「車いすの天才科学者」と呼ばれ、１４日に７６歳で死去した英理論物理学者のスティーブン・ホーキング博士。難病と闘いながら革新的な理論で謎に挑み続け、宇宙論の発展に偉大な足跡を残す一方、社会にも広く影響を与えた。（※３月２５日の記事を再掲載しています）

現代宇宙論の基礎となっているのは、アインシュタインが１９１６年に発表した一般相対性理論だ。時間と空間は重力によってゆがむことを示したもので、ニュートンが１７世紀に示した「時間と空間は何にも影響されない」という常識を覆す革命を起こした。

その後、宇宙は超高密度の状態で生まれ爆発的に膨張したとする「ビッグバン宇宙論」が誕生。２９年には米国の天文学者ハッブルが、遠くの銀河ほど速く遠ざかっていることを観測し宇宙の膨張を実証した。

宇宙の起源に関心を持ったホーキング氏は６０年代以降、革新的な理論を次々に発表した。まず、相対性理論に従って時間をさかのぼっていくことで、宇宙には始まりが確かにあったと数学的に証明し、ビッグバン宇宙論に貢献した。

その一方で、重大な問題も提起した。ビッグバンの発生時には巨大なエネルギーが一点に集中し、大きさがゼロで密度が無限大の「特異点」が生じる。ここでは時空が無限にゆがみ、相対性理論が成立しなくなるというものだ。

 

ゼロ除算の発見は日本：

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�
�算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

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

 

OUR HUMANITY AND DIVISION BY ZERO

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

 

5000年？？？？？

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

とても興味深く読みました：

 

 

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

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and 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 supporter
s 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 375　(2017.7.21)：ブラックホール、ゼロ除算、宇宙論

                        

本年はブラックホール命名５０周年とされていたが、最近、wikipedia で下記のように修正されていた：

名称[]                                    

“black hole”という呼び名が定着するまでは、崩壊した星を意味する”collapsar”（コラプサー）などと呼ばれていた。光すら脱け出せないに対して “black hole” という言葉が用いられた最も古い印刷物は、ジャーナリストのアン・ユーイング (Ann Ewing) が1964年1月18日の Science News-Letter の “‘Black holes’ in space” と題するの会合を紹介する記事の中で用いたものである。一般には、のが1967年に “black hole” という名称を初めて用いたとされるが、実際にはその年にニューヨークで行われた会�
�中で聴衆の一人が洩らした言葉をホイーラーが採用して広めたものであり、またホイーラー自身は “black hole” という言葉の考案者であると主張したことはない。

 

世界は広いから、情報が混乱することは　よく起きる状況がある。ブラックホールの概念と密接な関係のあるゼロ除算の発見（２０１４．２．２）については、歴史的な混乱が生じないようにと　詳しい経緯、解説、論文、公表過程など記録するように配慮してきた。

ゼロ除算は簡単で自明であると初期から述べてきたが、問題はそこから生じるゼロ除算算法とその応用であると述べている。しかし、その第１歩で議論は様々でゼロ除算自身についていろいろな説が存在して、ゼロ除算は現在も全体的に混乱していると言える。インターネットなどで参照出来る膨大な情報は、我々の観点では不適当なものばかりであると言える。もちろん学術界ではゼロ除算発見後３年を経過しているものの、古い固定観念に囚われていて、新しい発見は未だ認知されているとは言えない。最近国際会議でも現代数学を破壊するので、認められない等の意見が表明された（再生核研究所声明371（2017.6.27）ゼロ除算の講演―　国際会議　　報告）。そこで、初等数学から、５００件を超えるゼロ除算の証拠、効用の事実を示して、ゼロ除算は確定していること、ゼロ除算算法の重要性を主張し、基本的な世界を示している。

ゼロ除算について、膨大な歴史、文献は、ゼロ除算が神秘的なこととして、扱われ、それはアインシュタインの言葉に象徴される：

 

Here, we recall Albert Einstein’s words on mathematics:

Blackholes are where God divided by zero.

I don’t believe in mathematics.

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} (Gamow, G., My World Line (Viking, New York). p 44, 1970).

 

ところが結果は、実に簡明であった：

 

The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world

 

しかしながら、ゼロ及びゼロ除算は、結果自体は　驚く程単純であったが、神秘的な新たな世界を覗かせ、ゼロ及びゼロ除算は一層神秘的な対象であることが顕になってきた。ゼロのいろいろな意味も分かってきた。　無限遠点における強力な飛び、ワープ現象とゼロと無限の不思議な関係である。アリストテレス、ユークリッド以来の　空間の認識を変える事件をもたらしている。　ゼロ除算の結果は、数理論ばかりではなく、世界観の変更を要求している。　端的に表現してみよう。　これは宇宙の生成、消滅の様、人生の様をも表しているようである。　点が球としてどんどん大きくなり、球面は限りなく大きくなって行く。　どこまで大きくなっていくかは、　分からない。しかしながら、ゼロ除算はあるところで突然半径はゼロになり、最初の点に帰するというのである。　ゼロから始まってゼロに帰する。　――　それは人生の様のようではないだろうか。物心なしに始まった人生、経験や知識はどんどん広がって行くが、突然、死によって元に戻る。　人生とはそのようなものではないだろうか。　はじめも終わりも、　途中も分からない。　多くの世の現象はそのようで、　何かが始まり、　どんどん進み、そして、戻る。　例えばソロバンでは、願いましては　で計算を始め、最後はご破産で願いましては、で終了する。　我々の宇宙も淀みに浮かぶ泡沫のようなもので、できては壊れ、できては壊れる現象を繰り返しているのではないだろうか。泡沫の上の小さな存在の人間は結局、何も分からず、われ思うゆえにわれあり　と自己の存在を確かめる程の能力しか無い存在であると言える。　始めと終わり、過程も　ようとして分からない。

