Top 10 Greatest Philosophers in History FLAMEHORSE FEBRUARY 19, 2011

Top 10 Greatest Philosophers in History
FLAMEHORSE FEBRUARY 19, 2011

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This list examines the influence, depth of insight and wide-reaching interest across many subjects of various “lovers of wisdom,” and ranks them accordingly. It should be noted, first and foremost, that philosophy in its traditional sense was science – philosophers (like Aristotle) used rationality to come to scientific knowledge of the world around us. It was not until relatively modern times that philosophy was considered to be separate from the physical sciences.

10　John Locke
John-LockeThe most important thinker of modern politics is the most directly responsible for Thomas Jefferson’s rhetoric in the Declaration of Independence, and the rhetoric in the U. S. Constitution. Locke is referred to as the “Father of Liberalism,” because of his development of the principles of humanism and individual freedom, founded primarily by #1. It is said that liberalism proper, the belief in equal rights under the law, begins with Locke. He penned the phrase “government with the consent of the governed.” His three “natural rights,” that is, rights innate to all human beings, were and remain “life, liberty, and estate.”He did not approve of the European idea of nobility enabling some to acquire land through lineage, while the poor remained poor. Locke is the man responsible, through Jefferson primarily, for the absence of nobility in America. Although nobility and birthrights still exist in Europe, especially among the few kings and queens left, the practice has all but vanished. The true democratic ideal did not arrive in the modern world until Locke’s liberal theory was taken up.

9　Epicurus
EpicurusEpicurus has gotten a bit of an unfair reputation over the centuries as a teacher of self-indulgence and excess delight. He was soundly criticized by a lot of Christian polemicists (those who make war against all thought but Christian thought), especially during the Middle Ages, because he was thought to be an atheist, whose principles for a happy life were passed down to this famous set of statements: “Don’t fear god; don’t worry about death; what is good is easy to get; what is terrible is easy to endure.”He advocated the principle of refusing belief in anything that is not tangible, including any god. Such intangible things he considered preconceived notions, which can be manipulated. You may think of Epicureanism as “no matter what happens, enjoy life, because you only get one and it doesn’t last long.” Epicurus’s idea of living happily centered on just treatment of others, avoidance of pain and living in such a way as to please oneself, but not to overindulge in anything.He also advocated a version of the Golden Rule, “It is impossible to live a pleasant life without living wisely and well and justly (agreeing ‘neither to harm nor be harmed’), and it is impossible to live wisely and well and justly without living a pleasant life. “Wisely,” at least for Epicurus, would be avoidance of pain, danger, disease, etc.; “well” would be proper diet and exercise; “justly,” in the Golden Rule’s sense of not harming others because you do not want to be harmed.

8　Zeno of Citium
ZenoYou may not be as familiar with him as with most of the others on this list, but Zeno founded the school of Stoicism. Stoicism comes from the Greek “stoa,” which is a roofed colonnade, especially that of the Poikile, which was a cloistered piazza on the north side of the Athenian marketplace, in the 3rd Century BC. Stoicism is based on the idea that anything which causes us to suffer in life is actually an error in our judgment, and that we should always have absolute control over our emotions. Rage, elation, depression are all simple flaws in a person’s reason, and thus, we are only emotionally weak when we allow ourselves to be. Put another way, the world is what we make of it.Epicureanism is the usual school of thought considered the opposite of Stoicism, but today many people mistake one for the other or combine them. Epicureanism argues that displeasures do exist in life and must be avoided, in order to enter a state of perfect mental peace (ataraxia, in Greek). Stoicism argues that mental peace must be acquired out of your own will not to let anything upset you. Death is a necessity, so why feel depressed when someone dies? Depression doesn’t help. It only hurts. Why get enraged over something? The rage will not result in anything good. And so, in controlling one’s emotions, a state of mental peace is brought about. Of importance is to shun desire: you may strive for what you need, but only that and nothing more. What you want will lead to excess, and excess doesn’t help, but hurts.

