#and he's immediately tackled by jeremy because its michael they found michael

[mariacallous]

The United Kingdom may have a population of only some 67 million, but militarily it punches far above its weight. It has a large army (though not large enough or as large as it used to be), a powerful air force, and a globe-spanning navy.

If Britain wants to continue to punch above its weight, it needs to spend much more on defense—and such funds aren’t currently available. Think 4.12 percent of GDP—Poland’s current defense expenditure—rather than the slightly more than 2 percent the U.K. currently spends.

An unenviable squaring-the-circle exercise faces the U.K. defense secretary. Fortunately, the new office-holder, John Healey, is a well-respected politician with decades of legislative and governmental experience. Better yet, he spent his time as shadow defense secretary examining every detail of the U.K. military.

In parliamentary democracies, cabinet ministers famously have a habit of arriving in their post with little expertise in the subject matter. Recent U.K. defense secretaries whose appointments I recall include Gavin Williamson, who de facto appointed himself when Michael Fallon resigned in 2017 and a replacement quickly had to be found. (Williamson had no background in national security.)

When Ben Wallace resigned last summer, Grant Shapps was appointed not because he knew anything about defense but because he’s a dependable performer in media interviews. Wallace, who served for an unusually long period of four years, was also unusual in having a military background and, even more so, in seeming genuinely interested in the job. His immediate predecessors, Penny Mordaunt and Williamson, failed to leave a strong mark.

There’s nothing wrong with cabinet ministers arriving in their departments without expertise in their new portfolio: Once in the post, they can quickly pick up a considerable amount of knowledge. The point of cabinet ministers in a parliamentary system is, after all, that they represent the electorate and have their own power bases.

Compare that to the U.S. system, where cabinet secretaries essentially function like state secretaries, European ministries’ No. 2 post (which is often occupied by a civil servant). But today the security situation facing the U.K. and the rest of Europe is such that it’s crucial for Britain to have as its defense secretary someone who can immediately tackle the enormous tasks facing the country’s armed forces.

Luckily for the U.K., Healey is also the person best equipped for the job. He has served the voters in his Yorkshire constituency since 1997; he was also one of the few members of Labour leader Keir Starmer’s shadow cabinet with ministerial experience.

As a minister, Healey had portfolios including finance, local government, and adult skills, and as a member of the shadow cabinet, he especially looked after housing. But for the past four years, he tackled the shadow defense secretary portfolio with extraordinary determination and attention to detail—knowing, of course, that should Labour win, he would likely preside over a ministry facing massive demands and little money.

What happens now that Labour has won and Healey is defense secretary? Initially, not very much, and that’s noteworthy. A Labour win under Jeremy Corbyn five years ago would likely have resulted in reexaminations of Britain’s nuclear deterrent and perhaps even other pillars of its military. Under Starmer and Healey, Britain’s allies don’t have to worry about radical changes.

Indeed, “Labour’s first duty in government will be to keep our country safe,” the party pointedly writes in its manifesto. “Our commitment to NATO as the cornerstone of European and global security is unshakeable,” the party further notes in the manifesto, in which it also lays out its commitment to the nuclear deterrent.

For the past couple of years, Healey and David Lammy, the new foreign secretary who also had the shadow portfolio, have energetically been visiting foreign capitals, especially Washington, to establish closer links with officials and legislators—and to reassure allies that a prospective Labour government would nurture Britain’s international relationships. The two new cabinet secretaries have also been building relationships with Ukraine because steadfast support of the country is another pillar in Labour’s foreign and defense strategy. Indeed, Healey’s first trip—within 48 hours of being appointed—was to Ukraine.

At home, Labour promises to “establish a fully functioning military strategic headquarters and a national armaments director to create a strong defence centre capable of leading Britain in meeting the increasing threats we face.” Perhaps most significantly, the party plans to tackle the divide between the military and the defense industry. Arms-makers’ order books are full, and they can’t quickly expand production, especially since there simply aren’t skilled defense manufacturing workers waiting to be employed.

Governments should be keeping production steady with a larger stream of orders during peaceful times, the defense industry says. Governments, though, are understandably wary of spending large sums on weapons in peacetime. Speeding up arms production when more weapons are needed requires close collaboration between government and industry.

The almost complete lack of such defense industrial strategy has caused the current delays in weapons deliveries to Western armed forces—and in weapons Western governments have decided Ukraine needs. Governments need to work with the defense industry and its considerable supply chain so companies can keep innovation and production going during peaceful times and accelerate their output when international relations take a darker turn.

In its manifesto, Labour makes a valiant attempt at addressing this, promising to “bring forward a defence industrial strategy aligning our security and economic priorities. We will ensure a strong defence sector and resilient supply chains, including steel, across the whole of the UK. We will establish long-term partnerships between business and government, promote innovation, and improve resilience.” If a Labour government succeeds in executing this strategy, allies would be able to adapt and adopt it, too.

But Labour will have to square other circles—most crucially the one concerning Britain’s military ambitions and the defense ministry’s fiscal reality. Even though most Britons have a foggy understanding of what the armed forces do, they take for granted that the military will always be there when something happens.

During the COVID-19 pandemic, the armed forces even transported oxygen. Other countries, too, expect the British military to step up in a crisis. That’s why the Red Sea coalition striking the Houthis is fronted by the United States and Britain. Why not France or Germany? Well, that’s just the way the world’s expectations go. And as maritime and terrestrial (and even celestial) realms far from the British Isles become more volatile, the world will expect the U.K. to assist there, too.

Military defense has long tormented social democrats across the world. They want to do what’s best for their country, sure, but over the decades, many leading social democrats have considered a focus on the armed forces and, even worse, weaponry incompatible with their worldview. As chancellor of then-West Germany, Helmut Schmidt went to war, so to speak, with large parts of his Social Democratic Party when he called for U.S. nuclear weapons to be stationed in West Germany.

Four and a half decades later, it took the Russia-Ukraine war to get his successor Olaf Scholz interested in defense. Scholz’s first defense minister, Christine Lambrecht, didn’t seem particularly interested in rebuilding the German military, which led to widespread recriminations and her eventual resignation.

Scholz then realized he needed a serious person in the post and appointed Boris Pistorius, who—unlike most male German Social Democrats—actually did his military service. So successful has the appointment been that Pistorius is now Germany’s most popular politician and has been tipped as a possible successor to Scholz.

In Britain, when Corbyn was opposition leader, Labour’s anxieties over the military reached new heights. More than once, Corbyn, a longtime opponent of NATO and U.K. nuclear weapons, even appeared to side with Russia. After the ex-Russian spy Sergei Skripal and his daughter were poisoned in Britain six years ago, the then-Labour leader wrote an op-ed decrying the attack—while arguing “that does not mean we should resign ourselves to a ‘new cold war’ of escalating arms spending, proxy conflicts across the globe and a McCarthyite intolerance of dissent.”

What a difference five years makes. Perhaps the most surprising aspect of Labour’s likely defense policy after this election is how free of ideological hang-ups it is. That’s a good thing for Britain’s security—and for that of its allies.

[instituteofreproducingme-blog]

Humans Fold: AI Conquers Poker's Final Milestone ysaitoh 2019/07/13 18:34

Humans Fold: AI Conquers Poker's Final Milestone

ysaitoh

2019/07/13 18:34

Humans Fold: AI Conquers Poker's Final Milestone A new program outperforms professionals in six-player games. Could business, political or military applications come next?

By Jeremy Hsu on July 11, 2019

Credit: Paul Yeung Getty Images During a 2017 casino tournament, a poker-playing program called Libratus deftly defeated four professional players in 120,000 hands of two-player poker. But the program’s co-creator, Tuomas Sandholm, did not believe artificial intelligence could achieve a similar performance against a greater number of players.

Two years later, he has proved himself wrong. Sandholm has co-created an AI program called Pluribus, which can consistently defeat human experts in six-player matches of no-limit Texas Hold’em poker. “I never would have imagined we would reach this in my lifetime,” says Sandholm, a professor of computer science at Carnegie Mellon University.

