変わる質量の定義＝鴨志田公男

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奇抜なデザインが楽しいレスザンヒューマン。おしゃれアイテムにぜひ。

 

ラッセル × ゲーデル数学の哲学について

 

数学や論理学についての規約主義が信じられている間は、ゲーデルの「プラトニズム」など、検討される余地もなかった。数学的対象が我々の私意や理論とは無関係に（我々が知ろうと知るまいと）「客観的に」実在するなどということは、たとえ数学者の「実感」としてはそうであっても、そこに「数学の哲学」が成立するなんてことは考えられもしなかった。論理実証主義者たちが「形而上学」と切って捨てたどれよりも、すごぶるナンセンスであり、ある種の「信仰」告白をすませ色眼鏡で見られることも辞さない覚悟なにには、口にすることだってはばかられる「神学上の命題」と思われたのだ。
　論理実証主義者は、武器を持っていた。あの偉大なる先達たちラッセル＆ホワイトヘッドが、数学の体系を組み立ててみせたあの方法だ。我々の直感的対象であるかにみえた、自然数や単純な演算でさえも、彼らは「一から」作ってみせた。我々は記号使用の規則にしたがって、いまや全数学体系を構成することができる。数学的対象はあらかじめ存在している必要などない（余計なことだ）。むしろ規約の運用の結果（それは数学を行うこと、組み立てることだ）、はじめて浮かび上がってくるのが、数学的対象なのだ。
　ところが、規約は完全には定義されない。記号を他の記号で定義することはできる。それがラッセルたちがやった仕事のすべてだ。けれども全部の記号をそのようにして、定義することはできない。他の定義には用いることができても、それら自身は定義されない「原初記号」を我々は受け入れなければならない。受け入れるだけでなく（いや、「受け入れる」ということがそれだけでもう）、その運用法を定義された訳でない「原初記号」の使い方を我々は暗黙のうちに知っていなければならないのだ。つまるところ、規約主義は原理的に貫徹することは不可能であり、数学を構成してみせようという時に、あれほど嫌っていた直観や飛躍を必要としてしまうのである。我々は「一から」始めることはできても、「ゼロから」始めることはできないのだ。
　規約主義もまた、自らの足だけでは立つことができず、最終的にどこか論理や規約の外のものに頼らざるを得なかった。なれば、ゲーデルの信じた「数学的対象のプラトニズム」を、我々は「天下り的」と笑うことはできなくなる。規約主義にしろ、何にしろ、我々の作る論理体系は、「天下り的」である他ないからだ。
　たとえばゲーデルの立場からすれば、ラッセルがパラドクスに対処するため採用したロジカル・タイピングは、無用の長物に見えるだろう。いわゆる悪循環原理を採用する根拠は、数学的対象を「構成」しようとするラッセルにはあっても、はなっから数学的対象は実在するというゲーデルにはない。ゲーデルにいわせれば、ラッセルの対処法は、あまりに構成主義的な偏見に満ちている、ということになる。
　我々はまたしても、哲学者たちが長年に渡って経験し、１９世紀の化学者たちが「分子論」を受け入れる際に投げ込まれた、唯名論と実念論の戦いの最中にいる。かつて化学者のある者にとっては、「分子」なるものはただ理論を簡便にするための「便宜」にすぎなかったし、またある者にとってははっきりとした「実在」にちがいなかった。化学者同士の戦いに終止符を打ったのは、ブラウン運動を解明する理論と実験であった。
　数学的対象は、数学記号についての規約の運用によって構成されるにすぎないしろもの（ようするにコトバ）なのか、あるいは我々の数学的言説とは何の関係ももたない（少なくとも言説に影響されたりしない）形で客観的に実在するのか。数学（論理学）に関して、我々はこれらの考えのどちらを（あるいはもっと多くの選択肢からどれを）選ぶのか、どれよりどれが優れていると判断するのか、についての決定的根拠（ブラウン運動の理論や実験のような）を持っていないし、また持てそうにない。逆にいえば、このような事情の自覚こそ、真正な意味で「数学の哲学」のはじまりなのである。

 

 

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

 

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 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 r
eally 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 R
ay 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.

 

私は数学を信じない。　アルバート・アインシュタイン / I don’t believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。1423793753.460.341866474681。

 

Einstein’s Only Mistake: Division by Zero

 

#divide by zero

TOP 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

 

by  February 15, 2010

 

A cool article to understand humans who control TBS ‘s press department, making incredibly incoherent editing, extremely bad biased coverage of the TBS (Mainichi Broadcasting) program of the previous chapter, It is in the topic interview feature by Ms. Yoshiko Sakurai and Mr. Naoki Hyakuta of the monthly magazine WiLL released on the 25th, ‘Japan, regain the history!’