7　Avicenna
Avicenna2PaintingHis full name is Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā, the last two words of which were Latinized into the more common form in Western history. He lived in the Persian Empire from c. 980 AD to 1037. The Dark Ages were not so dark. Aside from his stature as a philosopher, he was also the world’s preeminent physician during his life. His two most well known works today are The Book of Healing (which has nothing to do with physical medicine) and The Canon of Medicine, which was his compilation of all known medical knowledge at that time.Influenced primarily by #1, his Book of Healing deals with everything from logic, to math, to music, to science. He proposed in it that Venus is closer than the Sun to Earth. Imagine not knowing that for a fact. The Sun looks a lot closer than Venus, but he got it right. He rejected astrology as a true science, since everything in it is based on conjecture, not evidence. He theorized that some fluid deep underground was responsible for the fossilization of bone and wood, arguing that “a powerful mineralizing and petrifying virtue which arises in certain stony spots, or emanates suddenly from the earth during earthquake and subsidences…petrifies whatever comes into contact with it. As a matter of fact, the petrifaction of the bodies of plants and animals is not more extraordinary than the transformation of waters.”This is not correct, but it’s closer than you might believe. Petrifaction can occur in any organic material, and involves the material, most notably wood, being impregnated by silica deposits, gradually changing from its original materials into stone. Avicenna is the first to describe the five classical senses: taste, touch, vision, hearing and smell. He may have been the world’s first systematic psychologist, in a time when people suffering from a mental disorder were said to be possessed by demons. Avicenna argued that there were somatic possibilities for recovery inherent in all aspects of a person’s body, including the brain.John Stuart Mill’s five methods for inductive logic stem mostly from Avicenna, who first expounded on three of them: agreement, difference and concomitant variation. It would take too long to explain them in this list, but they are all forms of syllogisms, and every philosopher and student of philosophy is familiar with them from the beginning of education in the subject. They are critical to the scientific method, and whenever someone forms a statement as a syllogism, s/he is using at least one of the methods.

6　Thomas Aquinas
Saint Thomas AquinasThomas will forever be remembered as the guy who supposedly proved the existence of God by arguing that the Universe had to have been created by something, since everything in existence has a beginning and an end. This is now referred to as the “First Cause” argument, and all philosophers after Thomas have wrestled with proving or disproving the theory. He actually based it on the notion of “ού κινούμενον κινεῖ,” of #1. The Greek means “one who moves while not moving” – or “the unmoved mover”.Thomas founded everything he postulated firmly in Christianity, and for this reason, he is not universally popular, today. Even Christians consider that, since he derived all his ethical teachings from the Bible, Thomas is not independently authoritative of any of those teachings. But his job, in teaching the common people around him, was to get them to understand ethics without all the abstract philosophy. He expounded on #2’s principles of what we now call “cardinal virtues:” justice, courage, prudence and temperance. He was able to reach the masses with this simple, four-part instruction.He made five famous arguments for the existence of God, which are still discussed hotly on both sides: theist and atheist. Of those five, which he intended to define the nature of God, one is called “the unity of God,” which is to say that God is not divisible. He has essence and existence, and these two qualities cannot be separated. Thus, if we are able to express something as possessing two or more qualities, and cannot separate the qualities, then the statement itself proves that there is a God, and Thomas’s example is the statement, “God exists,” in which statement subject and predicate are identical.

5　Confucius
KziMaster Kong Qiu, as his name translates from Chinese, lived from 551 to 479 BC, and remains the most important single philosopher in Eastern history. He espoused significant principles of ethics and politics, in a time when the Greeks were espousing the same things. We think of democracy as a Greek invention, a Western idea, but Confucius wrote in his Analects that “the best government is one that rules through ‘rites’ and the people’s natural morality, rather than by using bribery and coercion. This may sound obvious to us today, but he wrote it in the early 500s to late 400s BC. It is the same principle of democracy that the Greeks argued for and developed: the people’s morality is in charge; therefore, rule by the people.Confucius defended the idea of an Emperor, but also advocated limitations to the emperor’s power. The emperor must be honest and his subjects must respect him, but he must also deserve that respect. If he makes a mistake, his subjects must offer suggestions to correct him, and he must consider them. Any ruler who acted contrary to these principles was a tyrant, and thus a thief more than a ruler. Confucius also devised his own, independent version of the Golden Rule, which had existed for at least a century in Greece before him. His phrasing was almost identical, but then furthered the idea: “What one does not wish for oneself, one ought not to do to anyone else; what one recognizes as desirable for oneself, one ought to be willing to grant to others.” The first statement is in the negative, and constitutes a passive desire not to harm others. The second statement is much more important, constituting an active desire to help others. The only other philosopher of antiquity to advocate the Golden Rule in the positive form is Jesus of Nazareth.