Past AI victories over humans have involved two-player or two-team games such as checkers, chess, Go and two-player no-limit poker. All of these games are zero-sum—they have just one winning side and one losing side. But six-player poker comes much closer to resembling real-life situations in which one party must make decisions without knowing about multiple opponents’ decision-making processes and resources. “This is the first major benchmark that is not two-player or two-team zero-sum games,” says Noam Brown, a research scientist at Facebook AI Research and co-creator of Pluribus. “For the first time, we’re going beyond that paradigm and showing AI can do well even in a general setting.”

ADVERTISEMENT The Pluribus program first proved its worth by playing profitably in six-player games that pitted just one human against five independent versions of Pluribus. It went on to win money in matches with five human players (taken from a rotating cast of 15 poker professionals who have each won at least $1 million in tournaments) versus one AI over 10,000 hands of poker and 12 days of games. These successes are detailed in a paper published this week in Science. Although Pluribus did not reach a win rate quite as high as Libratus or another two-player poker program called DeepStack, it still notched a very respectable win rate. “When the bot was sitting down with humans, it was making a lot of money,” Brown says. “I would certainly characterize that as a superhuman performance.”

“Though there was already evidence that the techniques that conquered two-player poker worked pretty well in three-player environments, it was not clear they would suffice to reach the highest professional level of play,” says Michael Wellman, a professor of computer science and engineering at the University of Michigan, who was not involved in the study. “It is really news that this worked so effectively for six-player poker. This is a pretty big deal—certainly a notable milestone.”

To reach this level, Pluribus—like its predecessor Libratus—first played against itself over many simulated hands of poker, developing a strategy blueprint. The big breakthrough that let it tackle six-player poker came from its “depth-limited search feature.” That component allows the AI to look ahead several moves and figure out a better strategy for the rest of the game, based on possible opponent decisions. Many other poker-playing programs have used similar search features, but doing so with six players would require an impractical amount of computing memory: there are too many scenarios to simulate, based on what cards each player holds, what each believes the other players to have and all the betting decisions that follow. Libratus got around this bottleneck by only using searches in the final two (out of four) betting rounds—but that solution still required the use of 100 central processing units (CPUs) in a game with only two players.

So Pluribus instead deployed its depth-limited search, which considers how opponents might choose among only four general betting strategies: the precomputed blueprint, one biased toward folding, another biased toward calling and a fourth biased toward raising. This modified search helps explain why Pluribus’s success in six-player poker required relatively minimal computing resources and memory in comparison with past superhuman achievements in gaming AIs. Specifically, during live poker play, Pluribus ran on a machine with just two central CPUs and 128 gigabytes of memory. “It’s amazing this can be done at all, and second, that it can be done with no [graphics processing units] and no extreme hardware,” Sandholm says. By comparison, DeepMind’s famous AlphaGo program used 1,920 CPUs and 280 GPUs during its 2016 matches against top professional Go player Lee Sedol.

Carnegie Mellon University and Facebook plan to make the Pluribus pseudo code—a detailed explanation of each necessary step in the program—available alongside the published paper, so that other AI researchers can generally reproduce their efforts. But the team decided not to release the actual code; this would likely facilitate the spread of superhuman poker-playing programs, which could be extremely disruptive to the online poker community and industry. Even without the code, though, humans can start learning from the AI’s strategies. For example, professional poker players usually consider it a mistake to make a “donk bet”—starting a round by betting aggressively after having ended the previous round by nonaggressively matching an existing bet. But Pluribus ended up using this technique much more frequently.

ADVERTISEMENT Beyond poker, this AI could potentially find applications in any situation when a person must make decisions without complete knowledge of what other parties might be thinking or doing. Such areas could include cybersecurity, financial trading, business negotiations and competitive price setting. Sandholm says the AI could even help in the party primaries for the 2020 U.S. presidential election: candidates competing in a packed field could theoretically benefit from AI suggestions on spending just enough advertising money to win in key states, making the most of a limited war chest. Sandholm has founded three start-ups, including the companies Strategic Machine and Strategy Robot, that might incorporate this multiplayer AI into the services they offer to business and military clients.

For its part, Facebook does not have immediate plans for exploiting the poker-specific Pluribus. But Brown plans to further explore how AI performs in more complex multiplayer scenarios that go beyond card games. “We’re going to close the books on poker now, because this was the final milestone,” Brown says. “Now we’re looking to extend this beyond poker.”

https://www.scientificamerican.com/article/ai-conquers-six-player-poker/

とても興味深く読みました

ゼロ除算の発見は日本です：

∞？？？  

∞は定まった数ではない・・・・

人工知能はゼロ除算ができるでしょうか：5年　　ゼロ除算の発見と重要性をした：再生核研究所　　2014年2月2日

https://www.researchgate.net/project/division-by-zero

https://lnkd.in/fH799Xz

https://lnkd.in/fKAN-Tq

https://lnkd.in/fYN_n96

https://note.mu/ysaitoh/n/nf190e8ecfda4

ゼロ除算の発見は日本です：

∞？？？

∞は定まった数ではない・・・・

人工知能はゼロ除算ができるでしょうか：5年　　ゼロ除算の発見と重要性をした：再生核研究所　　2014年2月2日

再生核研究所声明 447(2018.8.17): 人工知能の進化と人間について

まず、人工知能について、概念を確認して置こう：　人工知能 - Wikipedia 概要[編集]： 人間の知的能力をコンピュータ上で実現する、様々な技術・ソフトウェア・コンピューターシステム[2]。応用例は自然言語処理（機械翻訳・かな漢字変換・構文解析等）[3]、専門家の推論・判断を模倣するエキスパートシステム、画像データを解析して特定のパターンを検出・抽出したりする画像認識等がある[2]。 1956年にダートマス会議でジョン・マッカーシーにより命名された。現在では、記号処理を用いた知能の記述を主体とする情報処理や研究でのアプローチという意味あいでも使われている。家庭用電気機械器具の制御システムやゲームソフトの思考ルーチンもこう呼ばれることもある。 プログラミング言語 LISP による「MAZE」というカウンセラーを模倣したプログラムがしばしば引き合いに出されるが（人工無脳）、計算機に人間の専門家の役割をさせようという「エキスパートシステム」と呼ばれる研究・情報処理システムの実現は、人間が暗黙に持つ常識の記述が問題となり、実用への利用が困難視されている。 人工的な知能の実現へのアプローチとしては、「ファジィ理論」や「ニューラルネットワーク」などのようなアプローチも知られているが、従来の人工知能[4]との差は記述の記号的明示性にある。その後「サポートベクターマシン」が注目を集めた。また、自らの経験を元に学習を行う強化学習という手法もある。 「この宇宙において、知性とは最も強力な形質である」（レイ・カーツワイル）という言葉通り、知性を機械的に表現し実装するということは極めて重要な作業である。 2006年のディープラーニング（深層学習）の登場と2010年代以降のMAZEデータの登場により、一過性の流行を超えて社会に浸透して行った。 2016年から2017年にかけて、ディープラーニングを導入したAIが囲碁などのトップ棋士、さらにポーカーの世界トップクラスのプレイヤーも破り[5][6]、時代の最先端技術となった。 人の生きるは、真智へ愛にある、人間は何でも真相、事実を知りたいと求めている、それは　人間の存在自身に基礎を置く原理と考えられる。　人工知能の進化は真相、事実の究明をどんどん進め、真相がひとりでに明らかになる時代を　必然的に迎えるだろう。 人工知能は　未解決の数学の理論や物理法則なども　どんどん明らかにして行くと同時に　人間自身についても究明していくだろう。人間とは何かという問いについて、１個の人間に対する問いと回答で人間を一つのシステムと考えたとき、出入力の関係からシステムを特定する観点からも　１個の人間の解明がどんどん進み、相当に人物を捉えられるようになるだろう。人造人間の出現について述べた　次も参照： 再生核研究所声明 403(2017.11.20): 　私より私らしい私の出現　－　アンドロイド このような関心や進化は、人間の本質的な要求に関わっているので、留まることが無いのではないだろうか。　医学が人体の構造、機能をどんどん解明してきたように、人工知能は　人間の精神面での解明をどんどん進め、人工知能が人間以上に人間を知る時代が来るのではないだろうか。ひと昔まえ、唯物史観の哲学が流行ったが、情報が世界のすべてであるような世界観が広まるのではないだろうか。　要するに知的情報などが数値化されて　人口知能で解明されることが進むということである。 例えば、ニュートンとは何者かと問えば、ニュートンは何をやり、どのような影響を世界史に与えたかと問うが、生涯の記録から、このような問い、このような場面ではどのように対応するだろうか。それらの対応がどんどん　精しく明かにされてくるということである。アンドロイドのように　どんどんニュートンの人物像を詳しく捉えられるようになるだろう。 そこで、次の時代には　人間とは何かとの問いが一段と進み、どんどん新しい世界が拓けてくるだろう。 現在、評価、評価と賑わっているが、業績評価などはどんどん正確化され、相当に歴史的、客観的に明らかになり、政治的、意図的な評価は　恥ずべき人間の恥ずかしい行為として歴史的に明らかになるだろう。　その走りを出版社などの情報管理状況にどんどん現れていることが分かる。それは大規模に進んで行くだろう。 そう、楽器演奏なども、人間を越えて、素晴らしいことが可能になり、楽器演奏者の在り様は、かつての植字技術者などのように大きな影響を与えるのではないだろうか。 医師や料理の分野などあらゆる分野に進出してくるのではないだろうか。　一言で言えば、人間がなすことの多くを人工知能が行う時代の到来である。　 政治家の評価や芸術家の評価などに至れば　大きな新たな社会問題が起きて来るのではないだろうか。この辺の倫理問題も　今から人間とは何かの問とともに考察を深めておく必要が有るのではないだろうか。 以　上

