2017年4月11日火曜日

READ THE FIRST CHAPTER OF WALTER ISAACSON'S EINSTEIN: HIS LIFE AND UNIVERSE

READ THE FIRST CHAPTER OF WALTER ISAACSON'S EINSTEIN: HIS LIFE AND UNIVERSE

"I promise you four papers,"  the young patent examiner wrote his friend. The letter would turn out to bear some of the most significant tidings in the history of science, but its momentous nature was masked by an impish tone that was typical of its author. He had, after all, just ad- dressed his friend as “you frozen whale” and apologised for writing a letter that was “inconsequential babble.” Only when he got around to describing the papers, which he had produced during his spare time, did he give some indication that he sensed their significance.
“The first deals with radiation and the energy properties of light and is very revolutionary,” he explained. Yes, it was indeed revolutionary. It argued that light could be regarded not just as a wave but also as a stream of tiny particles called quanta. The implications that would eventually arise from this theory—a cosmos without strict causality or certainty—would spook him for the rest of his life.
“The second paper is a determination of the true sizes of atoms.” Even though the very existence of atoms was still in dispute, this was the most straightforward of the papers, which is why he chose it as the safest bet for his latest attempt at a doctoral thesis. He was in the process of revolutionising physics, but he had been repeatedly thwarted in his efforts to win an academic job or even get a doctoral degree, which he hoped might get him promoted from a third- to a second-class examiner at the patent office.
 
