What interested Isaac Newton more than science?
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Sir Isaac Newton was born in 1642, the same year Galileo died. His mother was widowed twice, resulting in him being raised by his grandmother. He was sent off to grammar school and later went to Trinity College, Cambridge, 1661.
Sir Isaac Newton became a mathematician and a natural philosopher, discovering the laws of universal gravitation and formulating the three laws of motion, which aided in advancement of the discipline of dynamics. Newton was a discoverer of calculus and helped develop it into a comprehensive branch of mathematics. During the Plague of 1665-66, Newton moved to Woolsthorp, Lincolnshire.
He was honored to occupy the Lucasian Chair of Mathematics, 1669, and was elected Fellow of the Royal Society, 1672. Newton was given the position of Master of the Mint, 1699, and in 1701, entered Parliament. He constructed one of the first practical reflecting telescope. Using a prism, Newton demonstrated that a beam of light contained all the colors of the rainbow. He laid the foundation for the great law of energy conservation and developed the particle theory of light propagation. In 1703, Sir Issac Newton became the president of the Royal Society, and served in that position until his death.
Newton wrote one of the most important scientific books ever, Principia, 1687, in which he stated: “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. … All variety of created objects which represent order and life in the universe could happen only by the willful reasoning of its original Creator, whom I call the ‘Lord God.’ … This Being governs all things, not as the soul of the world, but as Lord over all; and on account of His dominion He is wont to be called ‘Lord God.’ … The supreme God exists necessarily, and by the same necessity He exists always and everywhere.”
Newton wrote in “Principia,” 1687: “From His true dominion it follows that the true God is a living, intelligent and powerful Being; and from His other perfections, that He is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, His duration reaches from eternity to eternity; His presence from infinity to infinity; He governs all things, and knows all things that are or can be done.”
Newton was cited in “Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton” by Sir David Brewster (Edinburgh, Thomas Constable and Co., 1855, Vol. II, 354): “God made and governs the world invisibly, and has commanded us to love and worship him, and no other God; to honor our parents and masters, and love our neighbors as ourselves; and to be temperate, just, and peaceable, and to be merciful even to brute beasts. And by the same power by which he gave life at first to every species of animals, he is able to revive the dead, and has revived Jesus Christ our Redeemer, who has gone into the heavens to receive a kingdom, and prepare a place for us, and is next in dignity to God, and may be worshiped as the Lamb of God, and has sent the Holy Ghost to comfort us in his absence, and will at length return and reign over us.”
Sir Isaac Newton wrote in “Optics,” 1704: “God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he formed them.”
Sir Isaac Newton devoted more time to the study of Scripture than to science (as cited in Tiner 1975): “I have a fundamental belief in the Bible as the Word of God, written by those who were inspired. I study the Bible daily.”
Sir Isaac Newton stated: “We account the Scriptures of God to be the most sublime philosophy. I find more sure marks of authenticity in the Bible than in any profane history whatsoever. … Worshiping God and the Lamb in the temple: God, for his benefaction in creating all things, and the Lamb, for his benefaction in redeeming us with his blood.”
Captivated by Bible prophecy, Sir Isaac Newton wrote “Observations on the Prophecies of Daniel and the Apocalypse of St. John” (published in 1733), in which he stated: “Daniel was in the greatest credit amongst the Jews, till the reign of the Roman Emperor Hadrian. And to reject his prophecies, is to reject the Christian religion. For this religion is founded upon his prophecy concerning the Messiah.”
He concluded his introductory chapter: “Daniel is most distinct in order of time, and easiest to be understood, and therefore in those things which relate to the last times, he must be made the key to the rest.”
In his preface to “The Prophecies of Daniel and the Apocalypse” (published 1733), Sir Isaac Newton quoted a letter to Richard Bentley, dated Dec. 10, 1692: “When I wrote my treatise about our System I had an eye upon such Principles as might work with considering men for the belief of a Deity and nothing can rejoice me more than to find it useful for that purpose.”
Sir Isaac Newton wrote in “Observations on the Prophecies of Daniel and the Apocalypse of St. John” (published 1733): “The Book of Revelation exhibits to us the same peculiarities as that of Nature. … The history of the Fall of Man – of the introduction of moral and physical evil, the prediction of the Messiah, the actual advent of our Savior, His instructions, His miracles, His death, His resurrection, and the subsequent propagation of His religion by the unlettered fishermen of Galilee, are each a stumbling-block to the wisdom of this world. … But through the system of revealed truth which this Book contains is, like that of the universe, concealed from common observation, yet the labors of the centuries have established its Divine origin, and developed in all its order and beauty the great plan of human restoration.”
In “Observations on the Prophecies of Daniel and the Apocalypse of St. John” (published 1733), Sir Isaac Newton wrote: “The folly of Interpreters has been, to foretell times and things, by this Prophecy, as if God designed to make them Prophets. By this rashness they have not only exposed themselves, but brought the Prophecy also into contempt. The design of God was much otherwise. He gave this and the Prophecies of the Old Testaments, not to gratify men’s curiosities by enabling them to foreknow things, but that after they were fulfilled they might be interpreted by the event; and his own Providence, not the Interpreters, be then manifested thereby to the world. For the event of things predicted many ages before, will then be a convincing argument that the world is governed by providence.”