 

ブラックホールとゼロ除算、ゼロ除算の発見とその後の数学の発展を眺めていて、そのような宇宙観、人生観がひとりでに湧いてきて、奇妙に納得のいく気持ちになっている。

 

以　上

数世紀にわたり人々を困惑させるパラドックス。古代の哲学者たちはなぜこんなにも複雑な問題を考えたのだろうか。今回は哲学界の超難問とそのパラドックスを5つ紹介しよう。

【その他の画像はコチラ→http://tocana.jp/2018/05/post_15887_entry.html】

■禿げの基準は紀元前4世紀から考えられていた

　紀元前4世紀、エウブリデスと言う男は、「The Heap」（ヒープ）と呼ばれるパラドックスを思いついた。ヒープは別名「ソリテス・パラドックス」ともいわれており、“度合い”についての古典的なパラドックスとしては最も早く誕生している。

　男性の頭に髪の毛が1本もない時、我々は「禿げている」と思う。しかし10,000本の毛があれば「禿げている」とは思わないだろう。では、髪の毛が0本の「禿げている」男性に、1本だけ髪の毛を追加してみたらどうだろう。まだこの男性は明らかに「禿げている」と思われるはずだ。では、さらに1,000本の髪の毛を追加するとしたら？ 先ほどよりもずっと多くの髪の毛があるが、頭皮は見えてしまっている。この時、男性は「禿げている」か「禿げていない」のどちらになるだろう。

　1粒の穀物を見て「山のように盛られた小麦粉」を考える人はいない。2粒に増えてもまだ「山のように盛られた小麦粉」とは考えないはずだ。1粒ずつ足していくと、いつまでたっても「山のよう」にはならないように思えてしまう。しかし、どこかの時点で小麦粉は「山のよう」な状態になるはず。髪の毛もどこまでが「禿げていない」と言えて、どこからが「禿げている」になるのだろうか。

■永遠に手に入らないソーダ？

　古代ギリシアの自然哲学者・ゼノンは“距離と動作”について「二分法パラドックス」を提唱した。

　ソーダを買いに家から店まで出掛ける時、家と店の“中間地点”に到達する瞬間がある。またその“中間地点”から店までの間にはもう一つの“中間地点”（家から店までの道のりの3/4）が存在するはず。さらに、そこまで到達した場合、その場所から店までの間にもう一つ中間地点が生まれる。

　このように“中間地点”を設け続ける限り、無限に中間地点が登場し、いつまでたっても店にたどり着けなくなってしまう。もちろん、現実には店についてソーダを買うことができるが、最後の“中間地点”はどこになるのだろうか。ゼノンは“どこで距離の線引きを行うか”という疑問に執着していたようだ。

■疑問が理解できない男たち

　プラトン著書の『メノン』には、彼とソクラテスが“徳とはなにか？”について行った対話が収録されている。対話の中には「The Paradox Of Inquiry」（質問のパラドックス）が登場し、“答えの探し方”について考えがめぐらされている。

　ある疑問に対して答えを探る時、自分がどんな答えを探っているのかを理解していなければ、そもそも答えを探求することは不可能だ。しかし、逆にどんな答えを探っているのかを知っているのであれば、もはや答えが出ているも同然なので探る必要はない。メノンは「疑問が理解できない時、どのようにその答えを見つけるか」というパラドックスを考えていたよう。

　このパラドックスは別名「メノンのパラドックス」と呼ばれており、ソクラテスは「男は自分の理解があるもの、理解がないものの答えを探すことはできない」「なぜなら何を探すべきなのか分かっていないから」とパラドックスを解説した。

■真と偽の超複雑な関係

　数学者のフィリップ・ジャーデインは、「Double Liar Paradox」（嘘つきのパラドックス）を考えた。例えば単語帳や紙の一方をA面、その裏をB面とし、A面には「B面に書いてある文は真実」、B面には「A面に書いてある文は嘘」と書く。B面の文が“真実”であるとしたら、A面が“嘘”ということになる。しかし、A面の文章が“嘘”であったなら、B面に書いてあることもまた“嘘”ということになってしまい、そうなると今度はA面が“真実”になるので、B面に書かれた文も“真実”に…。真実と嘘が同時に存在するという奇妙な現象が生じてしまうのがこのパラドックスだ。

■100万円をゲットするには？

　3つのドア（それぞれA、B、Cと仮定）が用意され、2つのドアの向こうにはヤギ（ハズレ）があり、残る1つのドアの向こうには100万円（アタリ）があるとする。

　ドアを開けられるのは1度だけだが、回答者がドアAを選択したとき、サービスとしてドアBがオープンされ、Bは“ハズレ”だったことが判明。この時、“回答者はAのドアを選択したままにすべきか、それともCに変えるべきか”というのが「モンティ・ホール問題」と呼ばれる難問だ。

