数字の「無」
ゼロは 数学の崩壊をもたらす
質量ゼロの光の粒子は 曲がる
空間の「無」
私たち自身も ほぼ真空だ
真空は 完全な無ではない
時空の「無」
宇宙は 時間も空間もない究極の無から生まれた
時間をさかのぼると 宇宙は一つの点に行き着く
数字の「無」
ゼロは 数学の崩壊をもたらす
質量ゼロの光の粒子は 曲がる
空間の「無」
私たち自身も ほぼ真空だ
真空は 完全な無ではない
時空の「無」
宇宙は 時間も空間もない究極の無から生まれた
時間をさかのぼると 宇宙は一つの点に行き着く
ニュートン式 超図解 最強に面白い!! 無
しかし科学者たちは、そうは考えない。実際の無は、実にダイナミックでエキサイティングだ。たとえば、空間から物質などをすべて取り除いて、完ぺきな「無」の空間をつくったとしても、そこには無数の粒子がひとりでにわきたっているという。また、時間も空間さえも存在しない「無」から、宇宙が生まれるという仮説も提案されている。無は現代の物理学にとって重要な要素であり、無のすべてを知る者は、すべてを知りつくすといわれるほどだ。
本書では無を、数字、空間、時空の三つの観点から、“最強に”面白く紹介する。
≪目次≫
ーーー
イントロダクション
古代から研究されてきた「無」
三つの「無」から世界の本当の姿がわかる
コラム 漢字の「無」の由来
1.数字の「無」の誕生
ゼロは長らく,数とみなされなかった
ゼロは,数学の崩壊をもたらす
コラム 博士! 教えて!! 1÷0の答えは?
コラム 無洗米の「無」
古代人は,ゼロを単なる記号として使った
数としてのゼロが,インドで生まれた
コラム ローマ数字は3999まで
コラム テニスの0点は,なぜラブ?
2.自然界に登場する「無」の数
温度には,絶対0度という下限がある!
リニアモーターカーは,電気抵抗ゼロの超電導で走る
液体の粘り気がゼロになる! ふしぎな超流動現象
質量ゼロの光の粒子は,重力の影響を受ける
コラム 糖類ゼロってどういうこと?
ブラックホールは,大きさゼロに向かって縮んでいる
ブラックホールの近くでは,速度がゼロに見える
コラム 実在する!? ホワイトホール
4コマ ブラックホールとオッペンハイマー
4コマ 原子爆弾の開発
3.空間の「無」の発見
アリストテレスは, 空っぽの「真空」の存在を否定した
17世紀のトリチェリが,真空をつくりだした
蛍光灯の中は,ほどよい真空に保たれている
宇宙空間は,本当の真空ではない
私たちの目の前には,真空が存在している!
私たち自身も,ほぼ真空だった
コラム 博士! 教えて!! 真空はどこまで実現できる?
4コマ トリチェリの問題
4コマ ガリレオの弟子
4.「無」の空間には何かが満ちている
真空は,完全な無ではない!
真空でも,磁石のNとSは引き合う
宇宙空間には,光が満ちている
光は,真空中の「場」をゆらして伝わる
真空を埋めつくす何かが,素粒子にまとわりつく
ヒッグス場の存在が,実験でたしかめられた
コラム 宇宙で生身だと,体は破裂する?
真空では,素粒子が生まれては消える
陽子の中は,混み合った真空状態だった
からっぽの無の空間も,曲がったり,波打ったりする
普通の物質をとりのぞいても,ダークマターが残る
真空には,宇宙を膨張させるエネルギーが満ちている
真空の正体の解明が,物理学の課題
コラム 博士! 教えて!! 素粒子の大きさはどのくらい?
5.時空の「無」が宇宙を生んだ
宇宙は,時間も空間もない究極の無から生まれた
時間をさかのぼると,宇宙は一つの点に行き着く
宇宙の卵は,生成と消滅をくりかえしたのかもしれない
宇宙は,エネルギーの山をすりぬけて急膨張した
大きさゼロの宇宙の卵が,私たちの宇宙になった
コラム 博士! 教えて!! 宇宙の膨張はなぜわかったの?
誕生直後の宇宙に,虚数時間が流れていたのかもしれない
虚数時間で,エネルギーの山は谷になる
生まれ変わる宇宙は,無からはじまったのか?
