あなたのLESS THAN HUMANライフをサポートします！
CNN 10
The Upcoming Talks Between the U.S. and North Korea; Tributes Being Paid to Former First Lady Barbara Bush; The Challenges Posed By Plastics
Aired April 19, 2018 – 04:00 ET
THIS IS A RUSH TRANSCRIPT. THIS COPY MAY NOT BE IN ITS FINAL FORM AND MAY BE UPDATED.
CARL AZUZ, CNN 10 ANCHOR: Never before has a sitting U.S. president met with the sitting leader of North Korea. But with plans for a meeting in the works, CNN 10 starts today by explaining how it could come together and what`s changed between the two rival countries to make it possible.
First, U.S. President Donald Trump said earlier this week that discussions about the meeting had been happening at, quote, very high levels. The White House says the president hasn`t directly spoken to North Korean dictator Kim Jong Un, but President Trump says CIA Director Mike Pompeo, who`s also the president`s pick to be the next secretary of state, met with Kim in North Korea on Easter weekend.
So, the ground works are being laid for a face-to-face meeting of the two countries` leaders, and that could be held in late May or early June. But where?
President Trump said five places are being considered. He didn`t give specifics, but other U.S. government officials have suggested several possibilities, including the nations of Mongolia, Singapore, or Malaysia, a natural European country, a South Korean island, the demilitarized zone between North Korea and South Korea, or even a ship at sea.
Wherever the meeting may be, the big goal for the U.S. is to get North Korea to give up its nuclear weapons program, which is illegal as far as the United Nations is concerned. The goals for North Korea could include international recognition and relief from the sanctions put on the country for its nuclear program. But there`s still doubt about how sincere the Asian country is.
(BEGIN VIDEOTAPE)
REPORTER: There`s been a lot of change happening between North Korea and the world recently. So, how did we get here?
It started with a speech. New Year`s Day 2018, North Korean leader Kim Jong-un signaled he`d be willing to send athletes to the Winter Olympics in the South. Just six weeks later, they were there, competing, in some cases, as one thing, marching under one flag. Then, there were talks between the North and the South, the highest profile in years. And then this —
CHUNG EUI-YONG:, SOUTH KOREAN NATIONAL SECURITY CHIEF: President Trump officiated the briefing and said he would meet Kim Jong-un by May.
REPORTER: Putting in motion a potential meeting between Kim Jong-un and U.S. President Donald Trump.
So, what changed?
WILL RIPLEY, CNN INTERNATIONAL CORRESPONDENT (via telephone): This would have been unthinkable last year, when North Korea was launching missiles and testing nuclear devices.
REPORTER: That`s Will Ripley, an international correspondent with CNN who`s reported from North Korea more than a dozen times.
RIPLEY: Now, there`s been this breathtaking about-face. Kim Jong-un wants to stay in power for many decades to come and in order to do that, he feels that right now, the best course of action is diplomacy and that`s what we`re seeing him do.
REPORTER: Sanctions impacting trade also seemed to be playing a big role, especially with China on board.
LISA COLLINS, CENTER FOR STRATEGIC AND INTERNATIONAL STUDIES (via telephone): According to reports coming out of China, and the border between China and North Korea, the trade between the two countries has been decreasing over the last several months and most people attribute that to sanctions.
REPORTER: Lisa Collins is a political analyst specializing in Korean relations. Perhaps that explains this, an unprecedented visit by Kim Jong-un to Beijing, his first known trip out of North Korea since becoming leader in 2011.
RIPLEY: As quickly as things have changed in this direction, we always to keep in mind, they can change any other direction as well. We have seen this movie play out in the past, when North Korea has opened up after time (INAUDIBLE) tension, diplomacy has looked very promising and then the situation has spiraled back downward.
REPORTER: Does Kim want more bargaining or more money flowing into North Korea? It`s hard to say. Maybe both.
One thing that there`s no question about is that North Korean relations have changed. The next question is, whether they will last?
(END VIDEOTAPE)
AZUZ: Across the U.S., people are remembering and honoring a former first lady. Barbara Bush passed away Tuesday at age 92. She was the wife of the 41 president, George H.W. Bush, and the mother of the 43rd president, George W. Bush. She`d been fighting COPD, a lung disease, as well as congestive heart failure. But despite, Mrs. Bush stayed active in her last years, raising money for charity and continuing her legacy of promoting literacy.