　残りのドアはヤギか100万円かのどちらかなので、Aを選んでもCを選んでも100万円をゲットできる確率は50％ずつのはず。しかし1990年に発行されたニュース雑誌『Parade』で、ギネスブックに「最も高いIQ」を有しているとして認定されたことで知られる、コラムニストのマリリン・ボス・サバントは「ドアを変更した場合はアタリを選ぶ確率が2倍になる」と回答した。当時も多くの議論を呼んだこの回答だが、モンティホール問題は今でも人々の頭を悩ませ続けている。
（文＝山下史郎）

※イメージ画像は、「Thinkstock」より

 

とても興味深く読みました：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

ゼロ除算関係論文・本

 

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 (a
bsence 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 gua
rd 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.

 

ゼロ除算は定義が問題です：

 

再生核研究所声明　１４８（2014.2.12）　100/0=0,  0/0=0　－　割り算の考えを自然に拡張すると　―　神の意志 

 

再生核研究所声明１７１（2014.7.30）掛け算の意味と割り算の意味　―　ゼロ除算100/0=0は自明である？

 

 

Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

 

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

 

Einstein’s Only Mistake: Division by Zero

 

#divide by zero

TOP DEFINITION

  

A super-smart math teacher that teaches at HTHS and can divide by zero.

Hey look, that genius’s IQ is over 9000!

    

by  October 21, 2009

 

 

Dividing by zero is the biggest  known to mankind. It is a proven fact that a succesful division by zero will constitute in the implosion of the universe.

You are dividing by zero there, Johnny. Captain Kirk is not impressed.

Divide by zero?!?!! OMG!!! Epic failzorz

    

 

3

  

 by  is undefined.

Divide by zero is undefined.

    

by  October 28, 2006

 

1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist.

2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up on  or something. Pretty confusing shit.

3) A reason for an error in programming

Hey, I divided by zero! …Oh shi-

a/0

Run-time error: ’11’: Division by zero

    

by  September 08, 2006

 

When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says “yeah, there’s kind of an answer, but it ain’t just some number.”

It’s when mathematicians become philosophers.

:
Let’s say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with

 because of dividing by zero:
Let’s say there are THREE apples, and ZERO people. How many apples does each person get? Friggin… How the  should I know! How can you figure out how many apples each person gets if there’s no people to get them?!? You’d think it’d be infinity, but not really. It could almost be any number, cause you could be like “each person gets 400 apples” which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it’s still wrong.

        

by  February 15, 2010

 

 

おはようございます。本日は哲学の日ということで、GWイヴです。4月27日です。
哲学者ソクラテスが、時の権力者から死刑宣告を受けて、刑の執行として獄中で毒を飲んで亡くなった日ということに由来していますが、理由があんまりハッピーなものでなくてショック。それでは振り返ってみましょう。

 

とても興味深く読みました：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

 

2017年11月15日(水)
テーマ：

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

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

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

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

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

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

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

 

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

 

 

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

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

 

OUR HUMANITY AND DIVISION BY ZERO

Lea esta bitácora en español
There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.
While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprov
e 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 ima
gine you hear lots of comparisons like that…

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

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

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

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

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

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

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

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

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

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

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

 

 

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

 

ゼロ除算の発見はどうでしょうか： 
Black holes are where God divided by zero： 

再生核研究所声明371（2017.6.27）ゼロ除算の講演―　国際会議　 
 

1/0=0、0/0=0、z/0=0 
 
1/0=0、0/0=0、z/0=0 
 
1/0=0、0/0=0、z/0=0 
 

ソクラテス・プラトン・アリストテレス　その他 
 

ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか 
 
〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか 
&t=3318s 
〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか 
 
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか 
 

再生核研究所声明 411(2018.02.02): 　ゼロ除算発見4周年を迎えて 
 

再生核研究所声明 416(2018.2.20): 　ゼロ除算をやってどういう意味が有りますか。何か意味が有りますか。何になるのですか　－　回答 
再生核研究所声明 417(2018.2.23): 　ゼロ除算って何ですか　－　中学生、高校生向き　回答 
再生核研究所声明 418(2018.2.24): 　割り算とは何ですか？　ゼロ除算って何ですか　－　小学生、中学生向き　回答 
再生核研究所声明 420(2018.3.2): ゼロ除算は正しいですか，合っていますか、信用できますか　－　回答 

2018.3.18．午前中　最後の講演：　日本数学会　東大駒場、函数方程式論分科会　講演書画カメラ用　原稿 
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18. 
 より

 

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.): Differential and Difference Equations with Applications: ICDDEA, Amadora, 2017. (Springer Proceedings in Mathematics and Statistics, Vol. 230) May 2018 587 pp. 

 

再生核研究所声明 424(2018.3.29): 　レオナ�
�ド・ダ・ヴィンチとゼロ除算

 

 

Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

 

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

1423793753.460.341866474681。

 

Einstein’s Only Mistake: Division by Zero

 

ゼロ除算は定義が問題です：

 

再生核研究所声明　１４８（2014.2.12）　100/0=0,  0/0=0　－　割り算の考えを自然に拡張すると　―　神の意志 

 

再生核研究所声明１７１（2014.7.30）掛け算の意味と割り算の意味　―　ゼロ除算100/0=0は自明である？

 

#divide by zero

TOP DEFINITION

  

A super-smart math teacher that teaches at HTHS and can divide by zero.