時空の無を考えない宇宙誕生のシナリオもある
4コマ ビレンキン苦難の道のり
4コマ 無からの宇宙創生論を発表
Nothing 無
Wikipedia
https://en.wikipedia.org/wiki/Nothing
Nothing, no-thing, or no thing, is the complete absence of anything as the opposite of something and an antithesis of everything. The concept of nothing has been a matter of philosophical debate since at least the 5th century BC. Early Greek philosophers argued that it was impossible for nothing to exist. The atomists allowed nothing but only in the spaces between the invisibly small atoms. For them, all space was filled with atoms. Aristotle took the view that there exists matter and there exists space, a receptacle into which matter objects can be placed. This became the paradigm for classical scientists of the modern age like Newton. Nevertheless, some philosophers, like Descartes, continued to argue against the existence of empty space until the scientific discovery of a physical vacuum.
Existentialists like Sartre and Heidegger (as interpreted by Sartre) have associated nothing with consciousness. Some writers have made connections between Heidegger’s concept of nothing and the nirvana of Eastern religions.
Modern science does not equate vacuum with nothing. The vacuum in quantum field theory is filled with virtual particles. The quantum vacuum is often viewed as a modern version of an aether theory.
Philosophy
Western
Some would consider the study of “nothing” to be absurd. A typical response of this type is voiced by the Venetian Giacomo Casanova (1725–1798) in conversation with his landlord, one Dr. Gozzi, who also happens to be a priest:
“Nothingness” has been treated as a serious subject for a very long time. In philosophy, to avoid linguistic traps over the meaning of “nothing”, a phrase such as not-being is often employed to make clear what is being discussed.
Parmenides
One of the earliest Western philosophers to consider nothing as a concept was Parmenides (5th century BC), a Greek philosopher of the monist school. He argued that “nothing” cannot exist by the following line of reasoning: To speak of a thing, one has to speak of a thing that exists. If one can speak of a thing in the past, this thing must still exist (in some sense) now, and from this he concluded that there is no such thing as change. As a corollary, there can be no such things as coming-into-being, passing-out-of-being, or not-being.
Other philosophers, for instance, Socrates and Plato largely agreed with Parmenides’s reasoning on nothing. Aristotle differs with Parmenides’s conception of nothing and says, “Although these opinions seem to follow logically in a dialectical discussion, yet to believe them seems next door to madness when one considers the facts.”
In modern times, Albert Einstein‘s concept of spacetime has led many scientists, including Einstein himself, to adopt a position remarkably similar to Parmenides. On the death of his friend Michele Besso, Einstein consoled his widow with the words, “Now he has departed from this strange world a little ahead of me. That signifies nothing. For those of us that believe in physics, the distinction between past, present and future is only a stubbornly persistent illusion.”
Leucippus
Leucippus (early 5th century BC), one of the atomists, along with other philosophers of his time, made attempts to reconcile this monism with the everyday observation of motion and change. He accepted the monist position that there could be no motion without a void. The void is the opposite of being. It is not-being. On the other hand, there exists something known as an absolute plenum, a space filled with matter, and there can be no motion in a plenum because it is completely full. But, there is not just one monolithic plenum, for existence consists of a multiplicity of plenums. These are the invisibly small “atoms” of Greek atomist theory, later expanded by Democritus (c. 460–370 BC), which allows the void to “exist” between them. In this scenario, macroscopic objects can come-into-being, move through space, and pass into not-being by means of the coming together and moving apart of their constituent atoms. The void must exist to allow this to happen, or else the “frozen world” of Parmenides must be accepted.
Bertrand Russell points out that this does not exactly defeat the argument of Parmenides but, rather, ignores it by taking the rather modern scientific position of starting with the observed data (motion, etc.) and constructing a theory based on the data, as opposed to Parmenides’ attempts to work from pure logic. Russell also observes that both sides were mistaken in believing that there can be no motion in a plenum, but arguably motion cannot start in a plenum. Cyril Bailey notes that Leucippus is the first to say that a “thing” (the void) might be real without being a body and points out the irony that this comes from a materialistic atomist. Leucippus is therefore the first to say that “nothing” has a reality attached to it.
Aristotle, Newton, Descartes
Aristotle (384–322 BC) provided the classic escape from the logical problem posed by Parmenides by distinguishing things that are matter and things that are space. In this scenario, space is not “nothing” but, rather, a receptacle in which objects of matter can be placed. The true void (as “nothing”) is different from “space” and is removed from consideration. This characterization of space reached its pinnacle with Isaac Newton who asserted the existence of absolute space. René Descartes, on the other hand, returned to a Parmenides-like argument of denying the existence of space. For Descartes, there was matter, and there was extension of matter leaving no room for the existence of “nothing”.
