Top 10 mathematical innovations

BY 

 

5:49PM, AUGUST 11, 2014

Of all the mathematical innovations since ancient times, only some are worthy of multicentenary celebrations. Certainly logarithms,  this year, are among them. Ranking where logarithms rate among the rest is subjective, of course, but I’d put them 10th (they’d be higher if everybody still used slide rules, though). Here are the rest of my Top 10 mathematical innovations, which you might as well read here because David Letterman isn’t going to get to them before he retires:

10. Logarithms (John Napier, Joost Bürgi, Henry Briggs)

A great aid to anybody who multiplied or messed with powers and roots, logarithms made slide rules possible and clarified all sorts of mathematical relationships in various fields.  and  both had the basic idea in the late 16th century, but both spent a couple of decades calculating log tables before publishing them. Napier’s came first, in 1614.  made them popular, though, by recasting Napier’s version into something closer to the modern base-10 form.

9. Matrix algebra (Arthur Cayley)

An ancient Chinese math text included matrix-like calculations, but their modern form was established in the mid-19th century by . (Several others, including Jacques Binet, had explored aspects of matrix multiplication before then.) Besides their many other applications, matrices became extremely useful for quantum mechanics. In fact, in 1925 Werner Heisenberg reinvented a system identical to matrix multiplication to do quantum calculations without even knowing that matrix algebra already existed.

8. Complex numbers (Girolamo Cardano, Rafael Bombelli)

Before , square roots of negative numbers had shown up in various equations, but nobody took them very seriously, regarding them as meaningless. Cardano played around with them, but it was  in the mid-16th century who worked out the details of calculating with complex numbers, which combine ordinary numbers with roots of negative numbers. A century later  made the first serious case that the square roots of negative numbers were actually physically meaningful.

7. Non-Euclidean geometry (Carl Gauss, Nikolai Lobachevsky, János Bolyai, Bernhard Riemann)

, in the early 19th century, was probably the first to figure out an alternative to Euclid’s traditional geometry, but Gauss was a perfectionist, and perfection is the enemy of publication. So  and  get the credit for originating one non-Euclidean approach to space, while , much later, produced the non-Euclidean geometry that was most helpful for Einstein in articulating general relativity. The best thing about non-Euclidean geometry was that it demolished the dumb idea that some knowledge is known to be true a priori, without any need to check it out by real-world observations and experiments. Immanuel Kant thought Euclidean space was the exemplar of a priori knowledge. But not only is it not a priori, it’s not even right.

6. Binary logic (George Boole)

 was interested in developing a mathematical representation of the “laws of thought,” which led to using symbols (such as x) to stand for concepts (such as Irish mathematicians). He hit a snag when he realized that his system required x times x to be equal to x. That requirement pretty much rules out most of mathematics, but Boole noticed that x squared does equal x for two numbers: 0 and 1. In 1854 he wrote a whole book based on doing logic with 0s and 1s — a book that was well-known to the founders of modern computer languages.

5. Decimal fractions (Simon Stevin, Abu’l Hasan Al-Uqlidisi)

 introduced the idea of decimal fractions to a European audience in a pamphlet published in 1585, promising to teach “how all Computations that are met in Business may be performed by Integers alone without the aid of Fractions.” He thought his decimal fraction approach would be of value not only to merchants but also to astrologers, surveyors and measurers of tapestry. But long before Stevin, the basic idea of decimals had been applied in limited contexts. In the mid-10th century, , in Damascus, wrote a treatise on Arabic (Hindu) numerals in which he dealt with decimal fractions, although historians differ on whether he understood them thoroughly or not.

4. Zero and 3. Negative numbers (Brahmagupta)

, a seventh-century Hindu astronomer, was not the first to discuss negative numbers, but he was the first to make sense of them. It’s not a coincidence that he also had to figure out the concept of zero to make negative numbers make sense. Zero was not just nothingness, but a meaningful number, the number you get by subtracting a number from itself. “Zero was not just a placeholder,” writes Joseph Mazur in his new book . “For what may have been the first time ever, there was a number to represent nothing.”

2. Calculus (Isaac Newton, Gottfried Leibniz)

You know the story —  gets all the credit, even though  invented calculus at about the same time, and with more convenient notation (still used today). In any event, calculus made all sorts of science possible that couldn’t have happened without its calculational powers. Today everything from architecture and astronomy to neuroscience and thermodynamics depends on calculus.