Current and former elected officials laid politics aside to praise Mrs. Bush. President Donald Trump, a Republican, and former President Barack Obama, a Democrat, recognized the Republican first lady for her work and her character.
Abigail Adams, who died in 1818, was the only other woman to have been both the first lady and the mother of a president.
(BEGIN VIDEOTAPE)
SUBTITLE: Barbara Bush: “The Enforcer”.
Barbara Bush was the second woman in history to be both a wife and a mother to a U.S. president.
BARBARA BUSH, FORMER FIRST LADY: If anyone can beat, I want to see it.
SUBTITLE: She met her husband, future President George H.W. Bush, at a dance in 1941. They married in 1945.
BUSH: I married the first man I ever kissed. You talk about a bore, I am the world`s worst.
SUBTITLE: She gave birth to future President George W. Bush shortly after.
While her husband built his career, she raised five children.
In 1966, George H.W. Bush was elected to his first political position.
Twenty-three years later, Barbara Bush became first lady of the United States.
INTERVIEWER: You`ve been speaking out a bit more than you did in the past. I notice (INAUDIBLE). You talked about Saddam Hussein as a dreadful man.
BUSH: Well, he`s a dreadful man. I don`t feel that`s controversial.
SUBTITLE: While she was first lady, she founded the Barbara Bush Foundation for Family Literacy.
BUSH: They were lima beans for dinner and I hate limas.
SUBTITLE: She was also an advocate for women`s health issues.
Her children nicknamed her “The Enforcer” for her tough responsibility.
BUSH: Instead of complaining about the problems we have, why not get in and try to solve some of them?
(END VIDEOTAPE)
(BEGIN VIDEO CLIP)
AZUZ (voice-over): Ten-second trivia:
Polyethylene terephthalate is a form of what?
Glass, amino acid, artificial flavor or plastic?
Also known as PET, polyethylene terephthalate is a widely used form of plastic.
(END VIDEO CLIP)
AZUZ: PET, because I don`t want to say that whole term again, is used to make everything from clothing and tennis balls to shampoo bottles and
especially water bottles. It`s inexpensive and lightweight. It`s strong and it doesn`t shutter. But it also doesn`t break down quickly in the environment. Scientists believe that can take centuries.
In 2016, researchers found the type of bacterium that does eat PET and they utilize it to make an enzyme that breaks down plastic even faster. This could help engineers better recycle plastics or get rid of them altogether before they become trash. In the meantime, we`re looking at the effects plastics have when they are thrown away and what we can do to use less of them.
(BEGIN VIDEOTAPE)
REPORTER: Plastic is big business and it`s a big threat to our environment. We produce about 300 million tons of it every year. The most popular things we make are things like these.
But of all the plastic ever created only 9 percent has been recycled, which means a lot of it ended up in a dump and our natural environment. In fact, eight millions tons of plastics is dumped into our oceans every year. By 2050, there will be more plastic than fish in our waters.
But the same durability that makes plastic so useful also makes it a danger to our marine environment. This stuff takes years to break down, and as it does, it can end up in the food chain where
it releases harmful toxins contaminating fish that we ourselves eat, though at this point, scientists don`t know exactly what eating contaminated fish does to human body. What we do know is that there are ways to help keep plastic from ending up in the dumps and our oceans in the first place.
Here are five things you can do to use less plastic:
Cut out plastic straws. Use stainless steel or card ones instead.
Bring a reusable carry bag with you, instead of relying on plastic ones.
Packed meals in reusable containers.
Invest in reusable bottles for drinks, instead of using plastic bottles or takeaway cups.
And here`s the surprising one, stop chewing gum. It`s made of synthetic rubber, which is a type of plastic.
So, remember, your plastic picks can make a change.
(END VIDEOTAPE)
AZUZ: Tumbleweeds, dried up parts of plants that detached and roll over wind swept landscapes are iconic elements of the American West. But this is ridiculous y`all. Victorville, California, has become a real life tumbleweed town. Powerful winds blew them in by the hundreds, stocking tumbleweeds so high in some places that residents called city officials to ask for help in getting rid of them. Someone even reportedly got trapped at home until the tumbleweeds were removed.