4　Rene Descartes
Rene-Descartes 1214990CDescartes lived from 1596 to 1650, and today he is referred to as “the Father of Modern Philosophy.” He created analytical geometry, based on his now immortal Cartesian coordinate system, immortal in the sense that we are all taught it in school, and that it is still perfectly up-to-date in almost all branches of mathematics. Analytical geometry is the study of geometry using algebra and the Cartesian coordinate system. He discovered the laws of refraction and reflection. He also invented the superscript notation still used today to indicate the powers of exponents.He advocated dualism, which is very basically defined as the power of the mind over the body: strength is derived by ignoring the weaknesses of the human physique and relying on the infinite power of the human mind. Descartes’s most famous statement, now practically the motto of existentialism: “Je pense donc je suis;” “Cogito, ergo sum;” “I think, therefore I am.” This is not meant to prove the existence of one’s body. Quite the opposite, it is meant to prove the existence of one’s mind. He rejected perception as unreliable, and considered deduction the only reliable method for examining, proving and disproving anything. He also adhered to the Ontological Argument for the Existence of a Christian God, stating that, because God is benevolent, Descartes can have some faith in the account of reality his senses provide him, for God has provided him with a working mind and sensory system and does not desire to deceive him. From this supposition, however, Descartes finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. In terms of the study of knowledge therefore, he can be said to have contributed such ideas as a rigorous conception of foundationalism (basic beliefs) and the possibility that reason is the only reliable method of attaining knowledge.

3　Paul of Tarsus
St Paul At St Peter'sThe wild card of this list, but give him fair consideration. Paul accomplished more with the few letters we have of his, to various churches in Asia Minor, Israel and Rome, than any other mortal person in the Bible, except Jesus himself. Jesus founded Christianity. But without Paul, the religion would have died in a few hundred years at best, or remained too insular to invite the entire world into its faith, as Jesus wanted. Paul had more than one falling out with Peter, primarily among the other Disciples. Peter insisted that at least one or two of the Jewish traditions remain as requirements, along with faith in Jesus, for one to be counted as Christian. Paul insisted that faith in Jesus is all that is required, and neither circumcision, refusal of certain foods or any other Jewish custom was necessary, because the world was now, and forevermore, under a state of Grace in Jesus, not a state of Law according to Moses. This principle of a state of grace, which is now central to all sects of Christianity, was Paul’s idea (if not Jesus’s), as was the concept of God’s moral law (in Ten Commandments) being innately understood by all men once they reach the age of reason, by which law God will hold all men accountable on his Day of Judgment.He is especially impressive to have systematized these principles flawlessly, having never met Jesus in person, and in direct opposition to Peter and several other Disciples. Many theologists and experts on Christianity and its history even call Paul, and not Jesus, the founder of Christianity. That may be going a bit too far, but keep in mind that the Disciples intended to keep Christianity for themselves, as the proper form of Judaism, to which only Jews could convert. Anyone could symbolically become a Jew by circumcision and obedience of the Mosaic Laws (every one of them, not just the Big Ten). Paul argued against this, stating that as Christ was the absolute greatest good that the world would ever see, and Almighty because he and the Father are one, then the grace of Christ is sufficiently powerful to save anyone from his or her sin, whether Jewish, Gentile or anything else. If the religion were to have lasted to present day without Paul’s letters championing the grace of Christ over the Law of Moses, Christianity would just a minor sect of Judaism.

2　Plato
Plato BustPlato lived from c. 428 to c. 348 BC, and founded the Western world’s first school of higher education, the Academy of Athens. Almost all of Western philosophy can be traced back to Plato, who was taught by Socrates, and preserved through his own writings, some of Socrates’s ideas. If Socrates wrote anything down, it has not survived directly. Plato and Xenophon, another of his students, recounted a lot of his teachings, as did the playwright Aristophanes. One of Plato’s most famous quotations concerns politics, “Until philosophers rule as kings or those who are now called kings and leading men genuinely and adequately philosophize, that is, until political power and philosophy entirely coincide, while the many natures who at present pursue either one exclusively are forcibly prevented from doing so, cities will have no rest from evils…nor, I think, will the human race.” What he means is that any person(s) in control of a nation or city or city-state must be wise, and that if they are not, then they are ineffectual rulers. It is only through philosophy that the world can be free of evils. Plato’s preferred government was one of benevolent aristrocrats, those born of nobility, who are well educated and good, who help the common people to live better lives. He argued against democracy proper, rule by the people themselves, since in his view, a democracy had murdered his teacher, Socrates.Plato’s most enduring theory, if not his political theories, is that of “The Forms.” Plato wrote about these forms throughout many of his works, and asserted, by means of them, that immaterial abstractions possess the highest, most fundamental kind of reality. All things of the material world can change, and our perception of them also, which means that the reality of the material world is weaker, less defined than that of the immaterial abstractions. Plato argued that something must have created the Universe. Whatever it is, the Universe is its offspring, and we, living on Earth, our bodies and everything that we see and hear and touch around us, are less real than the creator of the Universe, and the Universe itself. This is a foundation on which #4 based his understanding of existentialism.