1. Arabic numerals

Did you ever wonder why the Romans didn’t do much creative quantitative science? Try doing a complicated calculation with their numerals. Great advances in Western European science followed the introduction of Arabic numerals by the Italian mathematician  in the early 13th century. He learned them from conducting business in Africa and the Middle East. Of course, they should really be called Hindu numerals because the Arabs got them from the Hindus. In any case, mathematics would be stuck in the dark ages without such versatile numerals. And nobody would want to click on a Top X list. (Wait — maybe they would. But you won’t see any list like that on this blog.)

 

ゼロ除算の発見と重要性を指摘した：再生核研究所

2017年11月15日(水)
テーマ：

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

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

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

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

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

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

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

 

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

 

 

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

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

 

OUR HUMANITY AND DIVISION BY ZERO

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

 

5000年？？？？？

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

とても興味深く読みました：

 

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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

次のダ・ヴィンチの言葉を発見して、驚かされた：

ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在

我々の周りにある偉大なことの中でも、無の存在が最も素晴らしい。その基本は時間的には過去と未来の間にあり、現在の何ものをも所有しないというところにある。この無は、全体に等しい部分、部分に等しい全体を持つ。分割できないものと割り切ることができるし、割っても掛けても、足しても引いても、同じ量になるのだ。

レオナルド・ダ・ヴィンチ。ルネッサンス期を代表する芸術家、画家、彫刻家、建築技師、設計士、兵器開発者、科学者、哲学者、解剖学者、動物学者、ファッションデザイナーその他広い分野で活躍し「万能の人（uomo universale：ウォモ・ウニヴェルサーレ）」と称えられる人物

そもそも西欧諸国が、アリストテレス以来、無や真空、ゼロを嫌い、ゼロの西欧諸国への導入は相当に遅れ、西欧へのアラビヤ数字の導入は　レオナルド・フィボナッチ（1179年頃～1250年頃）によるとされているから、その遅れの大きさに驚かされる：

フィボナッチはイタリアのピサの数学者です。正確には「レオナルド・フィリオ・ボナッチ」といいますが、これがなまって「フィボナッチ」と呼ばれるようになったとされています。
彼は少年時代に父親について現在のアルジェリアに渡り、そこでアラビア数字を学びました。当時の神聖ローマ皇帝・フリードリヒ2世は科学と数学を重んじていて、フィボナッチは宮殿に呼ばれ皇帝にも謁見しました。後にはピサ共和国から表彰もされました。

ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大きな数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（

historicalmathematicians.blogspot.com/2012/03/blog-post.html　　02/03/2012 -）

ゼロや無に対する恐怖心、嫌疑観は現在でも欧米諸国の自然な心情と考えられる。ところが上記ダ・ヴィンチの言葉は　如何であろう。無について好ましいものとして真正面から捉えていることが分かる。ゼロ除算の研究をここ４年間して来て、驚嘆すべきこととして驚かされた。ゼロの意味、ゼロ除算の心を知っていたかのような言明である。

まず、上記で、無を、時間的に未来と過去の間に存在すると言っているので、無とはゼロのことであると解釈できる。ゼロとの捉え方は四則演算を考えているので、その解釈の適切性を述べている。足しても引いても変わらない。これはゼロの本質ではないか。さらに、凄いこと、掛けても割っても、ゼロと言っていると解釈でき、それはゼロ除算の最近の発見を意味している:  0/1 =1/0=0。－　ゼロ除算を感覚的に捉えていたと解釈できる。ところが更に、凄いことを述べている。

この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：

{\bf Fruitful world}\index{fruitful world}

\medskip

 

For example, in very and very general partial differential equations, if the coefficients or terms are zero, we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we see the converse, we see that the zero world is a fruitful one and it means some vanishin
g world. Recall \index{Yamane phenomena}Yamane phenomena, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.

\medskip

 

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

\medskip

 

As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.

\medskip

 

その意味は深い。我々はゼロの意味をいろいろと捉え考え、ゼロとはさらに　基準を表すとか、不可能性を示すとか、無限遠点の反映であるとか、ゼロの2重性とかを述べている。ゼロと無限の関係をも述べている。ダ・ヴィンチの鋭い世界観に対する境地に驚嘆している。

以　上

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

 

 

Commencement 2018

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As the pace of life becomes faster and faster, huge numbers of people follow an unhealthy lifestyle. Constipation is among the results of unhealthy eating and physical inactivity. Long-term constipation will heighten the burden from the body along with the damages will probably be worse and worse whether it lasts.