The third paper explained the jittery motion of microscopic particles in liquid by using a statistical analysis of random collisions. In the process, it established that atoms and molecules actually exist. 
“The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time.” Well, that was certainly more than inconsequential babble. Based purely on thought experiments—performed in his head rather than in a lab—he had decided to discard Newton’s concepts of absolute space and time. It would become known as the Special Theory of Relativity.
What he did not tell his friend, because it had not yet occurred to him, was that he would produce a fifth paper that year, a short addendum to the fourth, which posited a relationship between energy and mass. Out of it would arise the best-known equation in all of physics: E=mc 2.
Looking back at a century that will be remembered for its  willingness to break classical bonds, and looking ahead to an era that seeks to nurture the creativity needed for scientific innovation, one person stands out as a paramount icon of our age: the kindly refugee from op- oppression whose wild halo of hair, twinkling eyes, engaging humanity, and extraordinary brilliance made his face a symbol and his name a synonym for genius. Albert Einstein was a locksmith blessed with imagination and guided by a faith in the harmony of nature’s handi- work. His fascinating story, a testament to the connection between creativity and freedom, reflects the triumphs and tumults of the mod- ern era.
Now that his archives have been completely opened, it is possible to explore how the private side of Einstein his nonconformist personality, his instincts as a rebel, his curiosity, his passions and detachments intertwined with his political side and his scientific side. Knowing about the man helps us understand the wellsprings of his science, and vice versa. Character and imagination and creative genius were all related, as if part of some unified field.
Despite his reputation for being aloof, he was in fact passionate in both his personal and scientific pursuits. At college he fell madly in love with the only woman in his physics class, a dark and intense Serbian named Mileva Maric´. They had an illegitimate daughter, then married and had two sons. She served as a sounding board for his scientific ideas and helped to check the math in his papers, but eventually their relationship disintegrated. Einstein offered her a deal. He would win the Nobel Prize someday, he said; if she gave him a divorce, he would give her the prize money. She thought for a week and accepted. Because his theories were so radical, it was seventeen years after his miraculous outpouring from the patent office before he was awarded the prize and she collected.
Einstein’s life and work reflected the disruption of societal certain- ties and moral absolutes in the modernist atmosphere of the early twentieth century. Imaginative nonconformity was in the air: Picasso, Joyce, Freud, Stravinsky, Schoenberg, and others were breaking conventional bonds. Charging this atmosphere was a conception of the universe in which space and time and the properties of particles seemed based on the vagaries of observations.
Einstein, however, was not truly a relativist, even though that is how he was interpreted by many, including some whose disdain was tinged by anti-Semitism. Beneath all of his theories, including relativity, was a quest for invariants, certainties, and absolutes. There was a harmonious reality underlying the laws of the universe, Einstein felt, and the goal of science was to discover it.
His quest began in 1895, when as a 16-year-old he imagined what it would be like to ride alongside a light beam. A decade later came his miracle year, described in the letter above, which laid the foundations for the two great advances of twentieth-century physics: relativity and quantum theory.
A decade after that, in 1915, he wrested from nature his crowning glory, one of the most beautiful theories in all of science, the general theory of relativity. As with the special theory, his thinking had evolved through thought experiments. Imagine being in an enclosed elevator accelerating up through space, he conjectured in one of them. The effects you’d feel would be indistinguishable from the experience of gravity.
Gravity, he figured, was a warping of space and time, and he came up with the equations that describe how the dynamics of this curvature result from the interplay between matter, motion, and energy. It can be described by using another thought experiment. Picture what it would be like to roll a bowling ball onto the two-dimensional surface of a trampoline. Then roll some billiard balls. They move toward the bowl- ing ball not because it exerts some mysterious attraction but because of the way it curves the trampoline fabric. Now imagine this happen- ing in the four-dimensional fabric of space and time. Okay, it’s not easy, but that’s why we’re no Einstein and he was.
The exact midpoint of his career came a decade after that, in 1925, and it was a turning point. The quantum revolution he had helped to launch was being transformed into a new mechanics that was based on uncertainties and probabilities. He made his last great contributions to quantum mechanics that year but, simultaneously, began to resist it.  He would spend the next three decades, ending with some equations scribbled while on his deathbed in 1955, stubbornly criticising what he regarded as the incompleteness of quantum mechanics while attempting to subsume it into a unified field theory.
Both during his thirty years as a revolutionary and his subsequent thirty years as a resistor, Einstein remained consistent in his willingness to be a serenely amused loner who was comfortable not conforming. Independent in his thinking, he was driven by an imagination that broke from the confines of conventional wisdom. He was that odd breed, a reverential rebel, and he was guided by a faith, which he wore lightly and with a twinkle in his eye, in a God who would not play dice by allowing things to happen by chance.
Einstein’s nonconformist streak was evident in his personality and politics as well. Although he subscribed to socialist ideals, he was too much of an individualist to be comfortable with excessive state control or centralised authority. His impudent instincts, which served him so well as a young scientist, made him allergic to nationalism, militarism, and anything that smacked of a herd mentality. And until Hitler caused him to revise his geopolitical equations, he was an instinctive pacifist who celebrated resistance to war.