Preamble abridgment.

‘Spirit remodeling’ of GHQ to Japan

Orishima

After the US presidential election in 2016, the fairness of the press has become a worldwide problem as the word ‘fake news’ by President Trump has become a hot topic.

Even in Japan, unilateral criticism of the Abe administration of major media, public opinion manipulation by intentional editing, etc. are rampant.

Alright, when did such biased coverage come to be done?

Hyakuta

I am writing about Japanese history now.

The fact that I realize that I am studying again is that the Japanese ‘spirit remodeling’ by GHQ still has a lasting effect.

Sakurai

The occupation policy of GHQ was unprecedentedly harsh in world history.

Hyakuta

The mind of the Japanese was destroyed by ‘War Gilt Information program’ (masochistic thought) planting sense of atonement.

The American Education for Japan thought education took in the brainwashing know-how that the Chinese Communist Party gave to the prisoners of Japan and the Kuomintang at Yan’an and Nosaka Sanzo also cooperated with the occupation policy of GHQ.

Especially the press code was bad.

A total of 30 items ‘Japanese should not write’ to Japanese newspaper publishers and publishers, for example, criticism of the GHQ, the Allied Powers and the Tokyo Trial were strictly forbidden.

Moreover, criticism of Koreans was forbidden for some reason, too.

Sakurai

We should not say that the Constitution was made by the United States and we were also prohibited from promoting nationalism, so we could not look at Japan obediently.

Of course, we should not reveal the existence of the censorship system itself.

Hyakuta

Besides censorship, a burning book was also held.

They disposed thoroughly unfavorable publication for the Allied Powers at libraries and university museums.

Speaking of burning books, it is famous for history by Qin Shin Emperor and Nazis.

This is the worst cultural destruction, history destruction.

Sakurai

America has dyed hands the same way.

The United States, which says freedom of speech, thought and belief, applied full double standards to Japan.

Eto Jun was the one who pointed out that thing properly.

Hyakuta

Over 7 thousand books were forfeited, those who resist ‘Please leave it as an important document’ was harsh, being sentenced to imprisonment for ten years or less.

In Article 10 of the Potsdam Declaration, it is written that ‘The Government of Japan must promote democracy. Freedom of speech, religion and thought, and respect for fundamental human rights must be established.’

This is a violation of the obvious ‘Potsdam Declaration’ beyond mere double criteria.

Distorted learning

Sakurai

The expulsion of public officials was also terrible.

Because more than 200 thousand people who were assigned the important office, including the government office, were unable to work.

Hyakuta

Ichiro Hatoyama on the verge of being appointed prime minister was also expelled from the public office.

Even those who are not convenient for GHQ will be disposed of even by the Prime Minister candidate, much more ordinary people cannot speak much bad.

Especially, it was the educational circle that was terrible.

Sakurai

Excellent professors of Tokyo University and Kyoto University were also disposed of in large quantities.

Hyakuta

Prior to the war, anarchists and owner of revolutionary thought had been kicked out of the imperial university.

However, after the war, they returned to the teacher one after another finding favor with GHQ, and soon eventually dominated university education.

That idea has penetrated even higher and secondary education, and it reaches now.

Sakurai

There were cases where scholars who had a decent idea turned to change to be loved by GHQ.

A typical example is Toshiyoshi Miyazawa, a constitutional scholar.

Hyakuta

He was critical of the Constitution of Japan and the Constitution of Japan was said to be a ‘pressing constitution’ by GHQ.

However, witnessing the appearance of colleagues purged by GHQ, he changed his thought completely.

Sakurai

It has changed by a hundred and eighty degrees.

Hyakuta

The ‘August Revolutionary Theory’ was started to argue newly.

Briefly, acceptance of the Potsdam Declaration in August 1945 is a kind of revolution, at that time Japan changed from sovereignty of the Emperor to national sovereignty.

In other words, the idea that the Constitution of Japan is the right Constitution made possible by the revolution.

Sakurai

Mr. Miyazawa kept reigning at the top of the Tokyo University Constitutional Course since then.

Hyakuta

In a vertical society university, Miyazawa Constitution Studies will be handed over ‘Thankful words’ by assistant professors and assistant.

