は、より厚くなり、透過性が低くなる。この壁が乗り越えられないほどのものになると、アカデミックディベートの議論は世間から隔絶された純粋なシミュレーションの場として浮世離れし、学生は、まさしく仮説的であるといえる思考の下でクリティカルシンキングや議論の技法を実践することになる。
Although they may research and track public argument as it unfolds outside the confines of the laboratory for research purposes, in this approach, students witness argumentation beyond the walls of the academy as spectators, with little or no apparent recourse to directly participate or alter the course of events (see Mitchell 1995; 1998). 
彼らはリサーチを通して、実験室の外に広がる公的な議論を調べるかもしれない。しかしこのアプローチでは、学生は実験室の壁の向こうの議論を観客として眺めるにとどまり、実際の世界のできごとに直接参加したり、それを変えようとすることはほぼない(Mitchell 1995; 1998)。
The sense of detachment associated with the spectator posture is highlighted during episodes of alienation in which debaters cheer news of human suffering or misfortune. Instead of focusing on the visceral negative responses to news accounts of human death and misery, debaters overcome with the competitive zeal of contest round competition show a tendency to concentrate on the meanings that such evidence might hold for the strength of their academic debate arguments. For example, news reports of mass starvation might tidy up the “uniqueness of a disadvantage” or bolster the “inherency of an affirmative case” (in the technical parlance of debate-speak). Murchland categorizes cultivation of this “spectator” mentality as one of the most politically debilitating failures of contemporary education: “Educational institutions have failed even more grievously to provide the kind of civic forums we need. In fact, one could easily conclude that the principle purposes of our schools is to deprive successor generations of their civic voice, to turn them into mute and uncomprehending spectators in the drama of political life” (1991,p. 8).
この観客的なスタンスと関係をもつ「隔絶」の感覚
は、「ディベーターは他人の苦しみや不幸についてのニュースを望むものだ」というディベーターの現実からの乖離を語るエピソードで強調される。トーナメントにおける競争の熱気にやられたディベーターは、死や惨劇のニュースに我々誰しもが感じる否定的な感情に注目せず、そのようなエビデンスがディベートの試合においてもつだろう意味に注目する傾向を示す。例えば、大量飢餓のニュースは「デメリットの固有性」を整理したり、（ディベート用語で言うところの）「ケースの内因性」を強化したりするだろう。Murchlandはこの「観客」的スタンスを、政治の衰退を招く現代教育の最大の失敗の1つに分類する。「教育機関は、我々にとって必要な市民フォーラムを作れなかった。その失敗の仕方は悲惨だ。事実、我々の学校教育の主な目的は、次世代の人間から市民としての声を奪い、彼らを黙ったままで、なにも理解しない政治演劇の観客にすることだと言えてしまうだろう。」

Hahn,Hahn,Hobeika　”Finding Your Voice: A Comprehensive Guide to Collegiate Policy Debate” より

Kritiks were developed by debaters and coaches frustrated by the limitations of policy debate. They were looking for a way to investigate the resolution beyond asking if the Affirmative case was better than the status quo. This led first to radical counterplans, such as the anarchy counterplan, which endorsed the disbanding of the federal government. These counterplans expanded the strategic options available to Negative teams, but were also very susceptible to permutations because they still embraced a policy-making approach. Kritiks became a separate argument when they began to address the philosophical assumptions within a debate. This refocused the debate round from a place to analyze specific policies to a deliberation about the act of debate and policy making.

クリティークは政策ディベートの限界に不満を覚えたディベーター、コーチの手によって発展した。肯定側のケースが現状維持よりも望ましいのかという問いを超えたような論題の探求の仕方を彼らは探していた。これによって、まず初めに、連邦政府の解散を支持するアナーキーカウンタープランのようなラディカルなカウンタープランが生まれた。このようなカウンタープランは否定側が使用可能な戦略の選択肢に育ったが、それらがいまだ政策形成のアプローチであったためにパーミュテーションにとても弱かったというのもまた事実であった。そこで彼らがディベートに潜む哲学的な前提に切り込み始めたとき、クリティークは[政策の議論から]分離された議論になった。これはディベートの試合を、特定の政策を分析する場所としてではなく、ディベートや政策形成の行われ方について審議する場所として捉え直したのである。

William Shanahan “kritik of thinking”

Policy is not choking debate. An inflexible, narrowly defined vision of policy threatens debate. Not all transit cops hate graffiti artists.