In “Observations on the Prophecies of Daniel and the Apocalypse of St. John” (published 1733), Sir Isaac Newton wrote: “For the prophets and apostles have foretold that as Israel often revolted and brake the covenant, and upon repentance renewed it, so there should be a falling away among the Christians, soon after the days of the Apostles, and that in the latter days God would destroy the impenitent revolters, and make a new covenant with his people. And the giving ear to the prophets is a fundamental character of the true church. … For as the few and obscure Prophecies concerning Christ’s first coming were for setting up the Christian religion, which all nations have since corrupted, so the many and clear Prophecies, concerning the things to be done at Christ’s second coming, are not only for predicting but also for effecting a recovery and re-establishment of the long-lost truth, and setting up a kingdom wherein dwells righteousness. The event will prove the Apocalypse, and this Prophecy, thus proved and understood, will open the old Prophets and all together will make known the true religion, and establish it. … An angel must fly through the midst of heaven with the everlasting Gospel to preach to all nations, before Babylon falls, and the Son of man reaps his harvest.” (Revelation 14:6)
The “Encyclopedia of Philosophy” described Sir Isaac Newton: “Newton himself was a student of Old Testament prophecies and believed in the Scriptures as inerrant guides.”
In his book “Chronology,” Newton studied the sequence of historical events and inserted a geometric diagram of Solomon’s Temple, giving the lengths of the Temple in relation to the measurement of time. This was in accordance with the Renaissance view that the Temple was a microcosm of God’s creation embodying the order of the universe.
Economist John Maynard Keynes purchased all of Newton’s known manuscripts and personal notes at auction. After studying them, John Maynard Keynes wrote of Newton: “He regarded the universe as a cryptogram set by the Almighty, just as he himself wrapped the discovery of calculus in a cryptogram. … He looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher’s treasure hunt. …”
Regarding the Bible, Newton wrote: “The system of revealed truth which this Book contains is like that of the universe, concealed from common observation yet the labors of the centuries have established its Divine origin.”
Newton (as cited in Tiner 1975): “Atheism is so senseless. When I look at the solar system, I see the earth at the right distance from the sun to receive the proper amounts of heat and light. This did not happen by chance.”
Newton was cited by Sir David Brewster in “Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton” (Edinburgh, Thomas Constable and Co., 1855, Vol. II, p. 347-348): “Opposite to godliness is atheism in profession, and idolatry in practice. Atheism is so senseless and odious to mankind, that it never had many professors. Can it be by accident that all birds, beasts, and men have their right side and left side alike shaped, (except in their bowels); and just two eyes, and no more, on either side of the face; and just two ears on either side of the head; and a nose with two holes; and either two forelegs, or two wings, or two arms on the shoulders, and two legs on the hips, and no more?
“Whence arises this uniformity in all their outward shapes but from the counsel and contrivance of an Author? Whence is it that the eyes of all sorts of living creatures are transparent to the very bottom, and the only transparent members in the body, having on the outside a hard transparent skin, and within transparent humors, with a crystalline lens in the middle, and a pupil before the lens, all of them so finely shaped and fitted for vision, that no artist can mend them? Did blind chance know that there was light, and what was its refraction, and fit the eyes of all creatures, after the most curious manner, to make use of it?
“These, and suchlike considerations, always have, and ever will prevail with mankind, to believe that there is a Being who made all things, and has all things in his power, and who is therefore to be feared. We are, therefore, to acknowledge one God, infinite, eternal, omnipresent, omniscient, omnipotent, the Creator of all things, most wise, most just, most good, most holy. We must love him, fear him, honor him, trust in him, pray to him, give him thanks, praise him, hallow his name, obey his commandments.”
Sir Isaac Newton stated: “There is one God, the Father, ever-living, omnipresent, omniscient, almighty, the Maker of heaven and earth, and one Mediator between God and man, the man Christ Jesus. … To us there is but one God, the Father, of whom are all things, and one Lord Jesus Christ, by whom are all things, and we by Him. That is, we are to worship the Father alone as God Almighty, and Jesus alone as the Lord, the Messiah, the Great King, the Lamb of God who was slain, and hath redeemed us with His blood, and made us kings and priests.”
Sir Isaac Newton died March 20, 1727. Newton stated (as cited in “The Religion of Sir Isaac Newton,” Frank E. Manuel, editor, London, Oxford University Press, 1974, p. 112): “And when you are convinced, be not ashamed to profess the truth. For otherwise you may become a stumbling block to others, and inherit the lot of those Rulers of the Jews who believed in Christ, but yet were afraid to confess him lest they should be put out of the Synagogue. Wherefore, when you are convinced, be not ashamed of the truth, but profess it openly and endeavor to convince your Brother also that you may inherit at the resurrection the promise made in Daniel 12:3, that ‘they who turn many to righteousness shall shine as the stars for ever and ever.’ And rejoice if you are counted worthy to suffer in your reputation or any other way for the sake of the Gospel, for then, ‘great is thy reward’!”
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興味深く読みました：
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
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…
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
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
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
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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