It`s nothing to chafe at. People looking to branch out from the city, put down roots near the desert, thinking thistle be a place to call home. But if some folks amaranth like the wind from the tumbleweed takeover, planting the plant themselves or somewhere else, you can see why it`s certainly no desert rose.
I`m Carl Azuz for CNN 10.
END
LESS THAN HUMANの冒険
偽証罪で告発するにはいくつかのハードルが存在しているものの、佐川氏喚問のより詳しい検証と分析を行なうことは重要！
「明らかに偽証罪の疑いがある」として、野党間で詳しく内容を分析していることを明らかにしました。
このまま国会デモが大きくなり続け、
School Scandal May Get Japan’s PM Expelled — Can Abenomics Survive Without Abe?
6/20 #森友 学園が国有地を値引価格で購入
2017年
2/9 朝日新聞報道で土地取引にアベ関与の疑い
2/17「関与あれば辞任する」とアベ発言
2/27 昭恵が名誉校長辞任
4/21 森友が破綻
7/31 籠池夫妻逮捕
9月 解散総選挙
2018年
3/2 財務省が森友文書改竄と朝日報道
3/7 土地取引実務担当職員が自殺
公約を果たしていないアベノミクスも消えるだろう、と
日本の報道の自由度がアベの首相就任後に11位から74位に転落したこと、アベが特に森友問題をスクープした朝日新聞を敵対視していることも伝えています
「私や妻が関わっていたら総理も議員も辞める」から記事を書き出してる。
している。
【有本香】みのもんたのよるバズ! 2018年3月31日
このサイトはLESS THAN HUMANの集団会議
“The Country and the City” by Raymond Williams
Chapter 16: Knowable Communities
Contents: As a brilliant survey of English literature in terms of changing attitudes towards country and city, Williams’ highly-acclaimed study reveals the shifting images and associations between these two traditional poles of life throughout the major developmental periods of English culture. (from Amazon)
（完全に自分用の勉強メモ。Some class stuff. Let’s just get right to it then. ）
・”Most novels are in some sense knowable communities. […] the novelists offers to show people and their relationships in essentially knowable and communicable ways”(165) (reminds me of my grad school interview at the Univ. of Tokyo where the profs asked me about the significance of the fact that both flat and round characters are present in a same novel. I remember answering something about novels being various models of a community or a society that they respectively present.)(I could’ve added some stuff from this chapter, this ‘looking at a novel as a community’ type of thinking. Just a hindsight.)
・A contrast between the fiction of the city and the fiction of the country: “In the city kind, experience and community would be essentially opaque; in the country kind, essentially transparent.”(165)
・”The growth of towns and especially of cities and a metropolis; the increasing division and complexity of labour: in changes like these any assumption of a knowable community – a whole community, wholly knowable – became harder and harder to sustain” (165) (and this is also how the mystery genre develops – because of this kind of anonymity, partly.)
・”…But this is not the whole story […] we must be careful not to idealise the old and new facts of the country” (165) (OK, I take that point.)
・”What we have then to see, in the country writing, is not only the reality of the rural community; it is the observer’s position in and towards it; a position which is part of the community being known.”(165)
・”visible” country community: but it’s still “a matter of consciousness and of continuing as well as day-to-day experience” “In the village as in the city there is division of labour, there is the contrast of social position, and then necessarily there are alternative points of view.”(166)
・Jane Austen’s knowble community = face-to-face. The grammar of her morality. It is as an actual community very precisely selective. To be fact-to-face in this world is already to belong to a class. (166)
・”For just as the difference between Jonson and Crabbe is not the historical arrival of the poor labourious natives but a change in literary beaerings which allows them suddenly to be seen, so the difference between Austen and Eliot, and between both and Hardy, is not the sudden disintegration of a traditional rural order a but a change in literary bearings which brings into focus a persistent rural disturbance that had previously been excluded or blurred.” (166)
・Eliot’s Adam Bede:: setting = at the turn of the 18c to 19c (Austen’s time). →”Jane Austen had been prying and analytic, but into a limited group of people in their relations with each other. The analysis is now brought to bear without the class limitation; the social and economic relationships, necessarily, are seen as elemets, often determining elements, of conduct.” (167)
・Still about Adam Bede: Characteristically, Eliot represents the farmers and craftsmen mainly through speech; they are present audibly as a community. “In to a novel still predicated on the analysis of individual conduct, the farmers and craftsmen can be included as country people, but much less significantly as the active bearers of personal experience.” (168) “A problem in the social consciousness as a writer” (“her coneections with the farmers and craftsmen, her connections as Mary Ann Evans”) (my prof was saying that it’s rather unfair to judge like that.)(there’s much more to think about in regards to such representations made)
・gonna skip ahead a bit
・”The proble of the knowable community is then, in a new way, a problem of language.
