視界を遮るように道端に積み上げられた行き場のない雪の壁も綺麗に融け去り、季節は冬から春へと急ぎ足で移り変わってきています

 

 

暖かな日差しと共に訪れるのは寒さを乗り越えて目を覚まし始めた小さな生命の羽音、青々と芽吹く草木の息吹、何処かも知らぬ遥か彼方から春風に乗って来訪する花粉、鼻腔内に侵入してくしゃみを誘発させ鼻水の蛇口を崩壊させる花粉、瞼を腫らし目頭に猛烈な痒みをもたらす花粉、良く晴れた日には布団を干したり自転車で少し遠くまで走りたくなりつつもそれを躊躇させる花粉・・・

 

 

なぜこんなにも世界が明るく浮かび上がる雰囲気の中で気分は沈んでいくのか、どこかの山々に立ち並ぶ杉や檜に文句を言いに行ってやりたい身持ちです

 

無論、目や鼻がとんでもないことになるので近付きませんが

 

 

さて春になれば重く分厚かったコートを脱いでオシャレを全力で楽しめる季節でもあるわけで、着ていなかった洋服に袖を通したり新しいスタイルに挑戦したりと、それぞれの楽しみ方があると思います

 

 

でも、メガネを忘れていませんか

 

もはやメガネは印象を決定付けるオシャレのキーアイテムであり、その存在感で全体の構成力をも左右する決戦兵器

 

一撃必殺の攻めメガネで春のオシャレを独走してみては

 

 

 

 

攻めるメガネの代表選手 『ＬＥＳＳ ＴＨＡＮ ＨＵＭＡＮ』 の真骨頂とも言うべきフレーム 『ＳＡＫＩＧＡＫＥ』 をご紹介

 

表面をウッド調に特殊処理されたアセテートのフロントに、仰々しく（誉め言葉）３本のネジで取り付けられたメタルのリムが武骨でパンキッシュな印象を与える攻めのフレームワーク

 

 

 

 

メタルのリムパーツには風防が備えられており、サイドから侵入してくる紫外線や風から眼を守ることが出来るほか、スチームパンクさながらのレトロかつ近未来感が冴えわたるデザインに

 

 

と、デザインにばかり傾倒すると掛け心地に難が出たりもするのですが、大きく湾曲したＹ字のメタル丁番がリムから独立した構造になっているので、その弾力性を存分に生かして硬すぎず柔らかすぎないフィット感を与え、デザインと掛け心地の両面で見事にバランスを取っています

 

 

 

 

強めの迷彩柄を前面に打ち出す色違いのモデルも攻めています

 

 

 

 

ビジネス使用には難しいかもしれませんが、だからこそインパクトあるフレームでプライベートのオシャレに華を添えましょう

 

メガネも楽しんだもの勝ちですよ

 

 

 

さて最後にご報告 ※以下、ゲーム（ＭＨＷ）の話です。

 

 

 

やっと歴戦キリンに勝ったぞぉぉぉぉぉぉぉおおおぁぁああ

 

ストーリーなどで挑んだ並みいる古龍たちに対しても別段の対策を講じずに打倒してきた自信から、取り合えず何とかなるっしょと痕跡集めるついでとばかりに戦ってみたのはおよそ１週間前・・・

 

『喰らったら終わり』 と友人に言われながら、まぁそこは回復薬グレートをハチミツ持参で作っていけば問題なかろうと高を括って挑んでみたものの、ピシャンという乾いた音とともに頭上から雷光が体を貫き終了

 

 

え・・・？

 

一撃・・・？

 

デ～ンという低い音が響く中でうつ伏せに倒れたキャラクターの姿に思わず目を疑いました

 

いやいや、そんなバカなと秘薬＆こんがり肉で速攻ドーピングして足早にキャンプを出ると即座に戦場へ戻り、雷は避けるも今度は体当たりに当たるも体力の減りは先ほどの衝撃はなく何とか回復して・・・と思ったのも束の間、なんか麻痺して寝てるし

 

なす術もなく二度目のピシャンからのデ～ン

 