1Aristotle

Staatpowi-3 1Aristotle topped another of this lister’s lists, heading the category of philosophy, so his rank on this one is not entirely surprising. But consider that Aristotle is the first to have written systems by which to understand and criticize everything from pure logic to ethics, politics, literature, even science. He theorized that there are four “causes”, or qualities, of any thing in existence: the material cause, which is what the subject is made of; the formal cause, or the arrangement of the subject’s material; the effective cause, the creator of the thing; and the final cause, which is the purpose for which a subject exists. That all may sound perfectly obvious and not worth arguing over, but since it would take far too long for the purpose of a top ten list to expound on classical causality, suffice to say that all philosophers since Aristotle have had something to say on the matter, and absolutely everything that has been said, and perhaps can be said, is, or must be, based on Aristotle’s system of it: it is impossible to discuss causality without using or trying to debunk Aristotle’s ideas.Aristotle is also the first person in Western history to argue that there is a hierarchy to all life in the Universe; that because Nature never did anything unnecessary as he observed, then in the same way, this animal is in charge of that animal, and likewise with plants and animals together. His so-called “ladder of life” has eleven rungs, at the top of which are humans. The Medieval Christian theorists ran with this idea, extrapolating it to the hierarchy of God with Man, including angels. Thus, the angelic hierarchy of Catholicism, usually thought as a purely Catholic notion, stems from Aristotle, who lived and died before Jesus was born. Aristotle was, in fact, at the very heart of the classical education system used through the Medieval western world.Aristotle had something to say on just about every subject, whether abstract or concrete, and modern philosophy almost always bases every single principle, idea, notion or “discovery” on a teaching of Aristotle. His principles of ethics were founded on the concept of doing good, rather than merely being good. A person may be kind, merciful, charitable, etc., but until he proves this by helping others, his goodness means precisely nothing to the world, in which case it means nothing to himself. We could go on about Aristotle, of course, but this list has gone on long enough. Honorable mentions are very many, so list them as you like.http://listverse.com/2011/02/19/top-10-greatest-philosophers-in-history/