Hey look, that genius’s IQ is over 9000!

    

by  October 21, 2009

 

 

Dividing by zero is the biggest  known to mankind. It is a proven fact that a succesful division by zero will constitute in the implosion of the universe.

You are dividing by zero there, Johnny. Captain Kirk is not impressed.

Divide by zero?!?!! OMG!!! Epic failzorz

    

 

3

  

 by  is undefined.

Divide by zero is undefined.

    

by  October 28, 2006

 

1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist.

2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up on  or something. Pretty confusing shit.

3) A reason for an error in programming

Hey, I divided by zero! …Oh shi-

a/0

Run-time error: ’11’: Division by zero

    

by  September 08, 2006

 

When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says “yeah, there’s kind of an answer, but it ain’t just some number.”

It’s when mathematicians become philosophers.

:
Let’s say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with

 because of dividing by zero:
Let’s say there are THREE apples, and ZERO people. How many apples does each person get? Friggin… How the  should I know! How can you figure out how many apples each person gets if there’s no people to get them?!? You’d think it’d be infinity, but not really. It could almost be any number, cause you could be like “each person gets 400 apples” which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it’s still wrong.

        

by  February 15, 2010

 

Muslims take high pride and boast about the critical contributions “Islamic Sciences” to civilization. It would require considerable space just to recite the many so-called crucial discoveries were allegedly ascribed to Muslims’ inventions. We are told that Muslim scientists originated in the Islamic world laid the ground to public hospitals, libraries, and universities. Muslim scientists laid the foundations of agricultural science and invented the coffee. Muslim scientists developed theories of evolution long before Darwin and proposed laws of gravitation that were proved by Newton centuries later on; Muslim scientists invented “flight control surfaces” that are “believed to have come from the medieval Islamic world.”

It is amazing, in fact confusing and perplexing to enter Islamic internet sites, for example . The impression is that Islam has invented everything on Earth from the beginning of history, and continues to discover and invent everything. Unfortunately, it seems as if according to this site Islam has caused the emergence and the existence of humanity, without Islam human beings would have been perished. Here is the list most of Muslim propagators in the West mention as the greatest and the firsts. Most of them were highly influenced by the Mu’tazila ideology.

Muḥammad Ibn Mūsa al-Khwārizmi(d. 850), was a Mathematica scholar hailed as the algebra inventor. However, he was not an Arab but Persian in origin and Zoroastrian in his religion. There is widespread misconceptions that Muslims “invented algebra”. Maybe this fallacy is due to the fact that the word “algebra” is Arabic, derived from Khwarizmi’s book, Addition and Subtraction after the Method of the Indians. Yet, the name of his book also refers to the fact that it was based on Indian or Greek sources.

Khwarizmi did not “invent” algebra.  There are proven archaeological evidence that the roots of algebra date back to the ancient Babylonians, and were then developed in Egypt and Greece. The Chinese and especially the Indians also advanced algebra. The most important pre-modern scholar was Diophantus of Alexandria in the third century AD, called “the father of algebra.” He wrote series of books, Arithmetica, dealing with solving algebraic equations. Archimedes was the first mathematician to derive quantitative results from creation of mathematical models of physical problems. He was responsible for the first proof of the law of the lever and the basic principle of hydrostatics.

However, the most important mathematical text of Greek times, and probably of all time, the Elements of Euclid, written about 2300 years ago. In his book there are simply definitions, axioms, theorems, and proofs. Euclid’s work provided the field of Mathematics with a model of how ‘pure mathematics’ should be written, with precise definitions, carefully stated theorems, and logically coherent proofs. Euclid is thus first and foremost famous for creating a brilliant synthesis of the field.It is of note to mention that Diophantus and Euclid, like many other great Greeks taught and wrote at the most important institution of ancient time, the Library of Alexandria, founded by Ptolemy. This institution soon became a focal point of highest developments in Greek scholarship, both in the humanities and the sciences – and it was burned by the invading Arabs, headed by ‘Umar bin al-Khattab.

As for India, in 770, an Indian scholar brought two highly important mathematical works to Baghdad eg Brahmasiddhanta (Sindhind to Arabs) by the great 7th century Indian mathematician Brahmagupta, mathematician and astronomer, which contained early ideas of Algebra. The second manuscript contained a revolutionary system of denoting number and the concept of zero. Therefore, Khwarizmi took this work, combined it with Greek geometry (algebra developed by Hero of Alexandria). Indian numerals were used by Khwarizmi in algorithms (a Latinized version of his name) to solve certain mathematical problems. Hence Muslims certainly did not discover either zero or algebra and our so-called ‘Arabic Numerals’ are actually Indian (Hindu) Numerals.

Ibn Sīnā’ (Avicenna. d. 1037), and Abū Bakr ar-Rāzī (Rhazes. d. 925), were both great physiciansand significant thinkers. However, both were Persians and not Arabs, and both were at best highly unorthodox Muslims. ar-Razi didn’t believe a single word of the Islamic religion. Whatever contributions they made were more in spite of than because of Islam. Ibn Sina was always on the run of the fear of Islamic persecution, spent time in prison or had to write his works under the most severe circumstances. His greatest work, the Canon of Medicine, has become a standard work in Ehrope for the the next 600 years, but the Islamic rulers called hin an apostate (Murtad), and made his life intolerable as in his instruments he used to dissect pigs.