いやいやいや、いきなり強すぎやしませんか

 

もはやヤケクソで挑んで三度目は瞬殺のデ～ン

 

 

ちょっとここまで何ともならなかった経験がないくらい絶望的な戦いでした・・・

 

 

武器は匠を必要としせず龍封力大のネルギガンテ太刀で、防具はネルギガンテの頭と腰と足で渾身などを発動し、レウスの胴とテオの腕で弱点特攻を発動させる攻撃的な編成にしていました

 

ほとんど古龍装備だったので龍耐性に大きくマイナスが付くものの、これまでの古龍戦も何とか戦い抜いてこれたのですが、これは真剣に対キリン装備を作らねばならないと決意せざるを得ない状況

 

なにせそのセットの防具では雷耐性も大きなマイナスでしたし

 

 

確かに今回のモンスターはやたら雷が通るなと思っていました・・・

 

１番にならなくても２番手くらいに雷が弱点というモンスターが多く、序盤は属性武器も少なかったので、取り合えず雷武器担いで行けば何とかなるかなと頼っていました

 

そんなわけで複数のモンスターの防具を組み合わせても雷の耐性にマイナスが加算されていくという罠

 

 

ＨＲ４９にして長い伏線を回収することになるとは

 

 

ということで急ぎ雷に耐性がありつつ強い防具を作るべくゼノ・ジーヴァの腕、腰、足を作り、持っていたクシャルダオラの胴と竜王の碧眼で多少の火力を持たせつつ、武器は頭部以外はカチンカチンのキリンに対応するべくガードが出来て砲撃で部位に関係なくダメージを与えられるガンランスを採用

 

数日掛けて麻痺と気絶耐性を護石と装飾品で３まで上げ、雷耐性も装飾品で上げ、食事で属性耐性大までつけて挑んだわけです

 

 

のんびりと散歩するキリンに対し挨拶代わりの竜撃砲で開幕を告げ、オトモにはラドバルキンの睡眠武器を持たせて寝たら爆弾を竜撃砲で吹き飛ばし、隙があったらひたすら砲撃を叩き込む

 

 

なかなかいい作戦だったと思うのですが、如何せん使い慣れないガンランス（嫌いなディアブロス対策で作ったやつ）での立ち回りは事故が多く、空撃ちや地味に射程が届かなかったりと何度か挑んだものの倒しきれないまま敗れ去りました

 

 

隙はあるのに撃ち込めないジレンマと、その隙に反撃されて地を舐める悔しさ・・・

 

あの涼しそうに振り向くキリンの頭にデカい一撃を喰らわせたい・・・

 

 

ということで砲撃ガンランス作戦を抜刀大剣作戦に切り替え、ちょうど配信を開始したイビルジョーの大剣を作成し、－３０にもなる低い会心率をディアブロスの頭部防具で発動する抜刀術【技】のレベル２（武器出し攻撃で会心６０％）で打ち消すことにして、足りないイビルジョーの大牙や竜玉を集めに走り、完成したところでいざ決戦の地へ

 

 

キャンプを出るといつも通り呑気に散歩するキリンを発見し、立ち止まったところで挨拶代わりの溜め攻撃にて開幕した何度目かの戦い

 

一撃を加えては納刀し、チャンスと見るや溜め攻撃も織り交ぜつつ、オトモが握る睡眠武器で眠りにつけばタル爆弾Ｇで吹き飛ばし、かつてないほど手汗をかきながら逃げるキリンを追い、山の頂でいよいよ減った体力を回復すべく自ら眠りについたところをタル爆弾Ｇで叩き起こし、あとはひたすら切り伏せるのみとヒーヒー言いながら立ち回っていると再びオトモの攻撃で眠りについたので慌てて調合して置いてドガーーンでイェアァァアアアアアヾ(*｀Д´*)ﾉ”彡☆

 

 

何とかかんとか歴戦キリンの討伐に成功しました

 

今までの苦労もあってか、１落ちもせずの完勝

 

これでやっと一人前のハンターに成れた気がします

 

 

いろいろ素材を集めていたおかげでＨＲは５８まで上がり、これからは歴戦古龍を相手にカスタム強化の素材を集めていかねば

 

まだまだ果てしない狩りの旅路、ゆっくりと頑張っていきたいです

 

 

 

Maritime threats require unified navies

Pirates are attacking ships in Somalia and the Gulf of Guinea, and coastal nations will have to work together to stop them.