In fact, it seems that the University of Tokyo still teaches that the August Revolution theory is correct.

Judging from the fact that the August Revolution theory is also a common theory in the judicial examination, I cannot deny that the JFBA has become a strange organization.

‘Entry Elite’ who entered the University of Tokyo by entrance exam with only memorization let them study such outrageous theory.

Whether it is the Treasury Department or the Ministry of Education, the bureaucrats who are making noise news will surely come from the University of Tokyo law department.

Because they cannot think that things by themselves, ‘pretending to obey but secretly betraying’ and say it is only possible to pull the legs of politics.

Sakurai

A lot of bureaucrats who do not consider the national interest are seen also in the Ministry of Foreign Affairs.

Hyakuta

Another person I would like to introduce is Yokota Kisaburo.

He is also an authority of the university of Tokyo Faculty of Law, but continues to say that the Constitution of Japan is not pressing, and during the occupation it is also issuing a book called ‘Emperor System’ that advocated abolition of the Emperor System.

However, in the later years, when appointed Chief Justice of Japan, he gathered the pupils and purchased his books at an old book store in Kanda for disposal.

‘Indeed, the abolition of the Emperor System was unfavorable’ he thought.

So, I cannot find his book quite easily.

Sakurai

It has done without thinking being ashamed of the horrible thing, too.

What distorted academics is nothing but a tragedy.

The apostasy of the Asahi Newspaper

Hyakuta

If you turn backwards, that is how tightening of GHQ was strict.

Losing your job in Japan, then the poorest country in the world, is literally involved in life and death.

Sakurai

For the people who were expelled, it was such a terrible situation that they were thrown away by the abyss of living or dead in the sense that families had to cultivate.

Hyakuta

Another thing I would like to say is that the civil service bureau of GHQ, who led the expulsion of public office, cannot have enough people to list over 200,000 Japanese.

So, who was it that helped with this?

Sakurai

It is Japanese.

In cooperation with GHQ, there was a Japanese who banished the Japanese.

Hyakuta

Socialists and communists used opportunities of purge of public office to eliminate political enemies.

Even within the company, there seems to be a lot of cases in which the boss and his co
lleague were kicked off and the career was promoted.

* Mr. Takayama Masayuki taught that many Chongryon officials got jobs including NHK, had taken advantage of the mess after the war,

The reason why they, or their descendants, still dominate NHK, TV Asahi, TBS etc. is probably due to chasing down as above *

This draft continues.

El inmortal Leonardo

Con motivo de la publicación de dos libros sobre Leonardo da Vinci, Sánchez Ron aborda la obra del artística y científico, una de las mentes más creativas de la historia. “Nadie superó su polivalencia combinada con imaginación y creatividad en grado superlativo”, señala el académico.

Autorretrato (h. 1513) recogido en la biografía de Leonardo da Vinci de Walter Isaacson (Debate)

La mayor parte de las personas que han dejado una huella profunda en la historia de la humanidad, lo hicieron solo por una habilidad. En la ciencia tal “unicidad” se refiere a si trabajaron únicamente en una de sus diversas disciplinas, o a si fueron científicos teóricos o experimentales. Pocas veces los grandes científicos lo fueron en más de una especialidad, o simultaneando los dominios de la teoría y la experimentación. Entre las excepciones figuran  y Enrico Fermi, físicos que brillaron en ambas disciplinas. Newton sería recordado como uno de los grandes matemáticos de la historia aunque nunca hubiera escrito una línea sobre física. En sus escasos 53 años de vida, Fermi realizó contribuciones fundamentales a la física nuclear teórica y experimental (dirigió, por ejemplo, los trabajos que condujeron a la producción en 1942 de la primera reacción nuclear autosostenida; es decir, que producía tanta energía como la que se necesitaba para mantener el reactor en funcionamiento).

Salvando todas las diferencias que haya que salvar, no conozco grandes músicos que sobresalieran como pintores, escultores o escritores. Y pocos de éstos últimos -, eximio escultor y pintor, además de brillante arquitecto, es una de las excepciones- se distinguieron en artes que no fueran aquella por la que les recordamos. Si añadimos la ciencia a este grupo de materias, una excepción que merece la pena recordar es el caso de William Herschel, quien comenzó en Alemania una carrera musical, brillante aunque no extraordinaria, que lo llevó a Inglaterra, donde se convirtió en el mejor constructor de telescopios del mundo (con uno de ellos, descubrió Urano en 1781, el primer planeta del Sistema Solar identificado desde la antigüedad).