His tale encompasses the vast sweep of modern science, from the infinitesimal to the infinite, from the emission of photons to the expansion of the cosmos. A century after his great triumphs, we are still living in Einstein’s universe, one defined on the macro scale by his theory of relativity and on the micro scale by a quantum mechanics that has proven durable even as it remains disconcerting.
His fingerprints are all over today’s technologies. Photoelectric cells and lasers, nuclear power and fiber optics, space travel, and even semi- conductors all trace back to his theories. He signed the letter to Frank- lin Roosevelt warning that it may be possible to build an atom bomb, and the letters of his famed equation relating energy to mass hover in our minds when we picture the resulting mushroom cloud.
Einstein’s launch into fame, which occurred when measurements made during a 1919 eclipse confirmed his prediction of how much gravity bends light, coincided with and contributed to, the birth of a new celebrity age. He became a scientific supernova and humanist icon, one of the most famous faces on the planet. The public earnestly puzzled over his theories, elevated him into a cult of genius, and canonised him as a secular saint.
If he did not have that electrified halo of hair and those piercing eyes, would he still have become science’s preeminent poster boy? Sup- pose, as a thought experiment, that he had looked like a Max Planck or a Niels Bohr. Would he have remained in their reputational orbit, that of a mere scientific genius? Or would he still have made the leap into the pantheon inhabited by Aristotle, Galileo, and Newton?
The latter, I believe, is the case. His work had a very personal char- acter, a stamp that made it recognisably his, the way a Picasso is recognisably a Picasso. He made imaginative leaps and discerned great principles through thought experiments rather than by methodical in- ductions based on experimental data. The theories that resulted were at times astonishing, mysterious, and counterintuitive, yet they contained notions that could capture the popular imagination: the relativity of space and time, E=mc 2, the bending of light beams, and the warping of space.
Adding to his aura was his simple humanity. His inner security was tempered by the humility that comes from being awed by nature. He could be detached and aloof from those close to him, but toward mankind in general he exuded a true kindness and gentle compassion. Yet for all of his popular appeal and surface accessibility,  Einstein also came to symbolise the perception that modern physics was something that ordinary laymen could not comprehend, “the province of priest-like experts,” in the words of Harvard professor Dudley Herschbach.3 It was not always thus. Galileo and Newton were both great geniuses, but their mechanical cause-and-effect explanation of the world was something that most thoughtful folks could grasp. In the eighteenth century of Benjamin Franklin and the nineteenth century of Thomas Edison, an educated person could feel some familiarity with science and even dabble in it as an amateur.
A popular feel for scientific endeavours should, if possible, be re- stored given the needs of the twenty-first century. This does not mean that every literature major should take a watered-down physics course or that a corporate lawyer should stay abreast of quantum mechanics. Rather, it means that an appreciation for the methods of science is a useful asset for a responsible citizenry. What science teaches us, very significantly, is the correlation between factual evidence and general theories, something well illustrated in Einstein’s life.
In addition, an appreciation for the glories of science is a joyful trait for a good society. It helps us remain in touch with that childlike capacity for wonder, about such ordinary things as falling apples and elevators, that characterises Einstein and other great theoretical physicists.
That is why studying Einstein can be worthwhile. Science is inspiring and noble, and its pursuit an enchanting mission, as the sagas of its heroes remind us. Near the end of his life, Einstein was asked by the New York State Education Department what schools should emphasise. “In teaching history,” he replied, “there should be extensive discussion of personalities who benefited mankind through independence of character and judgment.”  Einstein fits into that category.
At a time when there is a new emphasis, in the face of global com- petition, on science and math education, we should also note the other part of Einstein’s answer. “Critical comments by students should be taken in a friendly spirit,” he said. “Accumulation of material should not stifle the student’s independence.” A society’s competitive advantage will come not from how well its schools teach the multiplication and periodic tables, but from how well they stimulate imagination and creativity.
Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualise how equations were reflected in realities—how the electro- magnetic field equations discovered by James Clerk Maxwell, for ex- ample, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.” 
That approach required him to embrace nonconformity. “Long live impudence!” he exulted to the lover who would later become his wife. “It is my guardian angel in this world.” Many years later, when others thought that his reluctance to embrace quantum mechanics showed that he had lost his edge, he lamented, “To punish me for my contempt for authority, fate made me an authority myself.” 
His success came from questioning conventional wisdom, challenging authority, and marvelling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on re- spect for free minds, free spirits, and free individuals. Tyranny repulsed him, and he saw tolerance not simply as a sweet virtue but as a necessary condition for a creative society. “It is important to foster individuality,” he said, “for only the individual can produce the new ideas.” 
This outlook made Einstein a rebel with a reverence for the harmony of nature, one who had just the right blend of imagination and wisdom to transform our understanding of the universe. These traits are just as vital for this new century of globalisation, in which our success will depend on our creativity, as they were for the beginning of the twentieth century when Einstein helped usher in the modern age.
Chapter sample from Einstein by Walter Isaacson. Published by Simon & Schuster. RRP $32.99. Out May.
 