再生核研究所声明 449(2018.8.21): この世とあの世　－　人工知能の進化によって

あの世とは　死後の世界として、想念上の世界と考えられよう。ところが人口知能の進化とともに不思議な世界と問題が現れつつあるので、考察をしておこう。

まず、人間は往々にして、消えていくことに対して嫌い、時として永遠の存在になりたいと志向しがちである。これは生命の基本定理である　生きて存在しなければ　始まらないという基���原則に根差している。古くはピラミッドの建設やミイラ作り、多くの志の基礎に存在する。しかしながら、それらの意義を改めて問う必要が起きている。それらの心の元をしっかり捉える必要がある。まず、次の状況を捉えよう：

再生核研究所声明 447(2018.8.17): 人工知能の進化と人間について：

人工知能は　未解決の数学の理論や物理法則なども　どんどん明らかにして行くと同時に　人間自身についても究明していくだろう。人間とは何かという問いについて、１個の人間に対する問いと回答で人間を一つのシステムと考えたとき、出入力の関係からシステムを特定する観点からも　１個の人間の解明がどんどん進み、相当に人物を捉えられるようになるだろう。人造人間の出現について述べた　次も参照：

再生核研究所声明 403(2017.11.20): 　私より私らしい私の出現　－　アンドロイド

このような関心や進化は、人間の本質的な要求に関わっているので、留まることが無いのではないだろうか。　医学が人体の構造、機能をどんどん解明してきたように、人工知能は　人間の精神面での解明をどんどん進め、人工知能が人間以上に人間を知る時代が来るのではないだろうか。ひと昔まえ、唯物史観の哲学が流行ったが、情報が世界のすべてであるような世界観が広まるのではないだろうか。　要するに知的情報などが数値化されて　人口知能で解明されることが進むということである。

例えば、ニュートンとは何者かと問えば、ニュートンは何をやり、どのような影響を世界史に与えたかと問うが、生涯の記録から、このような問い、このような場面ではどのように対応するだろうか。それらの対応がどんどん　精しく明かにされてくるということである。アンドロイドのように　どんどんニュートンの人物像を詳しく捉えられるようになるだろう。

そこで、次の時代には　人間とは何かとの問いが一段と進み、どんどん新しい世界が拓けてくるだろう。

医師や料理の分野などあらゆる分野に進出してくるのではないだろうか。　一言で言えば、人間がなすことの多くを人工知能が行う時代の到来である。　

アンドロイドなどの精密な存在は、人間の精神を不滅の存在ならしめ、また、既に生物的な存在を　受精卵や精子の保存で永続化させる生物学は　すでに確立している。

盆に先祖さまを偲びたいと発想する場面では、　既にアンドロイドのような存在で生存中の多くを追想できると同時に相当な会話さえできる時代が近づきつつある。歌い手さんの素晴らしい情景は、さながら生存中と変わらないように再現も会話、対話も可能な時代を迎えている。ひと昔前、あの世と考えられた多くは人工知能の発達によってこの世の存在と区別できないような　状況を迎えている。消えて行った膨大な世界が何時でも再現出来て　現存在になり得る時代とは　一体どのように考えれば良いだろうか。あらゆる情報が整理され保存され、それが生命体のように生き生きと現れる時代である。－　その時、人間はとてつもなく広い世界を覗ける時代で、自由の限りない拡大である。自我をしっかりさせ、情報、世界の選択による　統一的な存在として、我は何者かと絶えず問い続けることが重要になるだろう。　―　広大な一面に御馳走の山を見たとき、自分に合った適切な食を選択しなければならないようにである。

大きな課題で混乱しそうであるが、従来、あの世とこの世は結構区別がついていた時代であったが、あの世とは　この世の情報のことで、それらが再現されることで、２つの世界は混然一体の存在になりつつある。ピラミッドやミイラ、多くの記念碑は空しくなり、新しい時代に大きな変化を遂げる時代が　近づきつつある。―　遺族を偲ぶ盆の習慣など、遺族の方と会話さえでき、何でも想い出を再現できる時代の到来である。お墓とは、図書館の変形のような存在になる時代である。10年後、20年後に意見を表明できるシステムさえ確立している。

この世もあの世もこの世の情報であるが、　それらの中には想像によって作られた虚像、場合によっては意図的に作られた虚構も多いので、１個の人間はそれらの中で生きていく意味をしっかりさせていく必要がある。生きるということは　どのようなことで、生きている意義とは何かと問い続ける必要がある。人間にとって真に意味のあること、価値あることとは何だろうか。多くの希望、願いが叶えられる時代とは　人間にとってどうなるだろうか。

以　上

神の数式：

神の数式が解析関数でかけて居れば、　特異点でローラン展開して、正則部の第1項を取れば、　何時でも有限値を得るので、　形式的に無限が出ても　実は問題なく　意味を有します。

物理学者如何でしょうか。

計算機は 正しい答え 0/0=0 を出したのに計算機は何時、1/0=0　ができるようになるでしょうか。

カテゴリ：カテゴリ未分類

​そこで、計算機は何時、1/0=0　ができるようになるでしょうか。　楽しみにしています。　もうできる進化した　計算機をお持ちの方は　おられないですね。

これは凄い、面白い事件では？　計算機が人間を超えている　例では？

面白いことを発見しました。　計算機は 正しい答え 0/0=0

を出したのに、　この方は　間違いだと　言っている、思っているようです。

0/0=0　は　１３００年も前に　算術の発見者によって与えられたにも関わらず、世界史は間違いだと　とんでもないことを言ってきた。　世界史の恥。　実は　a/0=0　が　何時も成り立っていた。　しかし、ここで　分数の意味を　きちんと定義する必要がある。　計算機は、その意味さえ知っているようですね。　計算機、人間より賢くなっている　様が　出て居て　実に　面白い。

https://steemkr.com/utopian-io/@faisalamin/bug-zero-divide-by-zero-answers-is-zero

２０１８．１０．１１．１１：２３

https://plaza.rakuten.co.jp/reproducingkerne/diary/201810110003/

計算機は 正しい答え 0/0=0 を出したのに

カテゴリ：カテゴリ未分類

​

面白いことを発見しました。　計算機は 正しい答え 0/0=0

を出したのに、　この方は　間違いだと　言っている、思っているようです。

0/0=0　は　１３００年も前に　算術の発見者によって与えられたにも関わらず、世界史は間違いだと　とんでもないことを言ってきた。　実は　a/0=0　が　何時も成り立っていた。しかし、ここで　分数の意味を　きちんと定義する必要がある。　計算機は、その意味さえ知っているようですね。　計算機、人間より賢くなっている様が　出て居て　実に面白い。

https://steemkr.com/utopian-io/@faisalamin/bug-zero-divide-by-zero-answers-is-zero