“(171)
・Eliot “Emphasis as a class feeling” (172)
・”Eliot has gone further than Crabbe and yet is more self-conscious, more uneasily placating and appealing to what seems a dominant image of a particular kind of reader. The knowable community is this common life which she is glad to record with a necessary emphasis; but the known community is something else again – an uneasy contract, in language, with another interest and another sensibility.” (172-173)
・”Eliot’s novels are transitional between the form which had ended in a series of settlements, in which the social and economic solutions and the personal achievements were in a single dimension, and the form which, extending and complicating and then finally collapsing this dimension, ends with a single person going away on his own, having achieved his moral growth distancing or extrication.” (175)
・The complications of the inheritance plot → Wuthering Heights.
It takes the crisis of inheritance at its full human value, without displacement to the external and representative attitudes of disembodied classes. (176) →The complication of the plot is then sustained by a single feeling, which is the act of transdescence. ↔Eliot (a more critically realist world)
・Next, about Eliot’s attitude towards the rural past (177－178)
・”A valuing society, the common condition of a knowable community, belongs ideally in the past.” (nostalgia) “But the real step that had been taken is withdrawal from any full response to an existing society.” (ouch, this stings a bit.)(180)
・”The development that matters in the English novel is […] to the novels of Hardy” (181)
LESS THAN HUMAN あたらしい ふつうをつくる。
ればならない。 アダムにあってすべての人が死んでいるのと同じように、キリストにあってすべての人が生かされるのである。 ただ、各自はそれぞれの順序に従わねばならない。最初はキリスト、次に、主の来臨に際してキリストに属する者たち、」
る。 しかし感謝すべきことには、神はわたしたちの主イエス・キリストによって、わたしたちに勝利を賜わったのである。 だから、愛する兄弟たちよ。堅く立って動かされず、いつも全力を注いで主のわざに励みなさい。主にあっては、あなたがたの労苦がむだになることはないと、あなたがたは知っているからである。
、また、それは他の聖書のバージョン,版で翻訳されているように「幽霊」ではないと言ったのではなく、むしろ彼は肉と骨の、ある種のなにか超自然の体を持っていました。彼イエスは食べ、彼らと一緒に飲むような、ある種の天然の機能だけでなく、彼は壁を歩いて通り抜けるような、特定の超自然的な機能を実行する事ができました。
家にはいられた。 一緒に食卓につかれたとき、パンを取り、祝福してさき、彼らに渡しておられるうちに、 彼らの目が開けて、それがイエスであることがわかった。すると、み姿が見えなくなった。
LESS THAN HUMANは今月もトップ10ランキング入り、他店にはない商品を扱うレアもの専門店です
This Might Be The Biggest Misconception About Science
f you really want to teach someone something, starting with a misconception and working backwards is one of the best techniques.
A new video from Veritasium does just that.
In the episode, host Derek Muller debunks one of the most common misconceptions about science – namely, that science is simply a steady, gradual way of accumulating knowledge.According to Thomas Kuhn, author of The Structure of Scientific Revolutions, this conventional view of science isn’t entirely accurate.
Instead, Kuhn proposes two different types of science. The first is normal science, which is the slow, steady progression of ideas that most people associate with science.
The second, however, is called revolutionary science, and it’s entirely different from what we commonly imagine science is.
Most scientists work within normal science, but when an anomaly pops up, or the study doesn’t really fit into the pre-existing paradigm, scientists must turn to revolutionary science.
Before Copernicus, for instance, we thought Earth was the center of the universe, with other stars and planets revolving around it. Then Copernicus came along and suggested that maybe Earth was just another planet that revolved around the sun.
You’d think that everyone would see the logic of Copernicus’ idea straight away, but that wasn’t how it all shook out.
By the time Copernicus built his theory, the older Ptolemaic model of the universe had existed for so long and had been refined so much that it actually created better predictions than the Copernican model.
As a result, it took a long time for scientists to abandon their pre-existing paradigm and subscribe to Copernicus’ revolutionary new model.