The Benefits of taking exercise.Improving sleep quality. Taking exercise may help you fall asleep faster and thereby enhancing the sleep quality.Far away from mental illnesses.Doing something more important can distract the eye to the annoying things. Thus, taking some exercise can help you far from mental illnesses like anxiety and depression.Enhance the memory.

It’s accomplishment discover how white blood cells have impact on sperm, nonetheless it may have something connected to molecules produced by white blood cells called reactive oxygen species. These molecules have properties of fighting diseases. Studies show that reactive oxygen species are increased in semen samples from approximately 40% of infertile men.

Except for affecting human health insurance and environmental surroundings, tobacco use even offers connected with poverty and education. Many studies have shown that in the poorest households, shelling out for tobacco products often represents greater than 10% of total household expenditure, this means they generally spend less cash on food, education and healthcare. It’s reported that 10%4% of kids from tobacco-growing families miss class because of working in tobacco fields.

An Update On Fast Programs Of

The scariest condition of the prostate is cancer of the prostate, which can be fatal if not treated in the initial stage. It is estimated that 6.5 million American men visit doctors for an enlarged prostate every year. In 2007, around 223,000 men were clinically determined to have cancer of the prostate inside U.S., and 29,000 died through the disease. In 2011, about 240,890 new cases of cancer of prostate will be diagnosed in the United States, resulting in 33,270 men will die from cancer of prostate.

Although prostate complaints are more widespread in males over 50, they’re able to even be seen before this age, as well as men under this age, the most common dilemma is prostatitis. In men over 50, prostate enlargement makes up about the most typical problem, this also condition is additionally known as BPH (benign prostatic hyperplasia). While the likelihood of cancer of prostate raises with age, its occurrence is lesser than that of BPH. However, prostate cancer is amongst the premiere factors behind cancer related deaths inside the U.S.

First off, recognize that in case you have any problems urinating, you ought to get tested by the doctor and avoid the most common self diagnosis many people guys do. And if it is a personal prostate, then many of the symptoms you could possibly experience include having problems having your stream started, a burning feeling when you pee, a frequent urge to urinate, excessive “dribbling” afterwards as well as perhaps even painful urination.

Some of the symptoms of prostatitis can include anything from generally feeling unwell with all the chills as well as a fever (whether it is bacterial) to presenting your complete urinary and sexual systems feeling like they are burning in pain — which has a painful penis tip and base, scrotum, testicles, anus, spine and abdomen. You might also find blood with your urine or semen, or you might get unable to experience an erection. Or, should you get an erection maybe it’s painful, filled with painful ejaculations.

Taking care of your prostate can be carried out in varied ways. A very simple ways including changing in to a proper diet may be the primary to complete. Eating vegetables and fruit. Also avoid fatty foods, sugars and those that are already processed. Nettle and Pygeum are herbs which might be effective in relieving signs of enlarged prostate. In addition to this saw palmetto doubles. Taking in of supplement like vitamin A, vitamin C, vitamin E and selenium will assisted in the prevention in the oxidation with the tissues. This will lead to a healthier prostate. Starting today may be the best thing to perform, don’t wait till it’s past too far.

Picking Out Clear-Cut Solutions Of

How to decrease the nutrients loss? Before squeezing the fruits and vegetables, you should position them into boiling water for some minutes so the oxidase could be eliminated. Thus, loosing vitamins will be reduced as well as the juice yield will likely be increased. In addition, it’s beneficial to put some sour fruits like lemon towards the mixture to replenish the vitamin C. Tips for making fresh juice. Choose fresh fruits and vegetables which can be in season. Take several types of vegetables to blend with fruits in an attempt to slow up the level of sugar in the juice.Don’t add sugar or honey for the juice. Drink the fresh juice immediately to stop the vitamin loss and also the breeding of bacteria.

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

Preamble abridgment.

‘Spirit remodeling’ of GHQ to Japan

Orishima

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

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

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

Hyakuta

I am writing about Japanese history now.

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

Sakurai

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

Hyakuta

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

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

Especially the press code was bad.