Moreover, while they should be considered to have been competent physicians, the greatest revolution in the world history of medicine was the germ theory of disease, championed by the Frenchman Louis Pasteur and the German Robert Koch in late nineteenth century Europe. They were aided in this by the microscope, which was an exclusively European invention.Islam continues with its misleading approach even concerning today’s “inventions.” In an article relating to Islamic medicine it is stated that in 2007 Malaysian scientist, Muszaphar Shukor, “became the first to perform biomedical research in outer space.” No less. Perhaps that meant he was the first Muslim to perform biomedical research in space. But this is exactly Islam.

Muslims comment on Abū Fath ‘Umar al-Khayyāmi, known as Omar Khayyam (d. 1131), who was a Persian philosopher, and creative mathematician, but he was not an Arab, and even not Muslim. Omar Khayyam was a wine lover who could at best be described as an extremely unorthodox Muslim. By and large he has been held either in ignominy, contempt, total disregard and oblivion by almost the entire Muslim world, and especially the Arab countries. He loved wine, women, and songs. He admired and praised the Zoroastrian religion. At the end, scientifically, he did not leave an impression on any science. Praising him today by Muslim propagators may hint of their desperation. How a Western-style materialist was created in an Islamic environment in early Middle-Ages and seems to openly defy the puritanical mind-set of 21st century apocalyptic Islam?

There is also Abū Mūsā Jābir Ibn Ḥayyān(d. 815), is hailed by Muslim propagators as the father of chemistry, by systematizing a “quantitative” analysis of substances. He was a Persian and not an Arab chemist and alchemist. He did good work in alchemy for his time and may have been the first person to create some acids, but he falls far short of Antoine Lavoisier and those who developed modern chemistry in late eighteenth and early nineteenth century Europe. Muslim scientists have deepened their knowledge, however, their ideas are only to be found in fictional novels, rather than learning about their fundamental contributions from scientific databases.

Nasir al-Din al-Tūsī (d. 1274), was Persian and not an Arab physician and astronomer. According to Muslim Heritage, al-Tusi was a prolific writer in different fields of science. He wrote over 150 works in Arabic and Persian that dealt with mathematical sciences, philosophy, and the Islamic religious issues. By that he acquired the honorific title of Khwāja (distinguished scholar); Ustādh Bashariyah (teacher of mankind); and Mu’alimal-Thālith (third teacher, after Aristotle and al-Fārābī). He was the director of the Islamic astronomical observatory of Marāgha.However, astronomy was invented in India, based on the Ptolemaic Greek theoretical framework, and al-Tusi achievements made only some adjustments in the field.

Ḥunain Ibn Ishāq (d. 873), Johannitius in Latin,
was Christian Nestorian (Assyrian) in his origin and even not Muslim. He was one of the most prominent translators of Greek books into Syro-Aramaic and Arabic. Soon he, his son and his nephew had made Galen’s medical treatises as well as Hippocratic works and texts by Aristotle, Plato and others available in Arabic. Hunayn’s own compositions include two on ophthalmology: the Ten Treatises on the Eye and the Book of the Questions on the Eye. His books had some influence but his importance came by transmitting the pure Galenic theory of vision.

Abū Naṣr Muḥammad al-Farābī (d. 950) was not an Arab, but from Khorasam, nowadays state of Kazakhstan. He was a renowned philosopher, known in Islamic circles with honorific title “the Second Master” (after Aristotle). He is credited with preserving the original Greek texts during the Middle-Ages, but not their translator. Mohamad Abdalla claimed that in the twelfth century, the West discovered, via a translated catalogue of sciences (map of knowledge) by al-Farābīthe existence of a considerable body of Antiquity’s scientific work. The West started examining these sciences, including astronomy, biology, botany, mathematics, and medicine. In addition, medieval European university became the institutional manifestation of al-Farābī’s map of knowledge. The translated work of Islamic knowledge formed the basis and the scientific foundation of the university in its living reality “the reality of its syllabus, the content of its teaching.”

Abu Yūsuf Yaʻqūb al-Kindī (d. 873), known as “the Philosopher of the Arabs”, was an Arab Muslim philosopher, and is hailed as the “father of Islamic philosophy, for his synthesis, adaptation and promotion of Greek and Hellenistic philosophy. Abbasid Caliphs appointed him to translate “the philosophy of the ancients,” as Greek philosophy was often referred to by Muslim scholars, into Arabic. This had a profound effect on his intellectual development, and he wrote many original treatises in many subjects. al-Kindī also played an important role in introducing the Indian system of numbers, traced back to 500 BC. The Indian numerals was spread to Sassanid Persia and was also used by the Assyrian and Nestroians. He was one of the first to attempt to reconcile Islam with Greek philosophy, especially with Aristotle, a project that soon failed due to religious resistance. De Lacy O’Leary reflects the significant topic that almost all Muslim thinkers and philosophers were classed as Aristotelians, tracing their intellectual descent from al-Kindī and al-Farābī.This is a romantic and tranquil picture.However reality gives different picture. al-Mutawwakil, the Abassid caliph, was convinced that Kindī had dangerous beliefs, and ordered the confiscation of his personal library, and punishment of fifty lashes before a large crowd. Other scholars, like al-Rāzī, Ibn Sinā, and Ibn Rushd were also subjected to some degree of persecution, and a part of them had to flee their countries for their own safety from the persecuting Islam.