とても興味深く読みました：
 
再生核研究所声明353（2017.2.2）　ゼロ除算　記念日

2014.2.2　に 一般の方から100/0　の意味を問われていた頃、偶然に執筆中の論文原稿にそれがゼロとなっているのを発見した。直ぐに結果に驚いて友人にメールしたり、同僚に話した。それ以来、ちょうど３年、相当詳しい記録と経過が記録されている。重要なものは再生核研究所声明として英文と和文で公表されている。最初のものは

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

で、最新のは

Announcement 352 (2017.2.2):  On the third birthday of the division by zero z/0=0　

である。

アリストテレス、ブラーマグプタ、ニュートン、オイラー、アインシュタインなどが深く関与する　ゼロ除算の神秘的な永い歴史上の発見であるから、その日をゼロ除算記念日として定めて、世界史を進化させる決意の日としたい。ゼロ除算は、ユークリッド幾何学の変更といわゆるリーマン球面の無限遠点の考え方の変更を求めている。―　実際、ゼロ除算の歴史は人類の闘争の歴史と共に　人類の愚かさの象徴であるとしている。
心すべき要点を纏めて置きたい。

１）     ゼロの明確な発見と算術の確立者Brahmagupta (598 - 668 ?)　は　既にそこで、0/0=0　と定義していたにも関わらず、言わば創業者の深い考察を理解できず、それは間違いであるとして、１３００年以上も間違いを繰り返してきた。
２）     予断と偏見、慣習、習慣、思い込み、権威に盲従する人間の精神の弱さ、愚かさを自戒したい。我々は何時もそのように囚われていて、虚像を見ていると　真智を愛する心を大事にして行きたい。絶えず、それは真かと　問うていかなければならない。
３）     ピタゴラス派では　無理数の発見をしていたが、なんと、無理数の存在は自分たちの世界観に合わないからという理由で、―　その発見は都合が悪いので　―　、弟子を処刑にしてしまったという。真智への愛より、面子、権力争い、勢力争い、利害が大事という人間の浅ましさの典型的な例である。
４）     この辺は、２０００年以上も前に、既に世の聖人、賢人が諭されてきたのに　いまだ人間は生物の本能レベルを越えておらず、愚かな世界史を続けている。人間が人間として生きる意義は　真智への愛にある　と言える。
５）     いわば創業者の偉大な精神が正確に、上手く伝えられず、ピタゴラス派のような対応をとっているのは、本末転倒で、そのようなことが世に溢れていると警戒していきたい。本来あるべきものが逆になっていて、社会をおかしくしている。
６）     ゼロ除算の発見記念日に　繰り返し、人類の愚かさを反省して、明るい世界史を切り拓いて行きたい。
以　上

追記：

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:

Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue  1, 2017), 1-16.　
http://www.scirp.org/journal/alamt　 　http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf

再生核研究所声明359（2017.3.20）　ゼロ除算とは何か　―　本質、意義

ゼロ除算の理解を進めるために　ゼロ除算とは何か　の題名で、簡潔に表現して置きたい。　構想と情念、想いが湧いてきたためである。
基本的な関数y=1/x を考える。　これは直角双曲線関数で、原点以外は勿論、値、関数が定義されている。問題はこの関数が、x=0 　で　どうなっているかである。結論は、この関数の原点での値を　ゼロと定義する　ということである。　定義するのである。定義であるから勝手であり、従来の定義や理論に反しない限り、定義は勝手であると言える。原点での値を明確に定義した理論はないから、この定義は良いと考えられる。それを、y=1/0=0　と記述する。ゼロ除算は不可能であるという、数学の永い定説に従って、1/0　の表記は学術書、教科書にもないから、1/0=0　の記法は　形式不変の原理、原則　にも反しないと言える。―　多くの数学者は注意深いから、1/0=\infty　の表記を避けてきたが、想像上では x　が　0　に近づいたとき、限りなく　絶対値が大きくなるので、複素解析学では、表現1/0=\infty　は避けても、1/0=\infty　と考えている事は多い。（無限大の記号がない時代、アーベルなどもそのような記号を用いていて、オイラーは1/0=\inftyと述べ、それは間違いであると指摘されてきた。　しかしながら、無限大とは何か、数かとの疑問は　続いている。）。ここが大事な論点である。近づいていった極限値がそこでの値であろうと考えるのは、極めて自然な発想であるが、現代では、不連続性の概念　が十分確立されていて、極限値がそこでの値と違う例は、既にありふれている。―　アリストテレスは　連続性の世界観をもち、特にアリストテレスの影響を深く受けている欧米の方は、この強力な不連続性を中々受け入れられないようである。無限にいくと考えられてきたのが突然、ゼロになるという定義になるからである。　しかしながら、関数y=1/xのグラフを書いて見れば、原点は双曲線のグラフの中心の点であり、美しい点で、この定義は魅力的に見えてくるだろう。
定義したことには、それに至るいろいろな考察、経過、動機、理由がある。―　分数、割り算の意味、意義、一意性問題、代数的な意味づけなどであるが、それらは既に数学的に確立しているので、ここでは触れない。
すると、定義したからには、それがどのような意味が存在して、世の中に、数学にどのような影響があるかが、問題になる。これについて、現在、初等数学の学部レベルの数学をゼロ除算の定義に従って、眺めると、ゼロ除算、すなわち、　分母がゼロになる場合が表現上現れる広範な場合に 新しい現象が発見され、ゼロ除算が関係する広範な場合に大きな影響が出て、数学は美しく統一的に補充，完全化されることが分かった。それらは現在、３８０件以上のメモにまとめられている。しかしながら、世界観の変更は特に重要であると考えられる：