再生核研究所声明312（2016.07.14）　ゼロ除算による　平成の数学改革を提案する

アリストテレス以来、あるいは西暦６２８年インドにおけるゼロの記録と、算術の確立以来、またアインシュタインの人生最大の懸案の問題とされてきた、ゼロで割る問題　ゼロ除算は、本質的に新しい局面を迎え、数学における基礎的な部分の欠落が明瞭になってきた。ここ７０年を越えても教科書や学術書における数学の基礎的な部分の変更は　かつて無かった事である。
そこで、最近の成果を基に現状における学術書、教科書の変更すべき大勢を外観して置きたい。特に、大学学部までの初等数学において、日本人の寄与は皆無であると言えるから、日本人が数学の基礎に貢献できる稀なる好機にもなるので、数学者、教育者など関係者の注意を換気したい。―　この文脈では稀なる日本人数学者　関孝和の業績が世界の数学に活かせなかったことは　誠に残念に思われる。
先ず、数学の基礎である四則演算において　ゼロでは割れない　との世の定説を改め、自然に拡張された分数、割り算で、いつでも四則演算は例外なく、可能であるとする。山田体の導入。その際、小学生から割り算や分数の定義を除算の意味で　繰り返し減法（道脇方式）で定義し、ゼロ除算は自明であるとし　計算機が割り算を行うような算法で　計算方法も指導する。―　この方法は割り算の簡明な算法として児童に歓迎されるだろう。
反比例の法則や関数y=1/xの出現の際には、その原点での値はゼロであると　定義する。その広範な応用は　学習過程の進展に従って　どんどん触れて行くこととする。
いわゆるユークリッド幾何学の学習においては、立体射影の概念に早期に触れ、ゼロ除算が拓いた新しい空間像を指導する。無限、無限の彼方の概念、平行線の概念、勾配の概念を変える必要がある。どのように、如何に、カリキュラムに取り組むかは、もちろん、慎重な検討が必要で、数学界、教育界などの関係者による国家的取り組み、協議が必要である。重要項目は、直角座標系で　ｙ軸の勾配はゼロであること。真無限における破壊現象、接線などの新しい性質、解析幾何学との美しい関係と調和。すべての直線が原点を代数的に通り、平行な２直線は原点で代数的に交わっていること。行列式と破壊現象の美しい関係など。
大学レベルになれば、微積分、線形代数、微分方程式、複素解析をゼロ除算の成果で修正、補充して行く。複素解析学におけるローラン展開の学習以前でも形式的なローラン展開(負べき項を含む展開)の中心の値をゼロ除算で定義し、広範な応用を展開する。特に微分係数が正や負の無限大の時、微分係数をゼロと修正することによって、微分法の多くの公式や定理の表現が簡素化され、教科書の結構な記述の変更が要求される。媒介変数を含む多くの関数族は、ゼロ除算　算法で統一的な視点が与えられる。多くの公式の記述が簡単になり、修正される。
複素解析学においては　無限遠点はゼロで表現されると、コペルニクス的変更（無限とされていたのが実はゼロだった）を行い、極の概念を次のように変更する。極、特異点の定義は　そのままであるが、それらの点の近傍で、限りなく無限の値に近づく値を位数まで込めて取るが、特異点では、ゼロ除算に言う、有限確定値をとるとする。その有限確定値のいろいろ幾何学な意味を学ぶ。古典的な鏡像の定説；原点の　原点を中心とする円の鏡像は無限遠点であるは、誤りであり、修正し、ゼロであると　いろいろな根拠によって説明する。これら、無限遠点の考えの修正は、ユークリッド以来、我々の空間に対する認識の世界史上に置ける大きな変更であり、数学を越えた世界観の変更を意味している。―　この文脈では天動説が地動説に変わった歴史上の事件が想起される。
ゼロ除算は　物理学を始め、広く自然科学や計算機科学への大きな影響が期待される。しかしながら、ゼロ除算の研究成果を教科書、学術書に遅滞なく取り入れていくことは、真智への愛、真理の追究の表現であり、四則演算が自由にできないとなれば、人類の名誉にも関わることである。ゼロ除算の発見は　日本の世界に置ける顕著な貢献として世界史に記録されるだろう。研究と活用の推進を　大きな夢を懐きながら　要請したい。
以　上
追記：
(2016) Matrices and Division by Zero z/0 = 0. Advances in Linear Algebra & Matrix Theory, 6, 51-58. 
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 DOI:10.12732/ijam.v27i2.9.


再生核研究所声明311（2016.07.05）　ゼロ0とは何だろうか

ここ２年半、ゼロで割ること、ゼロ除算を考えているが、ゼロそのものについてひとりでに湧いた想いがあるので、その想いを表現して置きたい。
数字のゼロとは、実数体あるいは複素数体におけるゼロであり、四則演算で、加法における単位元（基準元）で、和を考える場合、何にゼロを加えても変わらない元として定義される。積を考えて変わらない元が数字の１である：

Wikipedia:ウィキペディア：
初等代数学[編集]
数の 0 は最小の非負整数である。0 の後続の自然数は 1 であり、0 より前に自然数は存在しない。数 0 を自然数に含めることも含めないこともあるが、0 は整数であり、有理数であり、実数（あるいは代数的数、複素数）である。
数 0 は正でも負でもなく、素数でも合成数でも単数でもない。しかし、0は偶数である。
以下は数 0 を扱う上での初等的な決まりごとである。これらの決まりはxを任意の実数あるいは複素数として適用して構わないが、それ以外の場合については何も言及していないということについては理解されなければならない。
加法:x　+ 0 = 0 +x=x. つまり 0 は加法に関する単位元である。
減法:　x− 0 =x, 0 −x= −x.
乗法:x 0 = 0 ·x= 0.
除法:xが 0　でなければ0⁄x= 0 である。しかしx⁄0は、0 が乗法に関する逆元を持たないために、（従前の規則の帰結としては）定義されない（ゼロ除算を参照）。