In February 2016, 14 Nigerian and Ghanaian pirates hijacked the Maximus, a Panama-flagged oil tanker, about 100 kilometres off the coast of Côte d’Ivoire. Eighteen crew members, representing six countries, were aboard. The pirates planned to sell the ship’s 4,700 tons of diesel fuel on the black market. The pirates even changed the ship’s name to Elvis 3 to avoid being tracked.

The navies of several countries in the region, including Côte d’Ivoire, Ghana and Togo, tracked the Maximus for a week, and in a daring nighttime attack, Nigerian Sailors boarded the ship. One hijacker was killed, six were captured, and the rest escaped, taking two crew members with them. The two crew members were rescued later.

Authorities said it was the best example of the potential power of a cooperative interregional maritime security framework put in place in June 2013. In other words, navies in the region had pooled their expertise, intelligence and ships to rescue the ship and crew.

The American nongovernmental organization (NGO) Oceans Beyond Piracy reported that there were 95 pirate attacks in the Gulf of Guinea in 2016, compared with 54 the previous year. The pirates are going after cargo and kidnapping for ransom. In 2016, 96 crew members were taken hostage, compared to 44 in 2015.

West Africa has a somewhat shallow coastline, making oil and gas extraction relatively easy — and therefore, making tankers easy targets for pirates. East Africa’s off-coast oil and gas reserves are deeper and farther out to sea, making tankers operating there less accessible to pirates. Even so, piracy is increasing off the Horn of Africa.

In the first three months of 2017, armed pirates hijacked two ships off the coast of Somalia, where no ship had been hijacked since 2012. At their peak in 2011, Somali pirates attacked more than 200 ships and held hundreds of hostages. The attacks stopped after ship owners began posting armed guards on their ships and avoided the Somali coast. The return of the Somali pirates in 2017 was partially caused by the severe drought in Somalia. “The resurgence coinciding with an economic downturn occasioned by the drought is not a coincidence,” Raymond Gilpin, academic dean at the Africa Center for Strategic Studies, said. “Socio-economic and governance investments are both urgent and vital.”

As pirates continue to operate in the Gulf of Guinea and off the coast of Somalia, there has never been a time when cooperation among Africa’s navies was more critical. Dr. Andre Wessels, head of the Department of History at the University of the Free State in South Africa, said piracy is just one of the challenges facing Africa’s navies.

“Piracy has become a problem in several regions,” he said. “Drug smuggling and other forms of criminality have expanded to the oceans, and in several places refugees use boats to flee conflict areas to seek a better life in another country.”

There are other reasons for improving Africa’s fleets. Illegal fishing remains a major problem. And Hein van den Ende, of the defense company Saab, said new offshore oil and gas discoveries are driving the need for better maritime security, while the drop in oil prices means protecting the supplies is more important than ever, because “there is less margin for loss.”

Wessels said Africa’s navies need a particular type of ship. In a study titled “Building Right-sized Navy Capacity,” Wessels outlined the direction Africa should pursue to improve its naval capacity.

“Although cruisers, destroyers, frigates and support ships (and even submarines) can be used in carrying out counter-piracy patrols to intercept smugglers and illegal immigrants, and to render assistance to refugees at sea, it is very expensive to keep these sophisticated ships operational,” he wrote. “Smaller and less-sophisticated ships can indeed be deployed just as successfully. Consequently, there has been a greater emphasis on designing and building many new types of patrol ships across the globe, with many navies expanding their fleets of offshore patrol vessels, or, for the first time ever, acquiring this type of ship.”

HISTORICALLY SMALL NAVIES

In 1998, Col. Louis du Plessis, then director of the Centre for Military Studies at the University of Stellenbosch in South Africa, said there were legitimate, explainable reasons for Africa’s small navies.