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

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

Sakurai

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

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

Hyakuta

Besides censorship, a burning book was also held.

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

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

This is the worst cultural destruction, history destruction.

Sakurai

America has dyed hands the same way.

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

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

Hyakuta

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

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

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

Distorted learning

Sakurai

The expulsion of public officials was also terrible.

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

Hyakuta

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

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

Especially, it was the educational circle that was terrible.

Sakurai

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

Hyakuta

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

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

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

Sakurai

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

A typical example is Toshiyoshi Miyazawa, a constitutional scholar.

Hyakuta

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

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

Sakurai

It has changed by a hundred and eighty degrees.

Hyakuta

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

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

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

Sakurai

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

Hyakuta

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

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

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

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

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

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

Sakurai

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

Hyakuta

Another person I would like to introduce is Yokota Kisaburo.

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

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

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

So, I cannot find his book quite easily.

Sakurai

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

What distorted academics is nothing but a tragedy.

The apostasy of the Asahi Newspaper

Hyakuta

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

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

Sakurai

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

Hyakuta

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

So, who was it that helped with this?

Sakurai

It is Japanese.

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

Hyakuta

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

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

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

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

This draft continues.

中国衰退後の次期大国はインド。インドが権力抗争には入らないといっているのだから、平和世界は約束されたようなもの。

Prime Minister’s Keynote Address at Shangri La Dialogue (June 01, 2018)

June 01, 2018

Prime Minister Lee Hsien Loong, 
Thank you for your friendship, your leadership of India-Singapore partnership and a better future for the region.
Defence Ministers, 
Mr. John Chipman,
Dignitaries and Excellencies, 
Namaskar and a very good evening to all of you! 

I am pleased to return to a region, known to India since ancient times as सुवर्णभूमि, (the land of gold).

I am also happy to be here in a special year. In a land-mark year of India’s relationship with ASEAN.

In January, we had the unique honour of hosting ten ASEAN leaders on our Republic Day. The ASEAN-India Summit was a testimony of our commitment to ASEAN, and to our Act East policy.

For thousands of years, Indians have turned to the East. Not just to see the Sun rise, but also to pray for its light to spread over the entire world. The human-kind now looks to the Rising East, with the hope to see the promise that this 21st century beholds for the whole world, because the destiny of the world will be deeply influenced by the course of developments in the Indo-Pacific region.

Because, this new age of promise is also caught in shifting plates of global politics and the fault lines of history. I am here to say that the future we seek does not have to be as elusive as Shangri La; that we can shape this region in our collective hopes and aspirations. No where is it more apt to pursue this than in Singapore.This great nation shows us that when the oceans are open, the seas are secure, countries are connected, the rule of law prevails and the region is stable, nations, small and large, prosper as sovereign countries. Free and fearless in their choices.

Singapore also shows that when nations stand on the side of principles, not behind one power or the other, they earn the respect of the world and a voice in international affairs. And, when they embrace diversity at home, they seek an inclusive world outside.

For India, though, Singapore means more. It’s the spirit that unites a lion nation and a lion city.Singapore is our springboard to ASEAN. It has been, for centuries, a gateway for India to the East.For over two thousand years, the winds of monsoons, the currents of seas and the force of human aspirations have built timeless links between India and this region. It was cast in peace and friendship, religion and culture, art and commerce, language and literature. These human links have lasted, even as the tides of politics and trade saw their ebb and flow. 

Over the past three decades, we have re-claimed that heritage to restore our role and relationships in the region.For India, no region now receives as much attention as this. And, for good reasons.

Oceans had an important place in Indian thinking since pre-Vedic times. Thousands of years ago, the Indus Valley Civilisation as well as Indian peninsula had maritime trade. Oceans and Varuna – the Lord of all Waters – find a prominent place in the world’s oldest books- the Vedas. In ancient Puranas, written thousands of years ago, the geographical definition of India is with reference to the seas: उत्तरों यत समुद्रस्य meaning, the land which lies to the north of the seas.

Lothal, in my home state Gujarat, was among the world’s oldest ports. Even today there are remains of a dock. No wonder Gujaratis are enterprising and travel widely even today! The Indian Ocean has shaped much of India’s history. It now holds the key to our future. The ocean carries 90% of India’s trade and our energy sources. It is also the life line of global commerce. The Indian Ocean connects regions of diverse cultures and different levels of peace and prosperity. It also now bears ships of major powers.Both raise concerns of stability and contest. 