The idea that space can actually be empty was generally still not accepted by philosophers who invoked arguments similar to the plenum reasoning. Although Descartes’ views on this were challenged by Blaise Pascal, he declined to overturn the traditional belief, horror vacui, commonly stated as “nature abhors a vacuum”. This remained so until Evangelista Torricelli invented the barometer in 1643 and showed that an empty space appeared if the mercury tube was turned upside down. This phenomenon being known as the Torricelli vacuum and the unit of vacuum pressure, the torr, being named after him. Even Torricelli’s teacher, Galileo Galilei, had previously been unable to adequately explain the sucking action of a pump.
John the Scot
John the Scot, or Johannes Scotus Eriugena (c. 815–877) held many surprisingly heretical beliefs for the time he lived in for which no action appears ever to have been taken against him. His ideas mostly stem from, or are based on his work of translating pseudo-Dionysius. His beliefs are essentially pantheist and he classifies evil, amongst many other things, into not-being. This is done on the grounds that evil is the opposite of good, a quality of God, but God can have no opposite, since God is everything in the pantheist view of the world. Similarly, the idea that God created the world out of “nothing” is to be interpreted as meaning that the “nothing” here is synonymous with God.
G. W. F. Hegel
Georg Wilhelm Friedrich Hegel (1770–1831) is the philosopher who brought the dialectical method to a new pinnacle of development. According to Hegel in Science of Logic, the dialectical methods consists of three steps. First, a thesis is given, which can be any proposition in logic. Second, the antithesis of the thesis is formed and, finally, a synthesis incorporating both thesis and antithesis. Hegel believed that no proposition taken by itself can be completely true. Only the whole can be true, and the dialectical synthesis was the means by which the whole could be examined in relation to a specific proposition. Truth consists of the whole process. Separating out thesis, antithesis, or synthesis as a stand-alone statement results in something that is in some way or other untrue. The concept of “nothing” arises in Hegel right at the beginning of his Logic. The whole is called by Hegel the “Absolute” and is to be viewed as something spiritual. Hegel then has:
Existentialists
The most prominent figure among the existentialists is Jean-Paul Sartre, whose ideas in his book Being and Nothingness (L’être et le néant) are heavily influenced by Being and Time (Sein und Zeit) of Martin Heidegger, although Heidegger later stated that he was misunderstood by Sartre. Sartre defines two kinds of “being” (être). One kind is être-en-soi, the brute existence of things such as a tree. The other kind is être-pour-soi which is consciousness. Sartre claims that this second kind of being is “nothing” since consciousness cannot be an object of consciousness and can possess no essence. Sartre, and even more so, Jaques Lacan, use this conception of nothing as the foundation of their atheist philosophy. Equating nothingness with being leads to creation from nothing and hence God is no longer needed for there to be existence.
Eastern
The understanding of “nothing” varies widely between cultures, especially between Western and Eastern cultures and philosophical traditions. For instance, Śūnyatā (emptiness), unlike “nothingness”, is considered to be a state of mind in some forms of Buddhism (see Nirvana, mu, and Bodhi). Achieving “nothing” as a state of mind in this tradition allows one to be totally focused on a thought or activity at a level of intensity that they would not be able to achieve if they were consciously thinking. A classic example of this is an archer attempting to erase the mind and clear the thoughts to better focus on the shot. Some authors have pointed to similarities between the Buddhist conception of nothingness and the ideas of Martin Heidegger and existentialists like Sartre, although this connection has not been explicitly made by the philosophers themselves.
In some Eastern philosophies, the concept of “nothingness” is characterized by an egoless state of being in which one fully realizes one’s own small part in the cosmos.
The Kyoto School handles the concept of nothingness as well.
Taoism
Laozi and Zhuangzi were both conscious that language is powerless in the face of the ultimate. In Taoist philosophy, however real this world is, its main characteristic is impermanence, whereas the Tao has a permanence that cannot be described, predetermined, or named. In this way the Tao is different from any thing that can be named. It is nonexistence, in other words, nothing.
Taoists also have the related concept of wu wei.
Science
Despite the proven existence of vacuum, scientists through the 17th to 19th centuries thought there must be a medium pervading all space that allowed the transmission of light or gravity. Thus, in this period, it was not accepted that complete nothing was possible. Theories describing such a medium are collectively known as aether theories, so named as an evocation of the aether, the classical element from Greek philosophy. In particular, the medium that is supposed to allow the transmission of light is called the luminiferous aether. This became the centre of attention after James Clerk Maxwell proposed that light was an electromagnetic wave in 1865.