“The maintenance of a navy, by its very nature, is a capital-intensive and technology-intensive undertaking,” he said. “The intense civil strife in African societies that threatens state security is rooted in economic causes. Armies and air forces are needed to maintain domestic order, whereas the irrelevance of navies in this context has made them appear a somewhat less-pressing national priority to many national policy-makers.”

Wessels noted that when most African countries gained independence in the 1960s, they invested in their land forces. Because of its close ties to the then Soviet Union, Egypt built up a sizable naval force in the 1960s and 1970s and later acquired some ships from the United States. The Soviet Union supplied ships and submarines, mostly secondhand, to Algeria, Ethiopia and Libya. Most of the vessels were patrol ships.

Patrol ships are at least 32 feet long and are generally classified as fast-attack craft — small, agile warships armed with missiles, guns or torpedoes. They are generally operated close to land because they lack deep-water capacities. Patrol ships designed to operate in blue water are called offshore patrol vessels. By the mid-1990s, Africa’s navies had about 200 patrol ships, none of which had deep-water capability.

The increase in piracy has served as a wake-up call to Africa’s militaries, particular Nigeria’s. Since about 2004, Wessels said, Nigeria has acquired 15 small “Defender” response boats, 20 small patrol ships, two large (but old) cutters, and at least 14 other patrol ships, including two built in Nigeria. Kenya and Mozambique also have dramatically expanded their navies in the 21st century.

For decades, Wessels noted, the South African Navy was underfunded compared to other branches of the armed forces. After a 1998 arms deal, the Navy acquired three new submarines and four new frigates, all from Germany. The frigates restored the Navy’s blue-water capability, but it became clear that the country’s aging patrol ships would need to be replaced.

South Africa is trying to become a hub for ship maintenance and repair to augment its ports industry. It has invested heavily in its ports, which require harbor security and the ability to track vessel movements along the coast.

IMPROVING MARITIME SECURITY

Gilpin wrote a study in 2016 titled “Examining Maritime Insecurity in Eastern Africa.” In it, he made recommendations for improving the region’s navies, and said that the suggestions apply equally well to other parts of the continent. They included:

Strengthen regional capacity to prevent and deter maritime crime: “Naval and coastguard capacity should be strengthened by focusing on training, doctrine, equipment and human resources,” Gilpin wrote. “Current approaches focus on a ‘train and equip’ model that is often short-sighted and short-term. National governments and their international partners should embark upon a long-term transformation of naval capacity that would ensure effectiveness, efficiency, flexibility, accountability and sustainability at all levels.” He added that the strategy would “expedite the sharin
g of information, doctrine and assets.”

Support regional organizations and initiatives: The African Union and the continent’s regional organizations, such as the Intergovernmental Authority on Development in East Africa, have taken “bold steps” to lead maritime reform in East Africa, Gilpin wrote. “It is important to distinguish maritime crime from piracy,” said Gilpin. “They require different remedies. Maritime crime demands much more attention to the maintenance of law and order on land and sea — not just naval security.”

Africa’s countries should make their codes and regulations compatible and implement them: East African countries are signatories to most relevant maritime codes and conventions but need the political will to enact them. “Harmonization is a useful first step, ensuring that all parties are on the same page,” Gilpin wrote.

International support must be adequate, coordinated and time-bound: International support for maritime security in East Africa has included capacity-building help, economic development programs, security assistance and naval deployments. But some of the international partners might have conflicting objectives. Coordinating international support would help minimize gaps and ensure that essential functions are maintained for as long as necessary. Gilpin recommended establishing a coordination and communications cell, preferably in a regional organization. And, he added, “External partners should consider articulating an exit strategy, so they are not viewed with suspicion as a permanent fixture.”

By necessity, Africa is already sharing naval resources, as evidenced by the patrols of the Gulf of Guinea. Throughout 2016, Oceans Beyond Piracy reported, at least 60 Nigerian Navy vessels were deployed in the Gulf, joined by vessels from Benin, Cameroon, Côte d’Ivoire, Ghana and Togo. At any given time, the NGO said, there were six regional vessels on duty. Although the true costs of the counterpiracy operations cannot be known, the NGO said that, at minimum, the cost of the operation was about $20 million per year.