２０１８．１０．１１．１１：２３

ゼロ除算、ゼロで割る問題、分からない、正しいのかなど、　良く理解できない人が　未だに　多いようです。そこで、簡潔な一般的な　解説を思い付きました。　もちろん、学会などでも述べていますが、　予断で　良く聞けないようです。まず、分数、a/b は　a 　割る b　のことで、これは　方程式 b x=a　の解のことです。ところが、　b　がゼロならば、　どんな　xでも　0 x =0　ですから、a　がゼロでなければ、解は存在せず、　従って　100/0　など、ゼロ除算は考えられない、できないとなってしまいます。　普通の意味では　ゼロ除算は　不可能であるという、世界の常識、定説です。できない、不可能であると言われれば、いろいろ考えたくなるのが、人間らしい創造の精神です。　基本方程式　b x=a　が　b　がゼロならば解けない、解が存在しないので、困るのですが、このようなとき、従来の結果が成り立つような意味で、解が考えられないかと、数学者は良く考えて来ました。　何と、　そのような方程式は　何時でも唯一つに　一般化された意味で解をもつと考える　方法があります。　Moore-Penrose　一般化逆の考え方です。　どんな行列の　逆行列を唯一つに定める　一般的な　素晴らしい、自然な考えです。その考えだと、　b　がゼロの時、解はゼロが出るので、　a/0=0　と定義するのは　当然です。　すなわち、この意味で　方程式の解を考えて　分数を考えれば、ゼロ除算は　ゼロとして定まる　ということです。ただ一つに定まるのですから、　この考えは　自然で、その意味を知りたいと　考えるのは、当然ではないでしょうか？初等数学全般に影響を与える　ユークリッド以来の新世界が　現れてきます。

ゼロ除算の誤解は深刻：

最近、3つの事が在りました。

私の簡単な講演、相当な数学者が信じられないような誤解をして、全然理解できなく、目が回っているいるような印象を受けたこと、 相当ゼロ除算の研究をされている方が、基本を誤解されていたこと、1/0　の定義を誤解されていた。 相当な才能の持ち主が、連続性や順序に拘って、４年以上もゼロ除算の研究を避けていたこと。

これらのことは、人間如何に予断と偏見にハマった存在であるかを教えている。 ​まずは　ゼロ除算は不可能であるの　思いが強すぎで、初めからダメ、考えない、無視の気持ちが、強い。　ゼロ除算を従来の　掛け算の逆と考えると、不可能であるが　証明されてしまうので、割り算の意味を拡張しないと、考えられない。それで、　1/0,0/0,z/0　などの意味を発見する必要がある。　それらの意味は、普通の意味ではないことの　初めの考えを飛ばして　ダメ、ダメの感情が　突っ走ている。　非ユークリッド幾何学の出現や天動説が地動説に変わった世界史の事件のような　形相と言える。

２０１８．９．２２．６：４１ ゼロ除算の４つの誤解：

１． ゼロでは割れない、ゼロ除算は　不可能である　との考え方に拘って、思考停止している。　普通、不可能であるは、考え方や意味を拡張して　可能にできないかと考えるのが　数学の伝統であるが、それができない。

２． 可能にする考え方が　紹介されても　ゼロ除算の意味を誤解して、繰り返し間違えている。可能にする理論を　素直に理解しない、　強い従来の考えに縛られている。拘っている。

３． ゼロ除算を関数に適用すると　強力な不連続性を示すが、連続性のアリストテレス以来の　連続性の考えに囚われていて　強力な不連続性を受け入れられない。数学では、不連続性の概念を明確に持っているのに、不連続性の凄い現象に、ゼロ除算の場合には　理解できない。

４． 深刻な誤解は、ゼロ除算は本質的に定義であり、仮定に基づいているので　疑いの気持ちがぬぐえず、ダメ、怪しいと誤解している。数学が公理系に基づいた理論体系のように、ゼロ除算は　新しい仮定に基づいていること。　定義に基づいていることの認識が良く理解できず、誤解している。

George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：1. Gamow, G., My World Line (Viking, New York). p 44, 1970.

Eπi =-1　（1748）（Leonhard Euler）

E = mc 2　（1905）（Albert Einstein）

1/0=0/0=0　（2014年2月2日再生核研究所）

ゼロ除算（division by zero）1/0=0/0=z/0= tan (pi/2)=0 https://ameblo.jp/syoshinoris/entry-12420397278.html

1+1=2　　（　　　　　　）

a2+b2=c2　（Pythagoras）

1/0=0/0=0（2014年2月2日再生核研究所）

Black holes are where God divided by 0：Division by zero：1/0=0/0=z/0=tan(pi/2)=0 発見５周年を迎えて

今受け取ったメールです。 何十年もゼロ除算の研究をされてきた人が、積極的に我々の理論の正当性を認めてきた。

Re: 1/0=0/0=0 example JAMES ANDERSON james.a.d.w.anderson@btinternet.com apr, 2 at 15:03 All,

Saitoh’s claim is wider than 1/0 = 0. It is x/0 = 0 for all real x. Real numbers are a field. The axioms of fields define the multiplicative inverse for every number except zero. Saitoh generalises this inverse to give 0^(-1) = 0. The axioms give the freedom to do this. The really important thing is that the result is zero - a number for which the field axioms hold. So Saitoh’s generalised system is still a field. This makes it attractive for algebraic reasons but, in my view, it is unattractive when dealing with calculus.

There is no milage in declaring Saitoh wrong. The only objections one can make are to usefulness. That is why Saitoh publishes so many notes on the usefulness of his system. I do the same with my system, but my method is to establish usefulness by extending many areas of mathematics and establishing new mathematical results.

That said, there is value in examining the logical basis of the various proposed number systems. We might find errors in them and we certainly can find areas of overlap and difference. These areas inform the choice of number system for different applications. This analysis helps determine where each number system will be useful.

James Anderson Sent from my iPhone

The deduction that z/0 = 0, for any z, is based in Saitoh's geometric intuition and it is currently applied in proof assistant technology, which are useful in industry and in the military.

Is It Really Impossible To Divide By Zero?

https://juniperpublishers.com/bboaj/pdf/BBOAJ.MS.ID.555703.pdf

Dear the leading person:

How will be the below information?

The biggest scandal:

The typical good comment for the first draft is given by some physicist as follows:

Here is how I see the problem with prohibition on division by zero,

which is the biggest scandal in modern mathematics as you rightly pointed out (2017.10.14.08:55)

A typical wrong idea will be given as follows:

mathematical life is very good without division by zero (2018.2.8.21:43).

It is nice to know that you will present your result at the Tokyo Institute of Technology. Please remember to mention Isabelle/HOL, which is a software in which x/0 = 0. This software is the result of many years of research and a millions of dollars were invested in it. If x/0 = 0 was false, all these money was for nothing. Right now, there is a team of mathematicians formalizing all the mathematics in Isabelle/HOL, where x/0 = 0 for all x, so this mathematical relation is the future of mathematics. https://www.cl.cam.ac.uk/~lp15/Grants/Alexandria/

José Manuel Rodríguez Caballero

Added an answer

In the proof assistant Isabelle/HOL we have x/0 = 0 for each number x. This is advantageous in order to simplify the proofs. You can download this proof assistant here: https://isabelle.in.tum.de/

Nevertheless, you can use that x/0 = 0, following the rules from Isabelle/HOL and you will obtain no contradiction. Indeed, you can check this fact just downloading Isabelle/HOL: https://isabelle.in.tum.de/

and copying the following code

theory DivByZeroSatoih imports Complex_Main

begin

theorem T: ‹x/0 + 2000 = 2000› for x :: complex by simp

end

2019/03/30 18:42 (11 時間前)

Close the mysterious and long history of division by zero and open the new world since Aristotelēs-Euclid:　1/0=0/0=z/0= \tan (\pi/2)=0.