Early aether theories include those of Robert Hooke (1665) and Christiaan Huygens (1690). Newton also had an aether theory, but to Newton, it was not the medium of transmission since he theorised light was composed of “corpuscles” which moved by simple mechanical motion. He needed the aether instead to explain refraction. Early theories generally proposed a mechanical medium of some sort, allowing the possibility of the same medium supporting both light and gravity. Proof that light has a wave nature, rather than Newton’s corpuscles, was provided by Thomas Young in his 1803 interference experiment, seemingly confirming the need for an aether. The most well known attempt to detect the existence of the aether was conducted by Albert A. Michelson in an experiment of 1881, later repeated with Edward W. Morley in 1887 with more precision. This failed to show the desired effect, but reluctant to abandon the aether theory, various attempts were made to modify it to account for the Michelson-Morley result. Finally, Albert Einstein, building on the work of Hendrik Lorentz, published his theory of special relativity in 1905 which dispenses entirely with the need for a luminiferous aether to explain the transmission of light.
Although a physical medium was no longer required, the concept of aether still did not entirely vanish. It remained necessary to assign properties to the vacuum for various purposes. In some respects vacuum and aether are treated as synonyms by science. In modern quantum field theory, a completely empty vacuum is not at zero-point energy, the lowest possible energy state. First proposed by Paul Dirac in 1927, the lowest energy state has constant random vacuum fluctuations which bring into existence short-lived virtual particles. This is somewhat reminiscent of early philosophical plenum ideas, and means that vacuum and nothing are certainly not synonyms.
Emptiness 空
Wikipedia
https://en.wikipedia.org/wiki/Emptiness
Emptiness as a human condition is a sense of generalized boredom, social alienation, nihilism and apathy. Feelings of emptiness often accompany dysthymia, depression, loneliness, anhedonia, despair, or other mental/emotional disorders, including schizoid personality disorder, post-traumatic stress disorder, attention deficit hyperactivity disorder, schizotypal personality disorder and borderline personality disorder. A sense of emptiness is also part of a natural process of grief, as resulting death of a loved one, or other significant changes. The particular meanings of “emptiness” vary with the particular context and the religious or cultural tradition in which it is used.
While Christianity and Western sociologists and psychologists view a state of emptiness as a negative, unwanted condition, in some Eastern philosophies such as Buddhist philosophy and Taoism, emptiness (Śūnyatā) represents seeing through the illusion of independent self-nature.
In Western culture
Sociology, philosophy, and psychology
In the West, feeling “empty” is often viewed as a negative condition. Psychologist Clive Hazell, for example, attributes feelings of emptiness to problematic family backgrounds with abusive relationships and mistreatment. He claims that some people who are facing a sense of emptiness try to resolve their painful feelings by becoming addicted to a drug or obsessive activity (be it compulsive sex, gambling or work) or engaging in “frenzied action” or violence. In sociology, a sense of emptiness is associated with social alienation of the individual. This sense of alienation may be suppressed while working, due to the routine nature of work tasks, but during leisure hours or during the weekend, people may feel a sense of “existential vacuum” and emptiness.
In political philosophy, emptiness is associated with nihilism. Literary critic Georg Lukács (born in 1885) argued against the “spiritual emptiness and moral inadequacy of capitalism”, and argued in favour of communism as an “entirely new type of civilization, one that promised a fresh start and an opportunity to lead a meaningful and purposeful life.”
The concept of “emptiness” was important to a “certain type of existentialist philosophy and some forms of the Death of God movement”. Existentialism, the “philosophic movement that gives voice to the sense of alienation and despair”, comes from “man’s recognition of his fundamental aloneness in an indifferent universe”. People whose response to the sense of emptiness and aloneness is to give excuses live in bad faith; “people who face the emptiness and accept responsibility aim to live ‘authentic’ lives”. Existentialists argue that “man lives in alienation from God, from nature, from other men, from his own true self.” Crowded into cities, working in mindless jobs, and entertained by light mass media, we “live on the surface of life”, so that even “people who seemingly have ‘everything’ feel empty, uneasy, discontented.”
In cultures where a sense of emptiness is seen as a negative psychological condition, it is often associated with depression. As such, many of the same treatments are proposed: psychotherapy, group therapy, or other types of counselling. As well, people who feel empty may be advised to keep busy and maintain a regular schedule of work and social activities. Other solutions which have been proposed to reduce a sense of emptiness are getting a pet or trying Animal-Assisted Therapy; getting involved in spirituality such as meditation or religious rituals and service; volunteering to fill time and bring social contact; doing social interactions, such as community activities, clubs, or outings; or finding a hobby or recreational activity to regain their interest in life.