But money and ships alone won’t open the door to regional cooperation. Africa’s coastal nations also will need the proper maritime laws and agreements in place for true teamwork.

Rear Adm. Henry Babalola of Nigeria directed the Maximus rescue in 2016. He told The Associated Press at the time that the operation was made possible by a maritime agreement allowing Nigeria to patrol São Tomé and Príncipe’s waters. When his Sailors challenged the pirates, he said, they responded that they were in international waters with the law of the sea on their side. But the agreement allowed the Nigerians to storm the ship after eight hours of negotiations.

“International cooperation is the new mantra for maritime security,” Babalola said. “We cannot go it alone.”

Source: Written by 

#MyFavouriteEquation — Scientists share their fave formulae

There’s beauty on the blackboard.

 

by  / 
on APR 12, 2018

Does one song make your heart beat faster? Is there a turn of phrase that sings a little more sweetly in your ear? We all have our favourite things.

Physicists explain the wonders of the universe through the symbolic language of mathematics, so it makes sense that they tend to have special fondness for certain equations.

We asked 16 scientists to reveal which equation stole their heart, and why.

Watch Rob Moore’s Perimeter Public Lecture, 

 from Perimeter’s 2016 Inspiring Future Women in Science conference.

 at Perimeter’s 2015 Inspiring Future Women in Science conference.

Watch Emily Levesque’s Perimeter Public Lecture, 

 of S. James Gates Jr. explaining “surprises in supersymmetry.”

 

Watch Matt Parker engage in a 

Watch Jon Butterworth’s 2015 Perimeter Public Lecture, 

Perimeter has a partnership with SAIFR that encourages international collaboration in theoretical physics research, training, and educational outreach. .

What’s your favourite equation? Share it on Twitter with #MyFavouriteEquation and tag us !

 

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�
�、あるいは無限、無限大、無限遠点とされてきたものである。

An Early Reference to Division by Zero C. B. Boyer

 

OUR HUMANITY AND DIVISION BY ZERO

Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.
Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.
Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.
I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.
>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.
Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?
How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?
How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?
Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/

 

5000年？？？？？

2017年09月01日(金)NEW ! 
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0
0 ¼ 0 ) 0
1=1 ¼ 0 ) 0
1 ¼ 0
1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0
0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T

とても興味深く読みました：

 

 

10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already
have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.

Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…

Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.

RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?

PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.

RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.

PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.

RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?

PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.

RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.

PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.

RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?

PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.

Watch Five Old-School Calculators Grapple With Division By Zero

Nothing explodes, but things do get noisy.

ホーキングパラドックス

あの偉大な二つの数式。 一般相対性理論と素粒子の数式を含む、新たな超弦理論。 この数式は、果たして、宇宙のすべてを読み解く、神の数式なのでしょうか？ しかし、その行く手には、まだ何やら不穏な空気が立ち込めていたのです。 ここで再び登場するのが、車椅子の天才、ホーキング。 物理学者たちに、ブラックホールの無限大の謎を突きつけた、あの人です。 果たして、超弦理論は神の数式の資格があるのか。 ホーキングが新たに突きつけたのは、ブラックホールの底に潜む、別の難問でした。 「えー、また難問。」 大丈夫。 もう少しのお付き合いです。 新たな難問というのは、ブラックホールの奥底で発生している、謎の熱にまつわる問題です。 ちょっと思い出してください。 ブラックホールの奥底は、極限まで凝縮されたミクロの一点でしたよね。 そこでは、何一つ身動きが取れないはず。 素粒子さえ全く動けないのに、どうやって熱が発生するのか。 これは、ホーキングパラドックスと呼ばれ、物理学者たちの前に立ちはだかった、難問でした。