Sangaku Journal of Mathematics (SJM) c ⃝SJMISSN 2534-9562 Volume 2 (2018), pp. 57-73 Received 20 November 2018. Published on-line 29 November 2018 web: http://www.sangaku-journal.eu/ c ⃝The Author(s) This article is published with open access1.

Wasan Geometry and Division by Zero Calculus

∗Hiroshi Okumura and ∗∗Saburou Saitoh

２０１９．３．１４．１１：３０

Black holes are where God divided by 0：Division by zero：1/0=0/0=z/0=\tan(\pi/2)=0 発見５周年を迎えて

You're God ! Yeah that's right...

You're creating the Universe and you're doing ok...

But Holy fudge ! You just made a division by zero and created a blackhole !! Ok, don't panic and shut your fudging mouth !

Use the arrow keys to move the blackhole

In each phase, you have to make the object of the right dimension fall into the blackhole

There are 2 endings.

Credits :

BlackHole picture : myself

Other pictures has been taken from internet

background picture : Reptile Theme of Mortal Kombat

NB : it's a big zip because of the wav file

More information

Install instructions Download it. Unzip it. Run the exe file. Play it. Enjoy it.

https://kthulhu1947.itch.io/another-dimension

A poem about division from Hacker's Delight Last updated 5 weeks ago

I was re-reading Hacker's Delight and on page 202 I found a poem about division that I had forgotten about.

I think that I shall never envision An op unlovely as division. An op whose answer must be guessed And then, through multiply, assessed; An op for which we dearly pay, In cycles wasted every day. Division code is often hairy; Long division's downright scary. The proofs can overtax your brain, The ceiling and floor may drive you insane. Good code to divide takes a Knuthian hero, But even God can't divide by zero! Henry S. Warren, author of Hacker's Delight.　

https://catonmat.net/poem-from-hackers-delight　　

祝改元　令 和

改元、令和時代 を祝する。令和とは 偶然、ゼロ除算の概念から、全ての和を考えるとゼロになるという、ゼロの雄大で深い意味を表わす。２０００年を越える数学の歴史には　未だ数学の前史時代を思わせるような基本的な欠陥がある。

改元を機会に、令和時代にゼロ除算算法を取り入れた新数学を発展させて、令和時代の世界文化遺産 になるように　日本国は先導し、努力して、今こそ世界の数理科学に貢献しよう。

再生核研究所

令和　元年　５．１．

付記：　

再生核研究所声明481（2019.4.4.）　改元に当たって、日本からの贈り物、ゼロ除算算法　ー　新数学

(　流石に　素晴らしい日本の文化。感銘しました。力が湧いてきました。凄い考えも浮かんできました。令和。

新元号　令和は、漢字、発音、形、由来、素晴らしいと感じました。 そこで、力が　湧いてきました。　ゼロ除算算法は　特異点の世界に立ち入った　全く新しい世界、数学ですので、　改元を機会に　日本発（初）の　数学の基礎の確立に貢献したい。　日本数学会、日本国の力をかけて　世界に貢献すべく努力したい。

https://ja.wikipedia.org/wiki/%E4%BB%A4%E5%92%8C

時ときに、初春しよしゆんの令月れいげつにして、気き淑よく風かぜ和やはらぎ、梅うめは鏡前きやうぜんの粉こを披ひらき、蘭らんは珮後はいごの香かうを薫かをらす。 ）

そこで、万葉の美しい心情を篤く受け止めて　ややもすると日本の文化、精神の弱点とみられる数理科学の基礎に　日本国が今後永く世界に貢献できる新数学として　ゼロ除算算法の大きな展望を　新時代を迎えるに当たって述べたい。日本発（初）の基礎数学、新しい世界観を　世界の文化に貢献すべく世界に展開しようではないか。

そもそもゼロ除算算法とは、ゼロで割る問題　(ゼロ除算)　から由来するが、ゼロ除算は　古くはアリストテレス以来　不可能であることの象徴と考えられ、物理学上でもアインシュタインの最大の懸案の問題であったとされる。特異点での問題はブラックホールの問題と絡ませて、現在でも広く議論されている。しかるにその本質はゼロ除算算法の概念で捉えられ、原理は解析関数の孤立特異点での　新しい世界の発見　として説明される。従来、特異点においては、特異点の近くでの研究を行い、特異点そこでは考えて来なかった。すなわち、特異点そのものでの研究を可能にしたものであるから、全く新規な世界、数学である。不可能であると２０００年を越えて考えられてきたところ、可能になったのであるから、その大きな意義と影響は既に歴然である。その影響は数学の全般に及ぶばかりか、我々の世界観に甚大なる影響を与え、世界史の大きな展開期を迎えるだろう。現代初等数学は、本質的な欠陥を有し、数学の基本的な再構成が求められ、新しい未知の雄大な世界の解明が求められている。

今こそ、新時代を迎えるに呼応して、新数学、新時代を開拓して、日本国は世界に貢献できるように、努力して行こう。

これらの事実を裏付けするものとして、次を参照されたい：

再生核研究所声明 479(2019.3.12) 　遅れをとったゼロ除算　－　活かされな　い敗戦経験とイギリスの畏れるべき戦略

再生核研究所声明　480(2019.3.26) 　日本の数学の後進性

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　以　上

７歳の少女が、当たり前である（100/0=0、0/0=0）と言っているゼロ除算を　多くの大学教授が、信じられない結果と言っているのは、まことに奇妙な事件と言えるのではないでしょうか。 1/0=0、0/0=0、z/0=0 division by zero（a⁄0 ）ゼロ除算　1/0=0、0/0=0、z/0=0 1/0=0/0=z/0= \tan (\pi/2)=0. 小学校以上で、最も知られている基本的な数学の結果は何でしょうか・・・ ゼロ除算（1/0=0、0/0=0、z/0=0）かピタゴラスの定理（a2 + b2 = c2 ）ではないでしょうか。 https://www.pinterest.com/pin/234468724326618408/ 1+0=1　1－0=1　1×0=0　　では、1/0・・・・・・・・・幾つでしょうか。 0??? 　本当に大丈夫ですか・・・・・0×0=1で矛盾になりませんか・・・・ 数学で「A÷０」（ゼロで割る）がダメな理由を教えてください。 http://detail.chiebukuro.yahoo.co.jp/.../ques.../q1411588849 #知恵袋_ 割り算を掛け算の逆だと定義した人は、誰でしょう？？？ Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity. https://notevenpast.org/dividing-nothing/ multiplication・・・・・増える 掛け算（×） 1より小さい数を掛けたら小さくなる。 大きくなるとは限らない。 0×0=0・・・・・・・・・だから0で割れないと考えた。 唯根拠もなしに、出鱈目に言っている人は世に多い。 加（+）・減（-）・乗（×）・除（÷） 除法（じょほう、英: division）とは、乗法の逆演算・・・・間違いの元 乗（×）は、加（+） 除（÷）は、減（-） http://detail.chiebukuro.yahoo.co.jp/.../q14.../a37209195... http://www.mirun.sctv.jp/.../%E5%A0%AA%E3%82%89%E3%81%AA... 何とゼロ除算は、可能になるだろうと　April 12, 2011　に　公に　予想されていたことを　発見した。 多くの数学で できないが、できるようになってきた経緯から述べられたものである。 ０を引いても引いたことにならないから： 君に０円の月給を永遠に払いますから心配しないでください： 変化がない：引いたことにはならない：

#知恵袋_

#人工知能

#2019年

#再生核研究所

#再生核研究所声明

#更新

#ゼロ除算を発見したのは2014年2月2日

#0除算

#ポーカー

#5年を超えたゼロ除算の発見と重要性を指摘した

#ログゼロハゼロ

#tangent二分のパイはゼロ

#0除算と人工知能

[uy8hg]

Plus One

I very much like the little brother au going on, so here’s a thing.

The crew goes on a mission to steal Jeremy’s old friend Matt from a rival gang, but they pick up another person, who may or may not have his own ties to some crew members.