Christianity
In Austria philosopher/educator Rudolf Steiner‘s (1861–1925) thinking, spiritual emptiness was a major problem in the educated European middle class. In his 1919 lectures he argued that European culture became “empty of spirit” and “ignorant of the needs, the conditions, that are essential for the life of the spirit”. People experienced a “spiritual emptiness” and their thinking became marked by a “lazy passivity” due to the “absence of will from the life of thought”. In modern Europe, Steiner claimed that people would “allow their thoughts to take possession of them”, and these thoughts were increasingly filled with abstraction and “pure, natural scientific thinking”. The educated middle classes began to think in a way that was “devoid of spirit”, with their minds becoming “dimmer and darker”, and increasing empty of spirit.
Louis Dupré, a professor of philosophy at Yale University, argues that the “spiritual emptiness of our time is a symptom of its religious poverty”. He claims that “many people never experience any emptiness: they are too busy to feel much absence of any kind”; they only realize their spiritual emptiness if “painful personal experiences — the death of a loved one, the collapse of a marriage, the alienation of a child, the failure of a business” shock them into reassessing their sense of meaning.
Spiritual emptiness has been associated with juvenile violence. In John C. Thomas’ 1999 book How Juvenile Violence Begins: Spiritual Emptiness, he argues that youth in impoverished indigenous communities who feel empty may turn to fighting and aggressive crime to fill their sense of meaninglessness. In Cornell University professor James Garbarino‘s 1999 book Lost Boys: Why Our Sons Turn Violent and How We Can Save Them, he argues that “neglect, shame, spiritual emptiness, alienation, anger and access to guns are a few of the elements common to violent boys”. A professor of human development, Garbarino claims that violent boys have an “alienation from positive role models” and “a spiritual emptiness that spawns despair”. These youth are seduced by the violent fantasy of the US gun culture, which provides negative role models of tough, aggressive men who use power to get what they want. He claims that boys can be helped by giving them “a sense of purpose” and “spiritual anchors” that can “anchor boys in empathy and socially engaged moral thinking”.
Spiritual emptiness is often connected with addiction, especially by Christian-influenced addiction organizations and counsellors. Bill Wilson, the founder of Alcoholics Anonymous, argued that one of the impacts of alcoholism was causing a spiritual emptiness in heavy drinkers. In Abraham J. Twerski’s 1997 book Addictive Thinking: Understanding Self-Deception, he argues that when people feel spiritually empty, they often turn to addictive behaviors to fill the inner void. In contrast to having an empty stomach, which is a clear feeling, having spiritual emptiness is hard to identify, so it fills humans with a “vague unrest”. While people may try to resolve this emptiness by obsessively having sex, overeating, or taking drugs or alcohol, these addictions only give temporary satisfaction. When a person facing a crisis due to feeling spiritually empty is able to stop one addiction, such as compulsive sex, they often just trade it in for another addictive behaviour, such as gambling or overeating.
Fiction, film, design and visual arts
A number of novelists and filmmakers have depicted emptiness. The concept of “emptiness” was important to a “good deal of 19th–20th century Western imaginative literature”. Novelist Franz Kafka depicted a meaningless bizarre world in The Trial and the existentialist French authors sketched a world cut off from purpose or reason in Jean-Paul Sartre‘s La Nausée and Albert Camus‘ L’étranger. Existentialism influenced 20th century poet T.S. Eliot, whose poem “The Love Song of J. Alfred Prufrock” describes an “anti-hero or alienated soul, running away from or confronting the emptiness of his or her existence”. Professor Gordon Bigelow argues that the existentialist theme of “spiritual barrenness is commonplace in literature of the 20th century”, which in addition to Eliot includes Ernest Hemingway, Faulkner, Steinbeck and Anderson.
Film adaptations of a number of existentialist novels capture the bleak sense of emptiness espoused by Sartre and Camus. This theme of emptiness has also been used in modern screenplays. Mark Romanek‘s 1985 film Static tells the surreal story of a struggling inventor and crucifix factory worker named Ernie who feels spiritually empty because he is saddened by his parents’ death in an accident. Screenwriter Michael Tolkin’s 1994 film The New Age examines “cultural hipness and spiritual emptiness”, creating a “dark, ambitious, unsettling” film that depicts a fashionable LA couple who “are miserable in the midst of their sterile plenty”, and whose souls are stunted by their lives of empty sex, consumption, and distractions. The 1999 film American Beauty examines the spiritual emptiness of life in the US suburbs. Wes Anderson‘s 2007 film The Darjeeling Limited is about three brothers who “suffer from spiritual emptiness” and then “self-medicate themselves through sex, social withdrawal, and drugs.” The 2008 film The Informers is a Hollywood drama film written by Bret Easton Ellis and Nicholas Jarecki and directed by Gregor Jordan. The film is based on Ellis’ 1994 collection of short stories of the same name. The film, which is set amidst the decadence of the early 1980s, depicts an assortment of socially alienated, mainly well-off characters who numb their sense of emptiness with casual sex, alcohol, and drugs.