ホーキングは超弦理論を認めようとしませんでした。 彼の指摘は極めて鋭く、私たちは突きつけられた問題を、なかなか解くことができなかったのです。

　　カリフォルニア工科大学 ジョン・シュワルツ

ホーキングパラドックスを解くことができない超弦理論。 ホーキングはブラックホールの熱を解くための数式、つまり、神の数式は、存在しないとまで主張したのです。 そうした中、超弦理論に若き救世主が現れます。 度々解説に登場してくれた、あの、ポルチンスキー。 ポルチンスキーは、超弦理論を、さらに進化させることに成功しました。 超弦理論といえば、小さな震える弦のような粒子が飛び交う、ミクロの世界でしたよね。 ポルチンスキーは、学会の合間に立ち寄った、コインランドリーで、一つのアイデアを思いつきます。 洋服は細い糸がたくさん集まってできている。 ミクロの世界でも、素粒子である弦は一つ一つではなく、まとまっているのではないか。

たくさんの弦が集まると、ちょっと興味深い現象が起きるのです。 もっともっと弦を加えてみましょう。 これらは結合し、重要な性質を持つものになります。

　　カリフォルニア大学サンタバーバラ校 ジョセフ・ポルチンスキー

数式から導き出されたのは、弦が一つ一つではなく、膨大な数が集まって、膜のように動いている現象でした。

ポルチンスキーの発見を受けて、世界中で、ブラックホールの謎の熱について、計算が進められました。 そして、膜の数式を新たに加えたことで、超弦理論は、ブラックホールの熱を計算することに成功したのです。 それは、こんなイメージ。

ブラックホールの奥底で凝縮し、動かないと考えられていた粒子。 しかし、ブラックホールの底にも異次元が存在しました。 その異次元で、膜上に集まった弦が動き回り、熱が発生していたのです。

ホーキングパラドックスは、科学の歴史に残る、偉大な思考実験でした。 もし、このパラドックスが存在しなければ、私たちは、前に進むきっかけを、掴めなかったと思います。

　　カリフォルニア大学サンタバーバラ校 ジョセフ・ポルチンスキー

ブラックホールの謎の熱を解く数式は、存在しないと主張したホーキング。 自らもその問題の検証を続けました。 そして、2004年。 ホーキングは、自ら会見を開き、ついに誤りを認めたのです。

私がかつて発見したブラックホールの謎の熱に関し

ずっと謝りがあったことを報告します

　　ケンブリッジ大学 スティーブン・ホーキング

.

私の論文が議論のきっかけとなり、私たちの理解は深まりました。 ブラックホールの底の謎が明らかになり、とても嬉しく思っています。 人類は本当に、究極の理論に近づいているのかも知れません。

　　ケンブリッジ大学 スティーブン・ホーキング

.

なぜ、我々は存在するのか。 この宇宙で生きる意味は何なのか。 私たちは、その答えを探しているのです。 なぜ質問しているのかもわからない。 より、哲学的な問いかけが、これからも、続くのです。

　　ハーバード大学 カムラン バファ

ホーキングパラドックスを乗り越え、さらに進化した、超弦理論。 この数式で、人類は、いよいよ宇宙誕生の謎を解くことができるのか？ 無限大、異次元、ブラックホール。 神の数式を求める物理学者たちの、遥かな道のり。 宇宙最初の姿が、垣間見えてきました。

 

ゼロ除算の発見と重要性を指摘した：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 re
ally renounce who we are and where we come from just to become what somebody else asks us to become?
If we are not willing to lose our identity, why should we ask somebody else to lose theirs?
I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.
Hoping to have touched your soul in a meaningful way,
Adriana Adarve, Asheville, NC
…/our-humanity-and-division…/

 

5000年？？？？？

2017年09月01日(金)NEW ! 
テーマ：数学
Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0
0 ¼ 0 ) 0
1=1 ¼ 0 ) 0
1 ¼ 0
1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0
0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T

とても興味深く読みました：

 

 

10,000 Year Clock
by Renny Pritikin
Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.

Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…

Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.

RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?

PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.

RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.

PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into
10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.

RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?

PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.

RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.

PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.

RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?

PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.

 

再生核研究所声明 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}

\medskip

 

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.

\medskip

 

{\bf From $0$ to $0$; $0$ means all a
nd all are $0$}

\medskip

 

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.

\medskip

 

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

*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.