Pero si pienso en polivalencia, una polivalencia combinada con imaginación y creatividad en grado superlativo, nadie supera a  (1452-1519). Su virtuosismo como pintor lo iguala, si no supera, a los grandes de la pintura de todos los tiempos, los , Vermeer, , , … Pero fue mucho más que eso. Se adentró, bien con experimentos, reflexiones teóricas o elucubraciones, en prácticamente todos los campos de la ciencia y la tecnología de su época, y de las venideras. Dejó para la posteridad un variado, extenso y, con frecuencia desordenado, conjunto de anotaciones (en su escritura especular, más fácil tal vez para un zurdo) y maravillosos dibujos referentes a disciplinas como la mecánica, la anatomía, la botánica, la zoología, la arquitectura, la hidrodinámica, la aeronáutica y la tecnología. Es oportuno recordarlo una vez más porque se acaban de publicar dos magníficos libros sobre él: la biografía Leonardo da Vinci (Debate), de Walter Isaacson, y Leonardo da Vinci. El libro del agua (Abada), compuesto (editado no me parece en este caso la palabra justa) por  y . Isaacson tiene detrás de sí un reducido, pero notable, bagaje de biografías; cercana en el tiempo es la muy celebrada que dedicó a , recomendable pero inferior a la de Albrecht Fölsing, que desgraciadamente solo está disponible en alemán e inglés, y es también autor de otras de , Benjamin Franklin y Henry Kissinger. Esta de Leonardo es, de las que conozco, la mejor que existe sobre él. Entre sus virtudes se encuentra que permite comprender bien la dimensión científica de Da Vinci, a quien en ocasiones se ha considerado como un diletante, como alguien que se dejaba dominar por su desbordante imaginación y que suplía -al menos para la posteridad- sus carencias científicas mediante el atractivo de sus dibujos. Es preciso, sin embargo, no caer en el mayor pecado en el que se puede incurrir cuando se estudia el pasado: el anacronismo, el juzgar basándonos en lo que sabemos ahora. En este sentido, no es demasiado justa la aseveración de Isaacson cuando escribe: “La devoción de Leonardo hacia la experiencia iba más allá de la mera susceptibilidad ante su falta de cultura. También le llevó, al menos al principio, a minimizar el papel de la teoría. Como observador y experimentador por naturaleza, carecía de los conocimientos y de la preparación necesaria para enfrentarse a conceptos abstractos. Prefería la inducción a partir de los experimentos”. Cierta esa preferencia, justificada por otra parte porque ¿qué conceptos abstractos podía tener en cuenta? ¿Los de la física de Aristóteles, con sus movimientos naturales y forzados? En tiempos de Leonardo la ciencia del movimiento simplemente no existía; básicamente, la estableció Galileo casi un siglo después de la muerte del autor de la Mona Lisa. Y si nos detenemos a considerar sus estudios anatómicos, comprobamos cuánto se adelantó a su tiempo: hizo lo que reclamó Andrés Vesalio en 1543 en un libro justamente considerado capital, estudiar directamente el cuerpo humano mediante disecciones, algo que ciertamente no había hecho el gran Galeno, quien adjudicaba a la anatomía humana huesos que únicamente aparecían en monos. Como reconoce Isaacson, Leonardo pudo haberse adelantado a Vesalio.

Aunque se preparó para componerlo, no existió nunca El libro del agua que Lanceros y Barja han (re)creado en base a las muchas anotaciones y dibujos que dejó Leonardo. Y es una lástima -una más- porque el asunto, el agua, todavía considerada entonces uno de los cuatro elementos primordiales, junto a aire, fuego y tierra, lo merecía. Leonardo realizó muchos experimentos en ese campo, que ahora denominamos hidrodinámica, y en otra disciplina relacionada, la física del aire. Asimismo, se planteó muchas preguntas netamente científicas (la ciencia, debería ser ocioso recordarlo, progresa también de esta manera). Así, en El libro del agua, Leonardo “describe cómo las nubes se condensan e, igualmente, cómo se dispersan, y por qué se alza el vapor de agua de la tierra al aire; y habla sobre las causas de las nieblas y sobre el porqué del aire denso; y de por qué el aire nos parece algunas veces más azul y otras menos”. El porqué el aire es azul es algo que solo la física cuántica permitió entender realmente en el pasado siglo XX. 

 

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

 

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

 

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

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�
��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 h
ard 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.