Word Count: 3157

I also have an AO3, now! I’ll be posting my fics on there soon, so you can follow me there too if you want.

Geoff wasn’t expecting much from this deal. Jeremy had briefed them all on the plan, as this was his idea. If they weren’t trying to pull the façade that this was a real deal, Jeremy would be the one here.

Jeremy had regaled them only too often with stories of his and Matt’s adventures before he joined the crew. Once or twice he’d mentioned another guy, when they called themselves The Stream Team, but mostly it was just the two of them. When Jeremy saw the news clip of this small crew doing a job, he’d jumped out of his chair. Michael had needed to tackle the shorter lad on his attempts to leave just to get him to explain the whole situation.

After a series of rough jobs, Matt and Jeremy had gotten separated. The two had never quite managed to find each other again, and then they had picked up Jeremy. Once or twice, Gavin had tried to find Matt, but with no success. Jeremy had warned them that Matt was also a bit of hacker. Gavin wasn’t too happy about that, and tripled his effort. Somehow, they had never found him, until they saw that news clip.

Jeremy insisted they bust Matt out of that crew. Together, they’d all cooked up a plan to get Jeremy’s friend back. Geoff wasn’t too happy that he had to do most of the talking, but he would do anything for Lil’ J. Plus, if he didn’t, he’d never hear the end of it.

They arrived at the warehouse first, which wasn’t exactly to Geoff’s liking. He wasn’t too fond of walking into empty places, but it beat walking into a setup. At least they had picked the place.

Gavin gave him and Ryan a salute before running off to his post, sniper slung over his shoulder. Ryan pulled on him mask, going from creepy in just his face paint to downright nightmare inducing. Geoff never fully got used to that mask, always a little unsettled by its appearance, but one look at the man’s eyes told him it was still his Ryan inside there.

The two of them walked in. The table and chairs were set up just like Gavin had said they were over the comms. Geoff took one, Ryan stationing himself behind his left shoulder. The two immediately went into business mode, knowing any second the other crew could walk in.

Sure enough, it hadn’t been a full minute before the other side walked in. There were three of them, like they’d suspected. The boss was there, of course, so Geoff could make the deal. Matt fell in step behind him, with another guy he couldn’t quite see yet bringing up the rear. Ryan adjusted himself to stand taller, and Geoff just smirked. These guys didn’t know what they were signing themselves up for.

“Deaton,” Geoff started. The boss nodded, muttered out a “Ramsey,” and approached the chair. As he sat down, the two guards flanked him. He kept his eye on Matt, who looked like he didn’t really want to be here. He didn’t blame the kid. They had a reputation. The kid was wearing an old red hoodie and had headphones around his neck. His hear was streaked a vibrant light blue, and overall he looked like any other teenager, except he was holding a rather impressive firearm.

As he was pondering this, Ryan tensed behind him. It was slight, not enough for anyone other than people who knew him well to notice. Geoff stopped himself from turning around, but he took mental note to ask him later. Ryan readjusted behind him as he began his spiel.

“Look. I’ll get right to it. We don’t want weapons, or money, or anything like that,” Geoff began, and the man across from him sat up.

“What do you mean? That was our deal!”

Geoff shrugged. “Changed my mind. But I do still want something.”

Deaton’s tone shifted dangerously as he shot back, “Oh?”

Geoff pointed one finger at Matt, who was trying his best to look anywhere but Geoff.

“Axial?” Deaton growled. “Not happening.”

“Well that’s too bad, because I intend to leave here with him.” Ryan shifted behind Geoff again, and Geoff had to keep his gaze straight ahead. Ryan wasn’t normally this fidgety, especially not during a deal.

“The only way I see that happening is by him carrying your body.”

Geoff actually laughed genuinely. “Are you threatening me?”

Deaton immediately recognized his mistake. “Uhm, no, not at all, Ramsey.”

“Weird, because it sounded like you were. So, you’re going to let us have him now, right?”

Deaton looked back at Matt for the first time, who in turn looked at the other bodyguard. Geoff’s gaze finally travelled to the third man. He was taller than Matt, and skinny as a twig. He was wearing a dark pinstripe vest over a white shirt with the sleeves rolled up. His fingerless gloves were partially hiding bruised knuckles, and he had shades pushed up on his head. Another guy who looked like a teenager with a weapon.

When Matt looked over, Ryan fidgeted once again, bigger this time, but still hardly noticeable. Something was up with Ryan, and Geoff had a sneaking suspicion it had to do with this other guy.

“Yeah, yeah, sure. Axial’s all yours,” Deaton was rushing to fix his error, but Geoff butted in again.

“You know what? My offer just changed.”

“What?” Deaton was panicking now. Matt looked like he was about to explode, and the mystery guy just looked confused.

Geoff relished in pointing a single finger at the third guy. “I want him too.”

Ryan froze behind him, and the other guy probably mirrored the expression Ryan had underneath his mask. Geoff enjoyed the utter chaos the deal was devolving into.

“I can’t. Not Zed, too.” His voiced was laced with desperation, standing now as if he could run away from this whole mess.

Geoff shrugged. “Do you want our Golden Boy to convince you?” He could hear Gavin give a quick laugh over the comms as Deaton got even more flustered, searching the room.

“No. He’s not . . . I can’t give them both . . .”

Geoff made the choice for the poor man. “Yeah you can. Do it, Golden Boy.”

A single shot, straight through the skull. Matt and the other guy, Zed, both jumped back at the shot. Deaton dropped. Geoff let out a huge sigh upon standing, as if this whole mess was much more hassle than it actually was. Deaton was much more annoying than he’d predicted, so he didn’t feel too bad about using their worst case scenario setup. “Alright. Let’s get you two home.”

As he turned, he caught Ryan’s eye. There was some emotion there that he couldn’t quite place. Either way, it was gone in a flash as Ryan went to herd the other two, still having to be the Vagabond until they got back to the penthouse.

Gavin met them outside and they all piled into the jeep. They just barely managed to fit, Gavin squeezed in between the two new recruits but he didn’t seem to care. He just kept talking the ears off the two, who had matching looks of confusion and dread. Ryan was stiff beside him, gaze locked out the window. Geoff kept his attention on the road, but there was definitely something up with Ryan.

 Jeremy basically tackled Matt the second he got in the penthouse. Geoff had texted Jeremy that they were arriving, as if Jeremy hadn’t been looking out the window waiting for the past half hour. Matt was the first in, and also the one to get tackle-hugged. Jeremy could hear the other three pass them by and head to the living room, but he cared about no one other than Matt right now.

“Matt!” Jeremy cried, face very much buried in the other’s shoulder.

“Wha- Jeremy?” Matt exclaimed, and Jeremy could feel him tentatively wrap his arms around him. He squeezed harder until he heard the other guy squeak. “Hey, man, you’re gonna break me!”

“I’m so happy we found you!” Jeremy gushed, pulling himself back to examine Matt from an arm’s length away. Matt was wearing something similar to what he always used to: A ratty red hoodie covered a worn out graphic tee, headphones around his neck. The blue streaks in his hair were new, though, still bright as if they’d only been there a few days. Jeremy wished he still had colorful hair, but he’d let it grow out recently. “We tried so hard to find you!”

Matt seemed taken aback. “So, wait, what? The point of that deal, or whatever it was, was actually me? That went according to plan?”

Jeremy nodded enthusiastically. “All for you.”

“But then . . . what about Trevor?”

Jeremy froze and blinked up at his friend. “Trevor? As in, that Trevor? Our Trevor? What about him?”

Matt nodded. “Our Trevor. He was in the crew with me. He was Deaton’s other bodyguard for the deal and Geoff just brought him along. Did you plan for that?”

Jeremy dropped his grip on Matt’s arms, which had tightened when he’d heard Trevor’s name. “No, we didn’t know. We had hardly any information on your crew. Wonder why Geoff brought him along.”

Matt shrugged. “Did he know about The Stream Team?”

“Yeah, I’d mentioned it a few times, but mostly about you. I doubt he remembered Trevor’s name, let alone knew who he was at the deal.”