政策がディベートを息苦しくするのではない。凝り固まっていて、狭い定義をうけた政策観がディベートを脅かすのだ。交通警察全員がグラフィティアーティストを嫌っているわけではな�
��のと同じだ。

シチュエーション:差別を扱う論題で、相手チームが常識的には許されないレベルの差別的発言を含みながら1回目の立論のスピーチをした。

目標:それに対して自分たちの2回目の立論でKritikというかたちで異議を申し立て、それをvoterにすること。

この状況で目標を達成するために議論を作っていってみましょう。

1.まず、彼らの発言のどの部分をいまから問題にするのか、それを明確に指摘する必要があります。まあ、当たり前です。

1. Link…Kの対象にしたい相手の部分を明確に指摘します。例)言語K(発言に関する上記のようなK)における「manという言葉はジェンダーフリーではない」という指摘や、資本主義K(背後にある資本主義的思考を批判するK)における「持続可能な開発という概念は、環境への配慮をにおわせて実際は資本主義を礼賛している」という指摘など。
2. Impact/Implication…指摘された部分が悪影響をもたらすことを説明します。例)言語Kにおける「性差別語は女性の抑圧を生む」という議論や、資本主義Kにおける「資本主義がある限り地球環境は持続しえない。滅亡あるのみ。」という議論など。
3. Alternative…その代わりにどうしたらよいのか、その代わりにどう考えていけばよいのかを提示します。例)言語Kにおける「性差別語を排除することで女性抑圧的構造を1つ1つ解体していける」という議論や、資本主義Kにおける「とりあえず資本主義を排除することで闘いの道が拓かれる」という議論など。
4. Framework…kritikをなぜpolicyの議論よりも優先すべきなのかの説明。これはジャッジのパラダイムを政策形成パラダイムから別のパラダイムに移行させていると言えるかもしれません。

kritik自身はLink,Imp,Altの3要件を満たせば成立するというのが一般的な見解のようです。それをどう�
��価するべきかというFramewrokの議論はKと密接な関係をもっているにしても、どうも見ているとKそのものからは独立して扱われている感覚を受けます。AD/DAの議論とD-rule(判定基準)の議論とが別物であるとする感覚に近いイメージかもしれませんね。

ところでKの種類はいくつかあります。

さきほど例として用いた、発された言葉を対象に仕掛けるkritikをlanguage/rhetoric kritik──言語kritikと呼びます。個人的にこの名前はイマイチなんじゃないかと思うときがあります。「言語」というのはlanguageを訳したものだと思うのですが、「発話」とかのほうが個人的にはしっくりきます。

また、相手の議論の背後に隠れた価値観を対象として仕掛けられるkritikはvalue kritik──価値kritik──と呼ばれます。先ほどのcapitalism Kなんかはこれに分類されるのでしょうか。

他にもdebate kritikやthinking kritikというのもあります。これらはとても興味深いです！！

Hahn,Hahn,Hobeika　”Finding Your Voice: A Comprehensive Guide to Collegiate Policy Debate” より

Kritiks of debate challenge community assumptions about rules and standards by examining the role or potential role of marginalized arguments and voices in the debate round or community.

ディベートkritikは、試合やディベートコミュニティで周縁化される議論、声がもつ役割もしくは潜在的役割を考えることでルールやスタンダードについてのコミュニティの前提に異議を唱える。

このkritikについては以下の記事がイメージをつかむのにいいかもしれません。

The Atlantic “Hacking Traditional College Debate’s White-Privilege Problem”