Abū ‘AlīḤasan Ibn al-Haytham (Alhazen. d. 1040) was an Arab, and of all the list of the mentioned scientists, the highest-ranking contribution by any Muslim scholar. He was invited and remained in Egypt for the rest of his life, patronized by the Fatimi Caliph, al-Hākim. Indeed, Alhazen made significant contributions to the principles of optics, due to direct access to Greek optical theory. He relied heavily on the Greek scientific tradition, but the synthesis he created was new. His most important Book of Optics(Kitāb al-Manāzir), a great original scientific work written in Arabic has been ranked as one of influential books in the history of physics. He was perhaps the only Arab who was really important to scientific contributions.

Alhazen was a prolific writer on all aspects of science and natural philosophy, including some ninety of which he acknowledged authorship. These includes commentaries on the optical works of Euclid and Ptolemy, and analyses of Aristotle’s Physics. He read Hippocrates and Galen on medicine, Plato and Aristotle on philosophy and wrote commentaries on many Greek philosophers. His treatise on optics contains a substantially correct model of vision.The best analysis of the issue is by David C. Lindberg. According to him, Alhazen’s essential achievement was to obliterate the old battle lines. He was neither Euclidean nor Galenist nor Aristotelian, or else; he was all of them. Tragically enough, his Book of Optics was not widely used in the Islamic world afterwards. The reason, his work was considered as blasphemy, and some of his disciples were put on fire as apostates.

Moreover, the French thinker Rémi Brague, claims that Muslims lacked the European instinct for self-criticism and appreciation of the other. Even though Muslims did translate scientific works from Greek and a few other languages into Arabic, they didn’t bother to preserve the originals. This made the act of going back to the sources to really understand them impossible. However, Brague was wrong. The Muslims did not preserve the originals purposely and intentionally. From the beginning they wanted the immitaton to become the original. This is one of the Arab-Islamic significant traits perceiving the world being totally Islamic.

Brague also quotes Ibn Khaldun, who has refered to this in his Muqaddimah: “Muslims desired to learn the sciences of the nations, to make them their own through translations. They pressed them into the mold of their own views. They peeled off these strange tongues into their own idiom, and surpassed the achievements of the non-Muslims in them. The manuscripts in the non-Arabic languages were forgotten, abandoned, and scattered. All the sciences came to exist in Arabic. The systematic works on them were written in Arabic. Thus, students of the sciences needed a knowledge of Arabic writing.”

Analyzing scientific topics and academic faculties

Universities. Islam did not establish secular scientific universities. Islam did established religios universities, like al-Azhar. Even though al-Azhar was a center of education in the Islamic world, it was a center of religious learning and Sharī’ah alone, not secular learning and science. al-Azhar was created in the tenth century as an institute of Islamic religion studies. Contemporary Muslim propagators hail it as one of the oldest universities, but this is really a joke. It was never a university but an Islamic religious study institute.

Bassam Tibi relates to this: “Some Islamic historians wrongly translate the term Madrasa as university. This is plainly incorrect: If we understand a university as universitas litterarum, or consider, without the bias of Eurocentrism, the cast of the universitas magistrorum, we are bound to recognise that the university as a seat for free and unrestrained enquiry based on reason, is a European innovation in the history of mankind.Universities were the Assyrians and Buddhist invention. Among the best is the Great Monastery of Nalanda in India. It was not established by Muslims; in fact, it was destroyed by Muslims, as were so many cultural treasures in India, Central Asia and the Middle East. Though some texts were reintroduced to Europe via Arabic translations, but neither the inventions nor the translators were Arabs or Muslims. The Greek texts that were translated into Arabic were copied by Greek-speaking Byzantine Christians and others, and most tragically the originals disappeared or burnt.

Without the separation of church and state, the West would not have produced a deeply rooted natural philosophy that was disseminated through Europe by virtue of an extensive network of universities, which laid the foundation for the great scientific advances made in the sixteenth and seventeenth centuries. A striking number of the leading scholars in early modern Europe, from Copernicus to Galileo and Newton, had studied at these institutions. Although the Scientific Revolution began in the seventeenth century with the systematic us
e of the experimental method and a more critical view of the knowledge of the ancients, exemplified by individuals such as Galileo, the initial institutional basis for these developments was laid with the natural philosophers of the medieval universities.

It is an historical fact that scientific revolution happened in Europe. The foundations for the study of modern science were laid in the European universities. The natural sciences became “the foundation and core of a medieval university education.” The earliest European universities, such as the University of Bologna in Italy and Oxford in England, were created in the eleventh century, but many more were added during the twelfth and thirteenth centuries. The medieval European university represented a real innovation when the Greco-Roman heritage was slowly recovered. After the Crusades, translations directly from Greek via Byzantine manuscripts acquired from Constantinople. Unfortunately they were stopped after the Ottoman occupation of Constantinople. Again, Islam has proven to disruptive and distructive when it comes to sciences.