実数の場合には、数直線で、複素数の場合には複素平面を考えて、すべての実数や複素数は直線や平面上の点で表現される。すなわち、座標系の導入である。
これらの座標系が無ければ、直線や平面はただ伸びたり、拡がったりする空間、位相的な点集合であると考えられるだろう。―　厳密に言えば、混沌、幻のようなものである。単に伸びたり、広がった空間にゼロ、原点を対応させるということは　位置の基準点を定めること　と考えられるだろう。基準点は直線や平面上の勝手な点にとれることに注意して置こう。原点だけでは、方向の概念がないから、方向の基準を勝手に決める必要がある。直線の場合には、直線は点で２つの部分に分けられるので、一方が正方向で、他が負方向である。平面の場合には、原点から出る勝手な半直線を基準、正方向として定めて、原点を回る方向を定めて、普通は時計の回りの反対方向を　正方向と定める。これで、直線や平面に方向の概念が導入されたが、さらに、距離（長さ）の単位を定めるため、原点から、正方向の点（これも勝手に指定できる）を１として定める。実数の場合にも複素数の場合にも数字の１をその点で表す。以上で、位置、方向、距離の概念が導入されたので、あとはそれらを基礎に数直線や複素平面（座標）を考える、すなわち、直線と実数、平面と複素数を１対１に対応させる。これで、実数も複素数も秩序づけられ、明瞭に表現されたと言える。ゼロとは何だろうか、それは基準の位置を定めることと発想できるだろう。
―　国家とは何だろうか。国家意思を定める権力機構を定め、国家を動かす基本的な秩序を定めることであると原理を述べることができるだろう。
数直線や複素平面では　基準点、０と１が存在する。これから数学を展開する原理を下記で述べている：

しかしながら、数学について、そもそも数学とは何だろうかと問い、ユニバースと数学の関係に思いを致すのは大事ではないだろうか。この本質論については幸運にも相当に力を入れて書いたものがある：

No.81, May 2012(pdf 432kb)
19/03/2012
ここでは、数学とは何かについて考えながら、数学と人間に絡む問題などについて、幅.広く面白く触れたい。

複素平面ではさらに大事な点として、純虚数i　が存在するが、ゼロ除算の発見で、最近、明確に認識された意外な点は、実数の場合にも、複素数の場合にも、ゼロに対応する点が存在するという発見である。ゼロに対応する点とは何だろうか？
直線や平面で実数や複素数で表されない点が存在するであろうか？　無理して探せば、いずれの場合にも、原点から無限に遠ざかった先が気になるのではないだろうか？　そうである立体射影した場合における無限遠点が正しくゼロに対応する点ではないかと発想するだろう。その美しい点は無限遠点としてその美しさと自然さ故に１００年を超えて数学界の定説として揺るぐことはなかった。ゼロに対応する点は無限遠点で、1/0=∞　と考えられてきた。オイラー、アーベル、リーマンの流れである。
ところが、ゼロ除算は1/0=0　で、実は無限遠点はゼロに対応していることが確認された。
直線を原点から、どこまでも　どこまでも遠ざかって行くと、どこまでも行くが、その先まで行くと（無限遠点）突然、ゼロに戻ることを示している。これが数学であり、我々の空間であると考えられる。この発見で、我々の数学の結構な部分が修正、補充されることが分かりつつある。
ゼロ除算は可能であり、我々の空間の認識を変える必要がある。ゼロで割る多くの公式である意味のある世界が広がってきた。それらが　幾何学、解析学、代数学などと調和して数学が一層美しい世界であることが分かってきた。

全ての直線はある意味で、原点、基準点を通ることが示されるが、これは無限遠点の影が投影されていると解釈され、原点はこの意味で２重性を有している、無限遠点と原点が重なっている現象を表している。この２重性は 基本的な指数関数y=e^x　が原点で、0 と1　の２つの値をとると表現される。このことは、今後大きな意味を持ってくるだろう。

古来、ゼロと無限の関係は何か通じていると感じられてきたが、その意味が、明らかになってきていると言える。

２点から無限に遠い点　無限遠点は異なり、無限遠点は基準点原点の指定で定まるとの認識は面白く、大事ではないだろうか。
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再生核研究所声明310（2016.06.29）　ゼロ除算の自明さについて