To the East, the Malacca Strait and South China Sea connect India to the Pacific and to most of our major partners – ASEAN, Japan, Republic of Korea, China and the Americas.Our trade in the region is growing rapidly. And, a significant part of our overseas investments flow in this direction. ASEAN alone accounts for over 20%. 

Our interests in the region are vast, and our engagement is deep. In the Indian Ocean region, our relationships are becoming stronger. We are also helping build economic capabilities and improve maritime security for our friends and partners.We promote collective security through forums like Indian Ocean Naval Symposium. 

We are advancing a comprehensive agenda of regional co-operation through Indian Ocean Rim Association. And, we also work with partners beyond the Indian Ocean Region to ensure that the global transit routes remain peaceful and free for all.

Three years ago, in Mauritius, I described our vision in one word – Sagar, which means ocean in Hindi. And, Sagar stands for Security and Growth for All in the Region and, that is the creed we follow to our East now even more vigorously through our Act East Policy by seeking to join India, especially her East and North-East, with our land and maritime partners to the east.

South-east Asia is our neighbour by land and sea.With each Southeast Asian country, we have growing political, economic and defence ties. With ASEAN, from dialogue partners, we have become strategic partners over the course of 25 years. We pursue our relations through annual summits and 30 dialogue mechanisms. But even more through a shared vision for the region, and the comfort and familiarity of our old links.

We are active participants in ASEAN-led institutions like East Asia Summit, A.D.M.M. Plus and A.R.F. We are part of BIMSTEC and Mekong-Ganga Economic Corridor – a bridge between South and Southeast Asia.

Our ties with Japan – from economic to strategic – have been completely transformed. It is a partnership of great substance and purpose that is a corner-stone of India’s Act East Policy. There is a strong momentum in our cooperation with Republic of Korea. And, there is a fresh energy in our partnerships with Australia, as also New Zealand.

With several of our partners, we meet in formats of three or more.More than three years ago, I landed at dawn in Fiji to start a successful new phase of engagement with Pacific Island Nations. The meetings of the Forum for India-Pacific Islands Cooperation, or FIPIC, have bridged the distance of geography through shared interests and action.

Beyond East and Southeast Asia, our partnerships are strong and growing.It is a measure of our strategic autonomy that India’s Strategic Partnership, with Russia, has matured to be special and privileged.

Ten days ago in an informal summit at Sochi, President Putin and I shared our views on the need for a strong multi-polar world order for dealing with the challenges of our times. At the same time, India’s global strategic partnership with the United States has overcome the hesitations of history and continues to deepen across the extraordinary breadth of our relationship.It has assumed new significance in the changing world. And, an important pillar of this partnership is our shared vision of an open, stable, secure and prosperous Indo-Pacific Region. No other relationship of India has as many layers as our relations with China. We are the world’s two most populous countries and among the fastest growing major economies. Our cooperation is expanding. Trade is growing. And, we have displayed maturity and wisdom in managing issues and ensuring a peaceful border.

In April, a two-day informal Summit with President Xi helped us cement our understanding that strong and stable relations between our two nations are an importa
nt factor for global peace and progress. I firmly believe that, Asia and the world will have a better future when India and China work together in trust and confidence, sensitive to each other’s interests.

India has a growing partnership with Africa, propelled through mechanisms such as India-Africa Forum Summits. At its core are cooperation based on Africa’s requirements, and a history of warmth and mutual respect.

Friends, 

Coming back to our region, India’s growing engagement is accompanied by deeper economic and defence cooperation. We have more trade agreements in this part of the world than in any other. We have Comprehensive Economic Partnership Agreements with Singapore, Japan and South Korea.

We have Free Trade Agreements with ASEAN and Thailand. And, we are now actively participating in concluding the Regional Comprehensive Economic Partnership Agreement. I have just paid my first visit to Indonesia, India’s neighbour 90 nautical miles close, and not 90 nautical miles apart. 

My friend President Widodo and I upgraded India-Indonesia relations to a Comprehensive Strategic Partnership. Among other shared interests, we have a common vision for maritime cooperation in the Indo-Pacific. On way from Indonesia, I stopped over briefly in Malaysia to meet one of ASEAN’s most senior leaders, Prime Minister Mahathir. 