Contemporary architecture critic Herbert Muschamp argues that “horror vacui” (which is Latin for “fear of emptiness”) is a key principle of design. He claims that it has become an obsessive quality that is the “driving force in contemporary American taste”. Muschamp states that “along with the commercial interests that exploit this interest, it is the major factor now shaping attitudes toward public spaces, urban spaces, and even suburban sprawl.”
Films that depict nothingness, shadows and vagueness, either in a visual sense or a moral sense are appreciated in genres such as film noir. As well, travellers and artists are often intrigued by and attracted to vast empty spaces, such as open deserts, barren wastelands or salt flats, and the open sea.
In visual arts emptiness and absence were recognized as phenomena that characterize not only particular works of art (e.g. Yves Klein) but also as a more general tendency within the history of modern art and aesthetics. Following Davor Džalto‘s argument on the modern concept of art, the gradual elimination of particular elements that traditionally characterized visual arts, which results in emptiness, is the most important phenomenon within the history and theory of art over the past two hundred years.
In Eastern cultures
Buddhism
Main article: ŚūnyatāThe Buddhist term emptiness (Skt. śūnyatā) refers specifically to the idea that everything is dependently originated, including the causes and conditions themselves, and even the principle of causality itself. It is not nihilism, nor is it meditating on nothingness. Instead, it refers to the absence (emptiness) of inherent existence. Buddhapalita says:
In an interview, the Dalai Lama stated that tantric meditation can be used for “heightening your own realization of emptiness or mind of enlightenment“. In Buddhist philosophy, attaining a realization of emptiness of inherent existence is key to the permanent cessation of suffering, i.e. liberation.
The Dalai Lama argues that tantric yoga trainees need to realize the emptiness of inherent existence before they can go on to the “highest yoga tantra initiation”; realizing the emptiness of inherent existence of the mind is the “fundamental innate mind of clear light, which is the subtlest level of the mind”, where all “energy and mental processes are withdrawn or dissolved”, so that all that appears to the mind is “pure emptiness”. As well, emptiness is “linked to the creative Void, meaning that it is a state of complete receptivity and perfect enlightenment”, the merging of the “ego with its own essence”, which Buddhists call the “clear light”.
In Ven. Thubten Chodron’s 2005 interview with Lama Zopa Rinpoche, the lama noted that “ordinary beings who haven’t realized emptiness don’t see things as similar to illusions”, and one does not “realize that things are merely labeled by mind and exist by mere name”. He argues that “when we meditate on emptiness, we drop an atom bomb on this [sense of a] truly existent I” and to realize that “what appears true…isn’t true”. By this, the lama is claiming that what is thought to be real—our thoughts and feelings about people and things—”exists by being merely labeled”. He argues that meditators who attain knowledge of a state of emptiness are able to realize that their thoughts are merely illusions from labelling by the mind.
Taoism
In Taoism, attaining a state of emptiness is viewed as a state of stillness and placidity which is the “mirror of the universe” and the “pure mind”.
Null (mathematics)
Wikipedia
https://en.wikipedia.org/wiki/Null_(mathematics)
In mathematics, the word null (from
‹See Tfd›German: null meaning “zero”, which is from Latin: nullus meaning “none”) is often associated with the concept of zero or the concept of nothing. It is used in varying context from “having zero members in a set” (e.g., null set) to “having a value of zero” (e.g., null vector).
In a vector space, the null vector is the neutral element of vector addition; depending on the context, a null vector may also be a vector mapped to some null by a function under consideration (such as a quadratic form coming with the vector space, see null vector, a linear mapping given as matrix product or dot product, a seminorm in a Minkowski space, etc.). In set theory, the empty set, that is, the set with zero elements, denoted “{}” or “∅”, may also be called null set. In measure theory, a null set is a (possibly nonempty) set with zero measure.
A null space of a mapping is the part of the domain that is mapped into the null element of the image (the inverse image of the null element). For example, in linear algebra, the null space of a linear mapping, also known as kernel, is the set of vectors which map to the null vector under that mapping.
In statistics, a null hypothesis is a proposition that no effect or relationship exists between populations and phenomena. It is the hypothesis which is presumed true—unless statistical evidence indicates otherwise.