人間の感性の観点から、ゼロ除算の自明さについて触れて置きたい。ゼロ除算の発見は誠に奇妙な事件である。まずは、近似の方法から自然に導かれた結果であるが、結果が全然予想されたことのない、とんでもないことであったので、これは何だと衝撃を受け、相当にその衝撃は続いた。まずは、数学的な論理に間違いがないか、厳重に点検を行い、それでも信じられなかったので、多くの友人、知人に意見を求めた。高橋眞映山形大学名誉教授のゼロ除算の一意性定理は大事だったので、特に厳重に検討した。多くの友人も厳重に時間をかけて検討した経過がよく思い出される。その他、いろいろな導入が発見されても、信じられない心境は１年を超えて続いたと言える。数学的に厳格に、論理的に確立しても　心情的に受け入れられない感情　が永く続いた。そのような心境を相当な人たちが抱いたことが国際的な交流でも良く分かる。中々受け入れらない、ゼロ除算の結果はそうだと受け入れられない、認められない空気であった。ゼロ除算の発展は世界史上の事件であるから、経過など出来るだけ記録するように努めてきた。
要するに、世界中の教科書、学術書、定説と全く違う結果が　世に現れたのである。慎重に、慎重に畏れを抱いて研究を進めたのは　当然である。
そこで、証拠のような具体例の発見に努めた。明確な確信を抱くために沢山の例を発見することとした。最初の２，３件の発見が特に難しかった。内容は次の論文に、招待され、出版された：　http://www.ijapm.org/show-63-504-1.html　：
ゼロ除算を含む、山田体の発見、
原点の鏡像が（原点に中心をもつ円に関する）無限遠点でなく　ゼロであること、
x,y直角座標系で　y軸の勾配がゼロであること、
同軸２輪回転からの、ゼロ除算の物理的な意味付け、

これらの成果を日本数学会代数学分科会で発表し、また、ゼロ除算の解説(2015.1.14)を１０００部印刷広く配布してきた。２年間の時間の経過とともに我々の数学として、実在感が確立してきた。その後、広範にゼロ除算がいろいろなところに現れていることが沢山発見され、やがて、ゼロ除算は自明であり数学の初歩的な欠落部分であるとの確信を深めるようになってきている。
単に数学の理論だけでなく、いろいろな具体例が認識の有り様を、感性を変えることが分かる。そこで、何もかも分かったという心境に至るには、素朴な具体例で、何もかも当たり前であるという心理状況に至ることが大事であるが、それは、環境で心自体が変わる様をしめしている。本来１つの論文であった原稿は　招待されたため次の２つの論文に出版される：
(2016) Matrices and Division by Zero z/0 = 0. Advances in Linear Algebra
& Matrix Theory, 6, 51-58. 
http://www.scirp.org/journal/alamt　 　http://dx.doi.org/10.4236/alamt.2016.62007
Division by Zero z/0 = 0 in Euclidean Spaces：
International Journal of Mathematics and Computation 9 Vol. 28; Issue 1, 2017)。

沢山の具体例が述べられていて、ゼロ除算が基本的な数学であることは、既に確立していると考えられる。沢山の具体例が、そのような心境に至らしめている。
ゼロ除算の自明さを論理ではなく、簡単に　直感的な説明として述べたい。
基本的な関数y=1/xを考え、そのグラフを見よう。原点の値は考えないとしているが、考えるとすれば、値は何だろうか？　ゼロではないか　と　思えば、ゼロ除算は正解である。それで十分である。その定義から、応用や意味付けを検討すれば良い。―　誰でも値は　ゼロであると考えるのではないだろうか。中心だから、真ん中だから。あるいは平均値だからと考えるのではないだろうか。それで良い。
0/0=0　には違う説明が必要である。条件付き確率を考えよう。　A　が起きたという条件の下で、B　が起きる条件付き確率を考えよう。　その確率P(B|A)　は　AとBの共通事象ABの確率P(AB) と　A　が起きる確率P(A)との比　P(B|A)＝P(AB)/P(A) で与えられる。もし、Aが起きなければ、すなわち、P(A)　=0　ならば、もちろん、P(AB) =0.　意味を考えても分かるようにその時当然、P(B|A) =0である。 すなわち、0/0=0は　当たり前である。

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