Friends,

India Armed Forces, especially our Navy, are building partnerships in the Indo-Pacific region for peace and security, as well as humanitarian assistance and disaster relief. They train, exercise and conduct goodwill missions across the region. For example, with Singapore, we have the longest un-interrupted naval exercise, which is in its twenty fifth year now.

We will start a new tri-lateral exercise with Singapore soon and we hope to extend it to other ASEAN countries. We work with partners like Vietnam to build mutual capabilities. India conducts Malabar Exercise with the United States and Japan. A number of regional partners join in India’s Exercise Milan in the Indian Ocean, and participate in RIMPAC in the Pacific.

We are active in the Regional Cooperation Agreement on Combating Piracy and Armed Robbery against Ships in Asia – in this very city. Distinguished members of the audience, Back home, our principal mission is transforming India to a New India by 2022, when Independent India will be 75 years young. 

We will sustain growth of 7.5 to 8% per year. As our economy grows, our global and regional integration will increase. A nation of over 800 million youth knows that their future will be secured not just by the scale of India’s economy, but also by the depth of global engagement. More than any where else, our ties will deepen and our presence will grow in the region. But, the future we seek to build needs a stable bedrock of peace. And, this is far from certain.

There are shifts in global power, change in the character of global economy and daily disruption in technology. The foundations of the global order appear shaken. And, the future looks less certain. For all our progress, we live on the edge of uncertainty, of unsettled questions and unresolved disputes; contests and claims; and clashing visions and competing models.

We see growing mutual insecurity and rising military expenditure; internal dislocations turning into external tensions; and new fault lines in trade and competition in the global commons. Above all, we see assertion of power over re-course to international norms. In the midst of all this, there are challenges that touch us all, including the un-ending threat of terrorism and extremism. This is a world of inter-dependent fortunes and failures. And, no nation can shape and secure it on its own.

It is a world that summons us to rise above divisions and competition to work together. Is that possible ?

Yes. It is possible. I see ASEAN as an example and inspiration. ASEAN represents the greatest level of diversity of culture, religion, language, governance and prosperity of any grouping in the world.

It was born when Southeast Asia was a frontline of global competition, a theatre of a brutal war and a region of uncertain nations. Yet, today, ASEAN has united ten countries behind a common purpose. ASEAN unity is essential for a stable future for this region.

And, each of us must support it, not weaken it. I have attended four East Asia Summits. I am convinced that ASEAN can integrate the broader region. In many ways, ASEAN is already leading the process. In doing so, it has laid the foundation of the Indo-Pacific Region. The East Asia Summit and the Regional Comprehensive Economic Partnership – two important initiatives of ASEAN – embrace this geography.

Friends, 

The Indo-Pacific is a natural region. It is also home to a vast array of global opportunities and challenges. I am increasingly convinced with each passing day that the destinies of those of us who live in the region are linked. Today, we are being called to rise above divisions and competition to work together. 

The ten countries of South East Asia connect the two great oceans in both the geographical and civilizational sense. Inclusiveness, openness and ASEAN centrality and unity, therefore, lie at the heart of the new Indo-Pacific. India does not see the Indo-Pacific Region as a strategy or as a club of limited members. 

Nor as a grouping that seeks to dominate. And by no means do we consider it as directed against any country. A geographical definition, as such, cannot be. India’s vision for the Indo-Pacific Region is, therefore, a positive one. And, it has many elements.

One, 

It stands for a free, open, inclusive region, which embraces us all in a common pursuit of progress and prosperity. It includes all nations in this geography as also others beyond who have a stake in it.

Two,

Southeast Asia is at its centre. And, ASEAN has been and will be central to its future. That is the vision that will always guide India, as we seek to cooperate for an architecture for peace and security in this region.

Three, 

We believe that our common prosperity and security require us to evolve, through dialogue, a common rules-based order for the region. And, it must equally apply to all individually as well as to the global commons. Such an order must believe in sovereignty and territorial integrity, as well as equality of all nations, irrespective of size and strength. These rules and norms should be based on the consent of all, not on the power of the few. This must be based on faith in dialogue, and not dependence on force. It also means that when nations make international commitments, they must uphold them. This is the foundation of India’s faith in multilateralism and regionalism; and, of our principled commitment to rule of law.