Null
ウィキペディア
https://ja.wikipedia.org/wiki/Null
Null（ヌル、ナル）は、何もない、という意味で、プログラミング言語などコンピュータ関係では、「何も示さないもの」を表すのに使われる。同様のものとして、PascalにおけるNil（ニル）、PythonにおけるNone（ナン）、VB.NETにおけるNothing（ナッシング）のように、他のキーワード（予約語）や識別子が使われることもある。
ドイツ語において Null は数値の0（ゼロ）を意味し、発音は /nʊl/ である。一方、英語において null は /nʌl/ と発音される。ドイツ語においても、数値の0と区別するために、本記事の意味の Null は英語風に /nʌl/ と発音される場合がある。
日本においては「ヌル」という発音が定着しているが、英語読みに近い「ナル」という発音で呼ばれる場合もある。例えば、JISのJIS X 3005-1:2014「データベース言語SQL 第1部：枠組(SQL/Framework)」（日本産業標準調査会、経済産業省）のP4には「ナル値 (Null Value)」、JIS X 3010:2003「プログラム言語C」（日本産業標準調査会、経済産業省）のP4には「ナル文字 (Null Character)」という記述がある。この他にも専門書や国家試験でも見られる。
プログラミング言語などにおいて、nullやnilといったキーワード（予約語）あるいは識別子（定数名）などの意味がどういったものかは言語による。場合によっては同じ言語であっても処理系の実装や言語バージョンごとに違うことさえある。ポインタや参照のある言語では、ヌルポインタまたはヌル参照などと呼ばれる何も指さない特別なポインタや参照であることもあるし、Pythonのようにオブジェクトのひとつであることもある。古典的なLISPのように真理値の偽（の代表）や空リスト「()」を兼ねたもの（それらと同じもの）だったりすることもある。
2024年10月18日（金）
数学の「無」、物理学の「無」
今週の書物/
『ニュートン式 超図解 最強に面白い!! 無』
和田純夫 監修
ニュートンプレス、2020年刊
「無」とか「空」とか「ゼロ」とかは、気にしだすと気になってしまう。「無」や「空」や「ゼロ」のことは、考えても仕方のないことで、考えても何の答えも出ない。
「無」と「空」と「ゼロ」は、時には同じ意味を持ち、時にはまったく違う意味を持つ。哲学の問題として考えているうちは楽しいが、仕事のなかに入ってくると その扱いは難しい。
昔、統計の仕事に関わったことがあって、その時の難題のひとつが「無」と「ゼロ」だった。まったく無い「ゼロ」、値が小さすぎて「ゼロとしか表示できない（Not zero, but less than half of the unit）」、マイナスの値が小さすぎて「ゼロとしか表示できない（Not zero, but negative and less than half of the unit）」、その他にも「該当しない（not applicable）」とか「入手不可能（not available）」なんていうのもあって、いろいろ苦労したのをよく覚えている。
数学で「ゼロ（0）」は特別だ。0 は最小の非負整数で、0 の後続の自然数は 1。0 より前に自然数は存在しない。0 が自然数なのかどうかは わからないが、0 は整数で、有理数で、実数で、複素数で、いやそんなことよりも、割れなかったり 特異点だったり、とにかく特別だ。
で今週は、数学や物理学においての「無」について書かれた一冊を読む。『ニュートン式 超図解 最強に面白い!! 無』（和田純夫 監修、ニュートンプレス、2020年刊）だ。科学雑誌の Newton（ニュートン）を出している ニュートンプレス が発行元で、監修者の名前は書いてあっても、著者の名前は書いてない。最後のページに見えないような小さな字で「Editotial Management 木村直之」「Editorial Staff 井手 亮」と書いてある。ニュートンプレス の社員が仕事の一環として書いただけで、社員は著者ではないと言いたいのだろうか。
まあそんなことはともかく、表紙に「数字の無ゼロから物理の無まで 無がわかる決定版!!」と書いてある通り、数学や物理の分野にしぼって「無」のことを解説している興味深い本ではある。
説明はやや乱暴だ。原子の動きがほぼとまったときが「絶対 0度」という温度の下限。電気抵抗がゼロ（無）の「超電導」でリニアモーターカーが走る。液体の粘り気がゼロになり 力を加えなくても スルリと通り抜ける「超流動現象」。質量ゼロの「光子」は 重力の影響を受けて 曲がる。大きさゼロに向かって縮んでいる「ブラックホール」は宇宙に 無数 存在していて、その近くでは速度がゼロに見える。そんなことが、自然界にある「無」の例として挙げられる。