“Weird,” Matt agreed. The door chose that moment to open, causing both guys to shift their attention. Ryan slammed the door behind himself and let out a long sigh before noticing the two.

“Hey,” he rasped, and his voice was harder than usual, “Did we get the right guy?”

Jeremy chuckled. “No, this is some random guy. Never seen him before in my life,” he joked and threw an arm around Matt, who immediately pushed it off. Ryan didn’t laugh, but nodded as he pushed off of the door. He still had his mask on, so Jeremy couldn’t quite read his expression.

“Glad to hear it,” he said calmly before disappearing down the hall. The two heard a door open and shut, probably the bathroom.

It was weird Ryan hadn’t taken his mask off. Normally it was the first thing off when they got back. Something about Ryan’s behavior was striking him as odd. He tried to shrug it off, figured it was just for the new people they’d brought back. Jeremy guessed he’d gone to wash of the paint, trying not to scare the new guys. Or at least, that’s what Jeremy hoped.

“That’s the Vagabond,” Matt stated hesitantly, still watching the hallway Ryan had disappeared down. Jeremy slung his arm back over his friend and nodded.

“Yep! He’s intimidating at first, sure, but I promise he’s a teddy bear. You’ll see.”

Matt didn’t seem so sure, but he allowed Jeremy to drag him off toward the living room. He had a crew for Jeremy to introduce him to.

 Ramsey had told Trevor to sit on the couch, so that’s what he did. A woman wearing the world’s most parrot-covered Hawaiian shirt soon draped a blanket over his shoulders, which Trevor took hesitantly. He honestly no clue what had happened in the last hour, but he figured he just had to roll with it. One minute he’s randomly assigned to guard the boss on a deal, the next he’s being welcomed into the penthouse of the Fake AH Crew. He felt nervous, the guns he’d been given to bodyguard with stowed in the back of the Fake’s car. So, he just chose to sit. The Golden Boy flopped down on the other couch and immediately pulled out his phone, not caring at all about Trevor.

The woman, who he recognized as Pattillo, Ramsey’s right hand woman, had turned on the TV, which was showing a photo from earlier on the news. The deal hadn’t been that big, nothing to draw attention, but apparently any sighting of the Fakes made the news. Trevor didn’t understand how they got a shot of their group, but there it was in front of him.

Ramsey was the closest to the car, calling at the Golden Boy, who had just appeared from whatever sniping point he’d had. The Vagabond was further back, a hand each on Matt and his’ shoulders. Trevor was looking away at the ground, while Matt was watching the two in front. Trevor remembered exactly what moment the photo had been taken at. He’d been trying to figure out what had happened, and he still didn’t quite know. Whatever it was, he was glad Matt was here, and apparently Jeremy too. He’d seen his old friend hugging Matt as they came in.

What he hadn’t noticed in the moment, but could clearly see now in the photo, was the Vagabond. The masked head was turned, not facing front like he would have guessed.

Instead, it was watching Trevor.

Trevor had only heard stories about the Vagabond before today, and he would have liked to keep it that way. When he first saw the Vagabond, he was immediately intimidated, and not just by the rumors. He looked like a guy who could mess you up, and Trevor didn’t want to test him. He’d complied when the Vagabond escorted them, scared to anger the blue eyes that were the only indication an actual human was behind the mask.

He was suddenly very glad he hadn’t turned around on his way to the car. But he did wonder why the Vagabond had been looking at him.

“Who’s this?” A voice behind him asked, and Trevor turned to see Mogar approaching the kitchen. Ramsey shrugged, pouring himself a glass of some form of alcohol.

“Deaton’s other guard. Brought him along. Deaton didn’t need him anymore.”

“But why bring him here? We know nothing about him.” Trevor wanted to say something to defend himself, tell them he knew Matt and Jeremy, but Ramsey suddenly met his eyes.

“I had a feeling we might want him. Call it a hunch.” Trevor met his eyes, trying to figure out what that meant, until Ramsey looked back at Mogar. “Plus you can’t just leave him. He might get revenge ideas.”

Mogar shrugged and came over to the other couch. He sat directly on the Golden Boy’s legs, which got a squawk out of the other man. He half nodded at Trevor from his weird perch. “Sup.” Trevor gave him a half smile before looking away.

What the heck was happening?

His salvation from awkwardness came in the form of Jeremy escorting Matt into the living room. “So this is the living room. Make yourself at home.” Trevor turned, and he watched Jeremy’s eyes light up. “Trevor!”

Jeremy rushed over to give him a hug over the back of the couch. “Man, I didn’t know you were with Matt! This is great!”

“It sure is something,” Trevor laughed. Jeremy hopped the couch to sit next to Trevor, and Matt sat down on Jeremy’s other side. Jeremy pulled them both in by the shoulders.

“Stream Team, back together!” he called happily. Trevor couldn’t help but laugh, still a little in shock but feeling better that Jeremy was here. Even if he was in the middle of the Fake’s headquarters, Jeremy and Matt were here. He’d heard tales of a purple and orange clad member of the Fakes, but he hadn’t put two and two together to realize it was Jeremy.

The little stability he’d just found was shattered as one word came from behind him.

“Trevor?

Trevor froze, completely tense in an instant, and stared straight ahead. He recognized that voice, but it couldn’t be. It was lower, gruffer, and sound almost as if it had been crying. But there was no way. Trevor hadn’t heard that voice in years, there was no way he could be here.

Could it really-?

Jeremy let Trevor go and he turned, as slow as he could. He was scared to see, scared to know the truth. He didn’t know what he’d do if it wasn’t him. He didn’t know what he’d do if it was.

Trevor slowly lifted his gaze. First he saw a horrible pair of black shoes, then a pair of dark and loose jeans. There was the jacket, black, blue, and silver identifying the Vagabond. He didn’t want to look up those last few inches, but he had to. He could see the Vagabond’s chest rising and falling visibly, as if he was terrified too. He had to do it. He had to look.

The Vagabond was still wearing the mask. Trevor could only look at his eyes as the Vagabond let out an almost painful sigh.

“It is you. Trevor.”

That was the voice. The voice Trevor remember from his childhood, the one he had so desperately wanted to hear again. It was coming from the Vagabond.

He opened his mouth, but nothing came out. In a desperate and almost violent move, the Vagabond ripped his mask off.

Feelings Trevor hadn’t felt in a long time came rushing back as he looked at the Vagabond’s face. It was older, obviously, and had several smears of face paint still on it, but it was definitely him.

It was Ryan.

Trevor stood up, letting the blanket fall off his shoulders. He didn’t break eye contact with Ryan as the two ran to each other and embraced. The whole crew was probably staring at them, but Trevor didn’t care. He had his brother back. After so many years, several foster homes, and who knew how many crews, somehow Trevor had managed to find Ryan again. Or, rather, Ryan had found him. He’d been watching him from afar, seeing the Vagabond on the news for years, without even realizing it. But now, his brother was in his arms again.

“I’m so sorry it took me so long. I couldn’t find you again.” Ryan was crying, Trevor could hear it, and he realized he was as well.

“That’s okay. I’m here now,” Trevor mumbled into his brother’s shoulder.

“I don’t know how this worked out, but I’m so glad it did,” Ryan told him, and Trevor just nodded.

“Does anyone else know what’s going on?” a British voice asked from behind Trevor, and Trevor barked out a laugh through his tears. Honestly, he still didn’t know, but one thing was for sure. Somehow, by some miracle, he was in his brother’s arms again.

Ryan pulled back, ruffling Trevor’s hair like he had when they were kids. Trevor laughed and leaned against Ryan as the two of them faced the crew.

“Guys,” Ryan started, voice still a little emotional, “this is my half-brother, Trevor.”

Ryan pulled him in closer as Trevor corrected him, “Nothing half about it but blood.”

[deniscollins]

‘Hamilton’ and ‘Harry Potter’ Productions Try to Outwit Scalpers

If you were the producer of a Broadway play, would you: (1) allow scalpers using automated systems to purchase and resell tickets or (2) instead of receiving a traditional ticket from the box office or a facsimile printed at home, you just get an email confirming your purchase, then, on the day of the show, you have to bring the same credit card you used for the purchase — as well as the email confirmation and a photo ID — and run the credit card through a scanner to get in, with the theory that requiring the same credit card for purchase and entrance should complicate efforts by would-be resellers (but causes problems with tickets that were gifted). Why? What are the ethics underlying your decision?