Toby E. Huff quotes: Something like 87% of the European scientists born between 1450 and 1650 [who were] thought worthy of inclusion in the Dictionary of Scientific Biography were university educated.’ More importantly, ‘A large proportion of this group was not only university educated but held career posts at a university.’ For the period 1450-1650 this was 45 percent, and for 1450-1550, it was 51 percent. In short, sociological and historical accounts of the role of the university as an institutional locus for science and as an incubator of scientific thought and argument have been vastly understated. Indeed, Islam has nothing to do with this processes. Universities and Islam are contradictory.

The legal system that developed in 13th century Europe, which saw the absorption of Greek philosophy, Roman law, and Christian theology, was instrumental in forming a philosophically and theologically open culture that respected scientific development. European universities were legally autonomous and they could develop their own rules, scholarly norms, and curricula, depending on curiosity, skepticism, and inquisitiveness. It was only this attitude of inquiry that helped lay the foundation for modern science.

The network of universities facilitated the spread of information, knowledge and debate and served as an incubator for many later scientific advances in Europe. These developments had never occurred in the Arab lands. Moreover, all of these innovations were made centuries before European colonialism had begun. In fact, it was the time when Europe itself was a victim of Islamic colonialism and violent aggressive Jihad being waged by the Ottomans in the remaining Byzantine lands, and the Mediterranean coasts had suffered centuries of Islamic raids.

Mathematics, geometry trigonometry. Mohamad Abdalla claims that Muslims developed Greek geometry and then used it in designing wheels of all kinds, including waterwheels and other systems for drawing water, in improving farming equipment, and, inevitably, in devising engines and devices of war. In the ninth century, Thābit ibn Qurra wrote on cubatures and quadratures; advanced the study of parabolas; and translations of Appollonius’ Conics, Archimedes’ treatises, and Nicomachus’ Introduction to Arithmetic. Moreover, he continues legends, trigonometry was invented by the Arabs. They were the first to formulate explicit trigonometric functions. Khawarizmi, the Muslim mathematician and the first to establish algebra and algorithm and to compose many astronomical tables. Habbash al-Hāsib was the first to use tangents cotangent functions. Abu al-Wafā’ al-Buzanji, the first person to demonstrate the sine theorem for general spherical triangle, which is attributed to Copernicus. Bayruni was the first to write on spherical trigonometry, calculated the approximate value of a diagonal of one degree, and was the first to demonstrate that for a plane triangle.

The problem with this list is that all of them were not the first and all of them were not Arabs. Khawarizmi was a Persian mathematician and astronomer; Thabit ibn Qurrah was a Sabian mathematician and physician from Harran, Turkey; Habbash al-Hāsib Persian astronomer and mathematician; Abu al-Wafā’ al-Buzanji was a Persian mathematician; and al-Bayruni was born in todays’ Uzbekistan. There is no accurate information whether they were Muslims at all or forcibly converted to Islam. What is clear that their knowledge, whatever it worth, was not Islamic originated.

Persian scientific efforts contributed significantly to academic development of clinical pharmacology and medicine. One example is the practical production in food industry. Persian scientists improved the cooking process in such a way that long before others they could enjoy the taste of pure sugar. The list of Persian scientists that have enriched clinical chemistry, pharmacology, and thus medical therapy and medicine, is almost endless. The Persian poet, Ferdowsi composed in the 11th century his famous work Shahnameh, the ‘Book of Kings.” With this book the poet elevates the Persian language, 300 years after the destruction of Sassanid empire. While most of the conquered countries would lose their culture and language forever the Persian poet Ferdowsi prevented this tragedy for Persia. The Sumarians, one of the first Aryan peoples, integrated astronomy and medical science. The medical profession of doctor goes aback as far as 4000 years, with traces of medical instruments and recipes. Nothing Islamic.

Algebra already existed in ancient Mesopotamia. Algebraic symbolism was employed by Diophantus in Greco-Roman times. Muslims never made use of such symbols. Moreover, wheels of all kinds and farming equipment where all well-known to the Pharaonics and Assyrians long time before Islam; and geometry and trigonometry were invented in India, and some of them by Assyrians. And one more thing: please do not feel uncomfortable reading Muslim were the first of everything. History belongs to them, and everything was created for them and according to their will. They have the best example in Muhammad. He was the greatest human who ever lived and the best model for all humanity: al-Insān al-Kāmil, “the ideal perfect man” whose life is to be imitated by all Muslims and must be obeyed (3:32; 4:79; 8:20; 24:54). Muhammad is the uppermost “beautiful model of conduct” (33:21), a man of “sublime moral character” (68:4).

Medicine. Mohamed Abdalla assisted by Islamic Heritage site claims that “Muslims also excelled in and made original contributions to medicine… Muslims produced new medical knowledge, by systematizing the inconsistent Greco-Roman medical knowledge by writing encyclopedias and summaries. The influence of Islamic medicine in the West was critical, due to the mass of information it conveyed and because it helped establish medicine as a science. In this background Islamic medicine developed and advanced, and at its zenith produced such towering physicians like Ibn Sinā and al-Rāzi, considered to be among the greatest physicians ever known.”