アメリカ人のNDT関係者に聞いたのですが、アメリカにおいてアカデミックディベートは資源がモノを言う世界だそうです。リサーチは豊富なデータベースがあると圧倒的に有利だし、コーチの手腕も関わってくる。お金があれば遠征もたくさんできるしうんぬんかんぬん。そんなこんなで向こうのアカデミックディベートは白人エリート階級が特権を享受できる場所である(あった?)ようです。そんな状況だからこそ、上のようなタイプのKが出現し、さらには勝利をつかむのでしょうね。正確なところは分からないので間違っているかもしれませんが、2013年にNDTとCEDAの両方で優勝した(!!)EmporiaのElijah SmithとRyan Washのチームは、おそらくこのKを使っていたのではないでしょうか。彼らについては、その名前で検索をすればたくさんの情報が手に入れられます。

William Bennett “AN INTRODUCTION TO THE “KRITIK”” より

Thinking kritiks challenge the way participants construct and/or systemize their reasoning. This type of kritik sometimes challenges the framework or structure of debate (e.g.,by arguing for the narrative or storytelling approach to competition). Other examples include challenges to rational thought, and challenging the validity of the western world view as proper premise for debate.

議論法kritikは、試合をしている人間が議論を構築したり体系化したりする方法に異議を唱える。この種のkritikは時に、ディベートのフレームワークや構造に抗議する(例えば、語りやストーリーテリングで試合にアプローチすることを論じることなどによってそれはなされる)。理性的な考えや、ディベートにおいて適切な前提とされる西洋的な世界観の妥当性といったものに反対することも例として含まれる。

Thinking kritikを思考kritikと訳すのはなんだか違う気がしてしまったので、適当に訳してしまいました。すいません。なお、narrativeの原稿なんかは冒頭で紹介したcircuitdebaterで検索すると簡単に見つかります。とても面白いのでおすすめです。

このようにいろいろなKがありますが、大切なのはおそらく「政策ディベートを放ったらかしてまで主張したいこと」を見つけてくることだと思います。それさえ見つけてきて重要さをきちんと説明できれば、どんなものやどんな視点もkritikというかたちでディベートにぶつけることができるのではないかと思います。kritikはpolicy makingの体裁で掬いきれなかった声を掬う道具だとも言えると私は思っています。だからあまり分類にはこだわらないで、違和感を覚えたらそれが何であっても──rhetoricだろうとvalueだろうとthinkingだろうと──そんなことは気にせずにkritikにすればいいのではないでしょうか。実際、「きみがディベートをしているときになにか変だと感じたら、kritikの出番だ！」と英語で書かれているのをどこかで見ました。

さて、今回はそろそろこの辺で切り上げます。

altとframeworkについては先ほどの説明では個人的に不十分だと思うので、より詳しい説明を次の記事に掲載します。

というわけで次回は

altとframeworkについての自分なりの詳解

今回の大会で使用したkritikの観察/解説

肯定側がkritikに対してできる反論についての一般論

今回の大会で使用したkritikに対して肯定側ができる反論の考察

をがんばってしてみようかなと思っています。拙い文章で申し訳ありません。では。

Clothes form wordless introductions. If every man on the planet were to wear the same set of clothes, the world would consist of only one man or one kind of man. Clothes levy illusions of the body and carry them against a looseness of conscience. Clothed, he holds neither disparity nor similarity. Nudity resolves the valid human confusions.

A man without clothes is a disarmed man. A nude body is not a store house, it is a garage sale. Conditions are temporary and circumstantial; identity is unique and the unachieved whole.

by Tushar Jain. To know a man by what overlaps his skin, is to arrest him by his condition rather than his identity. A body is its element. Nudity cannot make man perceptible.

The first human walked naked on earth, says the bible. We must not fear our shells, and we must fear without them.

Partial nudity is similar to partial blindness. Nudity doesn’t provide one; correction: doesn’t need one. However, it is not the ideal. A man without judgment is so too. Hence, it bears an exaggeration of surface. 

Topically, it is redeemed as Fashion. But the Bible can be wrong. Nudity is not superficial, clothing is. If every man on the planet were to walk naked, we might still not have a perfect world, but surely a world less precious. Neither is significant to a wordless introduction. The flesh is where the harvest is. It works against their united cause.

Man is imperceptible. Beauty is a compromise on that demand. Nudity is the greatest opportunity that yields the nearest possibility to human perfection. Anything superficial allows manipulation. Inspite of which there is neither chaos nor dissatisfaction. I am wrong. Hence, it has a surface.