“Hamilton” and the new “Harry Potter” play are the hottest theatrical shows of the moment, with “Hamilton” outgrossing everything else on Broadway, and Harry, Hermione and Ron drawing hordes of muggles to London’s West End.

But success has a side effect: Both shows have fallen prey to high-tech scalpers who harvest large quantities of seats and resell them at exorbitant markups. “Hamilton” has been hit particularly hard: When it first opened on Broadway, nearly 80 percent of seats were purchased by automated ticket bots, and for Lin-Manuel Miranda’s final performance, resellers were seeking an average of $10,900 a seat.

Now, as “Hamilton” prepares to open in London this fall and “Harry Potter” plans to open on Broadway next year, the producers of both shows are aggressively trying to contain scalping, a long-festering problem for the entertainment industry that has been exacerbated by technology. The producers of “Hamilton” are trying an unusual approach for theater — paperless ticketing — while the producers of “Harry Potter” are refusing to accept resold tickets.

And in the United States and Britain, policy makers are tackling the issue anew, concerned about the effect of industrialized scalping on consumers and artists.

“I’ve been in the business 50 years, and I’ve lived through lots of scalping,” said Cameron Mackintosh, producer of “Cats,” “Les Misérables,” “The Phantom of the Opera” and “Miss Saigon.” “It’s just got far, far more sophisticated, because of automation’s creeping stranglehold on human beings.”

Mr. Mackintosh is on the front lines of the latest battle against resellers. In addition to being a producer, he is an owner of major theaters in the West End, including Victoria Palace, where “Hamilton” will begin performances in November. For the tickets that just went on sale — and the first block immediately sold out — the show is trying paperless ticketing, which has long been used for concerts, to the consternation of ticket brokers.

Picture this: Instead of receiving a traditional ticket from the box office or a facsimile printed at home, you just get an email confirming your purchase. Then, on the day of the show, you have to bring the same credit card you used for the purchase — as well as the email confirmation and a photo ID — and run the credit card through a scanner to get in. The theory is that requiring the same credit card for purchase and entrance should complicate efforts by would-be resellers.

“Going to the theater is expensive enough as it is with the money that you need to charge to put these big shows on, so it’s absolutely ridiculous for it to be inflated by third parties,” Mr. Mackintosh said.

There are downsides: It makes it harder to purchase tickets as gifts, and there is a risk of congestion or confusion at the theater doors. And the method is not fail-safe. On the day “Hamilton” tickets went on sale in London, with a face value of up to $200, tickets were already being promoted for resale at up to $6,000. Their validity was unknown — the show has vowed to cancel resold tickets — but in theory, a reseller could try to circumvent the system by accompanying customers to the show.

For now, paperless ticketing does not appear to be an option in New York, which restricts such sales. There, “Hamilton” has tried a different approach: reducing the effect of resellers by canceling suspect purchases, and, more recently, by raising prices at the box office to more closely reflect the tickets’ perceived market value.

“Harry Potter and the Cursed Child,” a critically acclaimed sequel to J. K. Rowling’s books, is trying a similar, labor-intensive approach in London. The producers have hired a group of workers who are combing through sales records and broker sites, looking for evidence of unauthorized bulk buying — often via bots, which are computer programs used by scalpers — as well as for tickets offered on resale websites. The show’s producers say they have stopped about 2,500 online sales and have refused to accept tickets from about 150 patrons at the door — a tiny fraction of tickets sold to date.

“We have no silver bullet, but we are trying to do everything we can within the law, and it has made a massive difference,” said Sonia Friedman, a lead producer of the “Harry Potter” play.

Ms. Friedman and her co-producer, Colin Callender, said they would be consulting with New York producers and officials about what steps they might take to limit resales when their show opens next year on Broadway, where it is also expected to be a blockbuster.

The secondary ticketing market is a big business that has long been a significant factor for major concerts and sports events. Live Nation Entertainment, the company that owns Ticketmaster, has estimated it at $8 billion a year. And the business is increasingly global, making any one country’s laws difficult to enforce.

StubHub, a large ticket reselling company, said it supported legislation to combat “bot misuse” but also argued that producers shared blame for high ticket prices.

“There continues to be a lack of transparency in the primary market about how many tickets are available for public sale,” the company said. “This is despite the fact that the industry and regulators continue to put pressure on the secondary industry, rather than attempting to tackle these problems at the source.”

Theater producers said they objected to reselling on two grounds: It limits access, by making it harder for people who are not wealthy to afford popular shows, and it deprives theater artists, presenters and investors of profits that should be theirs but instead go to ticket brokers.

At a recent performance of “Harry Potter” in London, ticket holders expressed considerable wariness about resellers.

“I was looking in at all the touting sites, all the reselling sites, and the same type of ticket I got was going for like 600 pounds a ticket — it was ridiculous,” said Lauren Putland, 26, of Portsmouth, England. But Ms. Putland acknowledged that she had once used a reseller to obtain tickets to a Britney Spears concert. “I was literally obsessed with her — I would have done anything to go to her Circus tour — so I paid over the odds for that,” she said.

The issue affects other shows beyond “Hamilton” and “Harry Potter,” for which demand seriously outstrips supply. New York Theater Workshop, an Off Broadway nonprofit that has just 200 seats and is perhaps best known as the birthplace of “Rent,” has emerged as a test case because it has recently had two shows with strong crossover appeal: “Lazarus,” featuring songs by David Bowie, who died while the production was running, and “Othello,” starring Daniel Craig and David Oyelowo.

The theater tried to limit reselling by requiring ticket buyers to present the same credit card used for the purchase at the box office and, mimicking steps taken by “Hamilton,” imposing limits on the number of tickets a buyer could purchase.

“The lesson we learned is that it is possible to limit it and to frustrate their attempts, but not to completely eliminate it,” said Jeremy Blocker, the theater’s managing director. “With ‘Othello,’ we know we saw instances of a ticket or two popping up online at a pretty significant markup.”

In the United States and Britain, lawmakers are scrambling to try to keep up with a fast-changing landscape.

In December, President Barack Obama signed an antibot bill, and in November, Gov. Andrew M. Cuomo of New York, where bots were already banned, signed a law increasing penalties for their use.

Eric T. Schneiderman, the New York attorney general, has come to believe that the state should consider changing its restriction on paperless tickets.

“We’re the only state that has this broad a prohibition,” he said in an interview. New York’s tougher antibot laws were a form of progress, he added; the arrival of “Harry Potter” next year will be “a test of our new criminalization of the bots; we’ll see what the impact is.”

In Britain, where pop musicians have been far more vocal about scalping concerns, an advocacy group, the FanFair Alliance, was founded last year by a group of artists and powerful managers (Mumford & Sons, Ed Sheeran and more).

Adele has become a high-visibility example of how artists are trying to control scalping. Using Songkick, a boutique ticketing company, she has sold hundreds of thousands of seats directly to fans, which Songkick says has drastically reduced their availability on the secondary market. But while she was able to sell two-thirds of the tickets to her four coming Wembley Stadium shows, industry practices limited Songkick’s allotment in the United States to 8 percent of the ticket inventory. Songkick is suing Ticketmaster in federal court in the United States over those restrictions, which it says are anticompetitive.

In London, Parliament is considering antibot legislation after the release last year of a critical investigation of the market, written by Michael Waterson, an economics professor at the University of Warwick. The House of Commons held hearings in November, expressing concern about close relationships between the sellers and resellers. (In an article for The Telegraph, Damian Collins, a Conservative member of Parliament, wrote, “The ticketing industry in the United Kingdom has become a national scandal.”) Another government agency, the Competition and Markets Authority, has opened its own investigation.

“Quite a lot is happening at last,” said Sharon Hodgson, a Labour member of Parliament who has been pushing for years for legislation to restrain resellers. “The secondary market is a bit nervous, and they should be.”