“That’s what I call revolutionary science,” said Muller.
“That’s a period where our entire notions of the Universe change.”
This article was originally published by .
Science As Fact is our sister site where we cover politics, debunking, fact checking, and humour. If you want more like this, head over to .
ゼロ除算の発見は日本
テーマ：
The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.
Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.
It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.
Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.
It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).
Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.
Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.
I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for
the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.
ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。
An Early Reference to Division by Zero C. B. Boyer
OUR HUMANITY AND DIVISION BY ZERO
Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/
5000年？？？？？
2017年09月01日(金)NEW !
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0 0 ¼ 0 ) 0 1=1 ¼ 0 ) 0 1 ¼ 0 1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0 0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T
とても興味深く読みました：
10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.
For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and in
genious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.
Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…
Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.
RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?
PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.
RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.
PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.
RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?
PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.
RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.
PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.
RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?
PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.
再生核研究所声明 424(2018.3.29): レオナルド・ダ・ヴィンチとゼロ除算
次のダ・ヴィンチの言葉を発見して、驚かされた：
ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在
我々の周りにある偉大なことの中でも、無の存在が最も素晴らしい。その基本は時間的には過去と未来の間にあり、現在の何ものをも所有しないというところにある。この無は、全体に等しい部分、部分に等しい全体を持つ。分割できないものと割り切ることができるし、割っても掛けても、足しても引いても、同じ量になるのだ。
レオナル
ド・ダ・ヴィンチ。ルネッサンス期を代表する芸術家、画家、彫刻家、建築技師、設計士、兵器開発者、科学者、哲学者、解剖学者、動物学者、ファッションデザイナーその他広い分野で活躍し「万能の人（uomo universale：ウォモ・ウニヴェルサーレ）」と称えられる人物
そもそも西欧諸国が、アリストテレス以来、無や真空、ゼロを嫌い、ゼロの西欧諸国への導入は相当に遅れ、西欧へのアラビヤ数字の導入は レオナルド・フィボナッチ（1179年頃～1250年頃）によるとされているから、その遅れの大きさに驚かされる：
フィボナッチはイタリアのピサの数学者です。正確には「レオナルド・フィリオ・ボナッチ」といいますが、これがなまって「フィボナッチ」と呼ばれるようになったとされています。
彼は少年時代に父親について現在のアルジェリアに渡り、そこでアラビア数字を学びました。当時の神聖ローマ皇帝・フリードリヒ2世は科学と数学を重んじていて、フィボナッチは宮殿に呼ばれ皇帝にも謁見しました。後にはピサ共和国から表彰もされました。
ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大きな数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（
historicalmathematicians.blogspot.com/2012/03/blog-post.html 02/03/2012 -）
ゼロや無に対する恐怖心、嫌疑観は現在でも欧米諸国の自然な心情と考えられる。ところが上記ダ・ヴィンチの言葉は 如何であろう。無について好ましいものとして真正面から捉えていることが分かる。ゼロ除算の研究をここ４年間して来て、驚嘆すべきこととして驚かされた。ゼロの意味、ゼロ除算の心を知っていたかのような言明である。
まず、上記で、無を、時間的に未来と過去の間に存在すると言っているので、無とはゼロのことであると解釈できる。ゼロとの捉え方は四則演算を考えているので、その解釈の適切性を述べている。足しても引いても変わらない。これはゼロの本質ではないか。さらに、凄いこと、掛けても割っても、ゼロと言っていると解釈でき、それはゼロ除算の最近の発見を意味している: 0/1 =1/0=0。－ ゼロ除算を感覚的に捉えていたと解釈できる。ところが更に、凄いことを述べている。
この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：
{\bf Fruitful world}\index{fruitful world}
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For example, in very and very general partial differential equations, if the coefficients or terms are zero, we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we see the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall \index{Yamane phenomena}Yamane phenomena, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.
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{\bf From $0$ to $0$; $0$ means all and all are $0$}
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As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.
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その意味は深い。我々はゼロの意味をいろいろと捉え考え、ゼロとはさらに 基準を表すとか、不可能性を示すとか、無限遠点の反映であるとか、ゼロの2重性とかを述べている。ゼロと無限の関係をも述べている。ダ・ヴィンチの鋭い世界観に対する境地に驚嘆している。
以 上