“ar-Rāzi is the keenest original thinker and greatest clinician not only of Islam but of all the Middle Ages. He was the Islamic world’s greatest original clinical and observational physician… He applied chemistry and physics to medicine… wrote a medical encyclopedia and a treatise on smallpox and measles that was the earliest of its kind and considered a masterpiece of Arabic medical literature. He was a pioneer in pediatrics, obstetrics, and ophthalmology… the inventor of the Seton in surgery, and the first to relate hay fever to a rose’s scent, and mastered by psychological shock and of using psychosomatic medicine and psychology. Another great figure Ibn Sinā, was the most renowned physician, philosopher, astronomer and mathematician… representing the climax of medieval philosophy… His book, Canon of Medicine, influenced Europe’s medical schools for
the next 600 years and was probably the most used of all medieval medical references.”

However, it is interesting that what is called Islamic medicine was in fact Assyrian and Jewish, and it was built on known traditions, mainly theoretical and practical knowledge developed in Greece and Rome, in Babylon, Persia and India. Here is what ar-Rāzi said about Islam: Muslims get angry and spill the blood of whoever confronts them with questions about their religion. They forbid rational speculation, and strive to kill their adversaries. This is why truth became thoroughly silenced and even concealed. Muslims claim that the Qur’an is miraculous and the infinite words of Allah, and ‘whoever denies it, let him produce a similar one.’ Indeed, we can produce thousands similar, which are more appropriately phrased and state the issues more succinctly. Muslims are talking about a work which recounts ancient myths, is full of contradictions and does not contain any useful information or explanation. Now, can one who utter such words be a Muslim?

As said before, both ar-Rāzi and Ibn Sinā’ were great physiciansand thinkers. However, both were Persians and not Arabs, both were highly unorthodox if they were Muslims at all, and both made their contributions in spite of Islam and not because of Islam. The fact is that as in almost every science, the observatory as a scientific and cultural institution failed to take root in the Arabic-Islamic world. European anatomists were practicing dissections on the pigs and also human body. Consequently, they had a considerable stock of empirical knowledge about human anatomy that was not available in the Arab-Muslim world. Engaged in a variety of practices that would have been forbidden in Islam, Middle Eastern medical education of the time was still based mainly on the memorization of authoritative texts. Moreover, Clear glass was used by Europeans to create eyeglasses for the correction of eyesight, and later for the creation of microscopes and telescopes and thus the birth of modern medicine and astronomy. The final breakthrough was made by the great physician, Vesalius, in his book On the Fabric of the Human Body from 1543.

Astronomy. In his website, George Saliba writes: “I study the development of scientific ideas from late antiquity to modern times, with a special focus on the various planetary theories that were developed within the Islamic civilization and the impact of such theories on European astronomy.” Moreover, Islamic heritage site explains that the medieval Islamic astronomers were not mere translators but also have played a key role in the Copernican revolution, which ultimately influenced Renaissance. The contribution of Islamic science was fundamental to the birth and subsequent development of astronomy in the West, for before this contribution the West had no advanced astronomy. The knowledge developed by Muslim astronomers produced changes in the West as regards the development of trigonometry, instruments, and the local star catalogues, and affected the growth and development of astronomical theory.

 

ゼロ除算の発見は日本です：

 

∞？？？

∞は定まった数ではない・・・

人工知能はゼロ除算ができるでしょうか：

 

とても興味深く読みました：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

ゼロ除算関係論文・本

 

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

 

ゼロ除算の発見はどうでしょうか： 
Black holes are where God divided by zero： 

再生核研究所声明371（2017.6.27）ゼロ除算の講演―　国際会議　 
 

1/0=0、0/0=0、z/0=0 
 
1/0=0、0/0=0、z/0=0 
 
1/0=0、0/0=0、z/0=0 
 

ソクラテス・プラトン・アリストテレス　その他 
 

ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか 
 
〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか 
&t=3318s 
〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか 
 
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか 
 

再生核研究所声明 411(2018.02.02): 　ゼロ除算発見4周年を迎えて 
 

再生核研究所声明 416(2018.2.20): 　ゼロ除算をやってどういう意味が有りますか。何か意味が有りますか。何になるのですか　－　回答 
再生核研究所声明 417(2018.2.23): 　ゼロ除算って何ですか　－　中学生、高校生向き　回答 
再生核研究所声明 418(2018.2.24): 　割り算とは何ですか？　ゼロ除算って何ですか　－　小学生、中学生向き　回答 
再生核研究所声明 420(2018.3.2): ゼロ除算は正しいですか，合っていますか、信用できますか　－　回答 

2018.3.18．午前中　最後の講演：　日本数学会　東大駒場、函数方程式論分科会　講演書画カメラ用　原稿 
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18. 
 より

 

再生核研究所声明 424(2018.3.29): 　レオナルド・ダ・ヴィンチとゼロ除算

 

 

Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

 

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

1423793753.460.341866474681。

 

Einstein’s Only Mistake: Division by Zero

 

2018.3.18．午前中　最後の講演：　日本数学会　東大駒場、函数方程式論分科会　講演書画カメラ用　原稿 
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18. 
 より

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.): Differential and Difference Equations with Applications: ICDDEA, Amadora, 2017. (Springer Proceedings in Mathematics and Statistics, Vol. 230) May 2018 587 pp. 

 

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