複素解析学で無限遠点は　その意味で1/0=0で、複素数0で表されること、アリストテレスの連続性の概念に反し、ユークリッド空間とも異なる新しい空間が　現れている。直線のコンパクト化の理想点は原点で、全ての直線が原点を含むと、超古典的な結果に反する。更に、ゼロと無限の関係が明らかにされてきた。
ゼロ除算は、現代数学の初等部分の相当な変革を要求していると考えられる。

以　上
付記：　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

Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh　International Journal of Mathematics and Computation Vol. 28(2017); Issue  1, 2017), 1 -16.　
http://www.scirp.org/journal/alamt　 　http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf

Relations of 0 and infinity
Hiroshi Okumura, Saburou Saitoh　and Tsutomu Matsuura：
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
 
再生核研究所声明357（2017.2.17）Brahmagupta　の名誉回復と賞賛を求める。

再生核研究所声明　３３９で　次のように述べている：

世界史と人類の精神の基礎に想いを致したい。ピタゴラスは　万物は数で出来ている、表されるとして、数学の重要性を述べているが、数学は科学の基礎的な言語である。ユークリッド幾何学の大きな意味にも触れている（再生核研究所声明315（2016.08.08）　世界観を大きく変えた、ユークリッドと幾何学）。しかしながら、数体系がなければ、空間も幾何学も厳密には　表現することもできないであろう。この数体系の基礎はブラーマグプタ（Brahmagupta、598年 – 668年?）インドの数学者・天文学者によって、628年に、総合的な数理天文書『ブラーマ・スプタ・シッダーンタ』（ब्राह्मस्फुटसिद्धान्त Brāhmasphuṭasiddhānta）の中で与えられ、ゼロの導入と共に四則演算が確立されていた。ゼロの導入、負の数の導入は数学の基礎中の基礎で、西欧世界がゼロの導入を永い間嫌っていた状況を見れば、これらは世界史上でも顕著な事実であると考えられる。最近ゼロ除算は、拡張された割り算、分数の意味で可能で、ゼロで割ればゼロであることが、その大きな影響とともに明らかにされてきた。しかしながら、　ブラーマグプタは　その中で 0 ÷ 0 ＝ 0 と定義していたが、奇妙にも１３００年を越えて、現在に至っても　永く間違いであるとされている。現在でも0 ÷ 0について、幾つかの説が存在していて、現代数学でもそれは、定説として　不定であるとしている。最近の研究の成果で、ブラーマグプタの考えは　実は正しかった　ということになる。　しかしながら、一般の　ゼロ除算については触れられておらず、永い間の懸案の問題として、世界を賑わしてきた。現在でも議論されている。ゼロ除算の永い歴史と問題は、次のアインシュタインの言葉に象徴される：

Blackholes are where God divided by zero. I don't believe in mathematics. George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist re-
marked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as the biggest blunder of his life [1] 1. Gamow, G., My World Line (Viking, New York). p 44, 1970.

物理学や計算機科学で　ゼロ除算は大事な課題であるにも関わらず、創始者の考えを無視し、割り算は　掛け算の逆との　貧しい発想で　間違いを１３００年以上も、繰り返してきたのは　実に残念で、不名誉なことである。創始者は　ゼロの深い意味、ゼロが　単純な算数・数学における意味を越えて、ゼロが基準を表す、不可能性を表現する、神が最も簡単なものを選択する、神の最小エネルギーの原理、すなわち、神もできれば横着したいなどの世界観を感じていて、0/0=0 を自明なもの　と捉えていたものと考えられる。実際、巷で、ゼロ除算の結果や、適用例を語ると　結構な　素人の人々が　率直に理解されることが多い。
１３００年間も　創始者の結果が間違いであるとする　世界史は修正されるべきである、間違いであるとの不名誉を回復、数学の基礎の基礎である算術の確立者として、世界史上でも高く評価されるべきである。　真智の愛、良心から、厚い想いが湧いてくる。

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　以　上

追記

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:
http://www.scirp.org/journal/alamt　 　http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf


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