また、「無」の空間には 何かが満ちているといって、「真空は 完全な無ではない」「宇宙空間は 私たちに見えない光で 満ちている」「光は 物質ではなく 真空の場をゆらして伝わる」「真空を埋めつくす何かが 素粒子にまとわりつく」「真空では 素粒子が生まれては消える」「陽子のなかは 混み合った真空状態」「陽子のなかは ほとんどからっぽ」「陽子のなかでは たくさんの仮想粒子が生じている」「からっぽの無の空間も 曲がったり 波打ったりする」「重力の正体は 時空のゆがみ」「無の空間でも 実態をもつ」「普通の物質をとりのぞいてもダークマターが残る」「ダークマターは 見ることができない」「真空には 宇宙を膨張させるエネルギーが満ちている」なんていうことを、次から次へと書き連ねる。
どのページを読んでも「そうなのかなあ」「そうとは思えないけど」「でも そうなんだろうなあ」というような よくわからない感想しか 持つことができない。それはまるで「この世は神が作り出した」とか「輪廻転生」といった話を聞いた時の感想だ。数学や物理学においての「無」についての本といいながら、アプローチは宗教そのものではないか。
最後の章の≪時空の「無」が宇宙を生んだ≫になると、宗教っぽさはより激しさを増す。「宇宙は 時間も空間もない 究極の無から生まれた」「時間をさかのぼると 宇宙空間は 特異点という 一つの点になってしまう」「10>-20以下の短い時間では 物質が ある ない という存在自体も定まらなくなる」「宇宙が 10-33cm よりも小さいときには 宇宙の存在自体がゆらいでいて 生成と消滅をくりかえしていた」というような説明は、にわかには受け入れられない。
「トンネル効果」の説明を読み、「小さな宇宙は 非常に高いエネルギーをもっている」「誕生直後の宇宙には 虚数時間が流れていた」「3次元空間の宇宙は 高次元空間に浮かぶ膜」というような 怪しい話 に付き合わされているうちに、我慢の限度を超え、私はこの本に対して敵愾心を抱く。
なんという本を読んでしまったのだろうという後悔と、物理学者の方々への憐憫の情とで、いっぱいになる。こんな荒唐無稽な理論を、ひとつひとつ「それは違う」といって否定していくのは、人生の無駄ではないか。この本を読んで、そんなことを考えた。本のなかの一つ一つの話は面白い。でも、この本を読んでも、無はわからない。少なくとも私には、物理の無はわからない。
優秀な人たちが物理学の分野に集まり、CERN (Conseil européen pour la recherche nucléaire, 欧州原子核研究機構) や ALMA (Atacama Large Millimeter/submillimeter Array, アタカマ大型ミリ波サブミリ波干渉計) といった巨大研究施設が作られるようになると、物理学の知識の集積は膨大な量になる。
物理学の領域があまりにも大きく広がり、複雑になりすぎて、もう誰にも全体を把握することができない。理論物理学の考察を行なうために習得しなければならない数学的手法や既存の物理理論も膨大な量になり、メインストリームの理論をすべて理解している人など、ひとりもいない。
メインストリームの理論のなかでも、標準モデル（Standard Model）、量子複雑性理論（Quantum complexity theory）、量子色力学（Quantum chromodynamics）、物理宇宙論（Physical cosmology）、曲がった時空における量子場の理論（Quantum field theory in curved spacetime）といった分野では、日々定説が覆されている。
標準モデルひとつとっても、標準モデルは一般相対性理論と矛盾していて、ある条件下（例えば、ビッグバンのような既知の時空特異点や事象の地平線を越えたブラックホールの中心など）では、一方または両方の理論が破綻してしまう。多くの研究者たちがこの問題を解決したと言ってきたが、いまだにコンセンサスは得られていない。
あたりまえのことだが、物理学には 強い CP 問題（strong CP problem）、ニュートリノ質量（neutrino mass）、物質と反物質の非対称性（matter–antimatter asymmetry）、暗黒物質と暗黒エネルギーの性質（nature of dark matter and dark energy）など、わかっていないことが数多くある。
今回 取り上げた本は、数多くの わかっていないことについて、まるで わかったことのように書いている。いくら 門外漢のための本だからといって、というか門外漢のための本だからこそ、わからないことは いまだにわかっていないと 書くべきではないか。
わかっていないことについて考え 探求するのが物理だとするならば、いや 科学だとするならば、この本は科学的ではない。まるで受験参考書のように、答えはこれだよというような本の作りは、教育的ではあっても科学的ではない。もっとも、今の日本人が望んでいるのが この本のようなものだと言われれば、返す言葉はない。
断定的なものの言い方や、短絡的に答えを求めようとする態度が、社会を覆っている。考えることが嫌われる社会に、明日はない。
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