Four, 

We should all have equal access as a right under international law to the use of common spaces on sea and in the air that would require freedom of navigation, unimpeded commerce and peaceful settlement of disputes in accordance with international law. When we all agree to live by that code, our sea lanes will be pathways to prosperity and corridors of peace. We will also be able to come together to prevent maritime crimes, preserve marine ecology, protect against disasters and prosper from blue economy.

Five, 

This region, and all of us, have benefitted from globalisation. Indian food is among the best examples of these benefits! But, there is growing protectionism – in goods and in services. Solutions cannot be found behind walls of protection, but in embracing change. What we seek is a level playing field for all. India stands for open and stable international trade regime. We will also support rule-based, open, balanced and stable trade environment in the Indo-Pacific Region, which lifts up all nations on the tide of trade and investment. That is what we expect from Regional Comprehnsive Economic Partnership. RCEP must be compre
hensive, as the name suggests, and the principles declared. It must have a balance among trade, investment and services.

Six, 

Connectivity is vital. It does more than enhance trade and prosperity. It unites a region. India has been at the crossroads for centuries. We understand the benefits of connectivity. There are many connectivity initiatives in the region. If these have to succeed, we must not only build infrastructure, we must also build bridges of trust. And for that, these initiatives must be based on respect for sovereignty and territorial integrity, consultation, good governance, transparency, viability and sustainability. They must empower nations, not place them under impossible debt burden. They must promote trade, not strategic competition. On these principles, we are prepared to work with everyone. India is doing its part, by itself and in partnership with others like Japan – in South Asia and Southeast Asia, in the Indian Ocean, Africa, West Asia and beyond. And, we are important stake-holders in New Development Bank and the Asian Infrastructure Investment Bank.

Finally, 

All of this is possible, if we do not return to the age of great power rivalries I have said this before: Asia of rivalry will hold us all back. Asia of cooperation will shape this century. So, each nation must ask itself: Are its choices building a more united world, or forcing new divisions? It is a responsibility that both existing and rising powers have. Competition is normal. But, contests must not turn into conflict; differences must not be allowed to become disputes. Distinguished members of the audience, It is normal to have partnerships on the basis of shared values and interests. India, too, has many in the region and beyond.

We will work with them, individually or in formats of three or more, for a stable and peaceful region. But, our friendships are not alliances of containment. We choose the side of principles and values, of peace and progress, not one side of a divide or the other. Our relationships across the world speak for our position. 

And, when we can work together, we will be able to meet the real challenges of our times. We will be able to protect our planet. We will be able to ensure non-proliferation We will be able to secure our people from terrorism and cyber threats.

In conclusion, let me say this again: India’s own engagement in the Indo-Pacific Region – from the shores of Africa to that of the Americas – will be inclusive. We are in-heritors of Vedanta philosophy that believes in essential oneness of all, and celebrates unity in diversity एकम सत्यम, विप्राः बहुदावदंति (Truth is one, the learned speak of it in many ways). That is the foundation of our civilizational ethos – of pluralism, co-existence, open-ness and dialogue. The ideals of democracy that define us as a nation also shape the way we engage the world. 

So, it translates into five S in Hindi: सम्मान (respect); सम्वाद (dialogue); सह्योग (cooperation), शांति (peace), and समृद्धि (prosperity). It’s easy to learn these words! So, we will engage with the world in peace, with respect, through dialogue and absolute commitment to international law. 

We will promote a democratic and rules-based international order, in which all nations, small and large, thrive as equal and sovereign We will work with others to keep our seas, space and airways free and open; our nations secure from terrorism; and our cyber space free from disruption and conflict. We will keep our economy open and our engagement transparent. We will share our resources, markets and prosperity with our friends and partners. We will seek a sustainable future for our planet, as through the new International Solar Alliance together with France and other partners. 

This is how we wish ourselves and our partners to proceed in this vast region and beyond. The ancient wisdom of the region is our common heritage. Lord Buddha’s message of peace and compassion has connected us all. Together, we have contributed much to human civilisation. And, we have been through the devastation of war and the hope of peace. We have seen the limits of power. And, we have seen the fruits of cooperation.

This world is at a crossroad There are temptations of the worst lessons of history. But, there is also a path of wisdom. It summons us to a higher purpose: to rise above a narrow view of our interests and recognise that each of us can serve our interests better when we work together as equals in the larger good of all nations. I am here to urge all to take that path.

Thank you. 
Thank you very much.