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Andrei Tarkovsky | 676 | Cinematic style | Tarkovsky developed a theory of cinema that he called "sculpting in time". By this he meant that the unique characteristic of cinema as a medium was to take our experience of time and alter it. Unedited movie footage transcribes time in real time. By using long takes and few cuts in his films, he aimed to give the viewers a sense of time passing, time lost, and the relationship of one moment in time to another. |
Andrei Tarkovsky | 676 | Cinematic style | Up to, and including, his film Mirror, Tarkovsky focused his cinematic works on exploring this theory. After Mirror, he announced that he would focus his work on exploring the dramatic unities proposed by Aristotle: a concentrated action, happening in one place, within the span of a single day. |
Andrei Tarkovsky | 676 | Cinematic style | Several of Tarkovsky's films have color or black-and-white sequences. This first occurs in the otherwise monochrome Andrei Rublev, which features a color epilogue of Rublev's authentic religious icon paintings. All of his films afterwards contain monochrome, and in Stalker's case sepia sequences, while otherwise being in color. In 1966, in an interview conducted shortly after finishing Andrei Rublev, Tarkovsky dismissed color film as a "commercial gimmick" and cast doubt on the idea that contemporary films meaningfully use color. He claimed that in everyday life one does not consciously notice colors most of the time, and that color should therefore be used in film mainly to emphasize certain moments, but not all the time, as this distracts the viewer. To him, films in color were like moving paintings or photographs, which are too beautiful to be a realistic depiction of life. |
Andrei Tarkovsky | 676 | Cinematic style | Director Ingmar Bergman commented on Tarkovsky: |
Andrei Tarkovsky | 676 | Cinematic style | My discovery of Tarkovsky's first film was like a miracle. Suddenly, I found myself standing at the door of a room the keys of which had until then, never been given to me. It was a room I had always wanted to enter and where he was moving freely and fully at ease. I felt encountered and stimulated: someone was expressing what I had always wanted to say without knowing how. Tarkovsky is for me the greatest, the one who invented a new language, true to the nature of film, as it captures life as a reflection, life as a dream |
Andrei Tarkovsky | 676 | Cinematic style | Contrarily, however, Bergman conceded the truth in the claim made by a critic who wrote that "with Autumn Sonata Bergman does Bergman", adding: "Tarkovsky began to make Tarkovsky films, and that Fellini began to make Fellini films [...] Buñuel nearly always made Buñuel films." This pastiche of one's own work has been derogatorily termed as "self-karaoke". |
Andrei Tarkovsky | 676 | Cinematic style | Tarkovsky worked in close collaboration with cinematographer Vadim Yusov from 1958 to 1972, and much of the visual style of Tarkovsky's films can be attributed to this collaboration. Tarkovsky would spend two days preparing for Yusov to film a single long take, and due to the preparation, usually only a single take was needed. |
Andrei Tarkovsky | 676 | Cinematic style | In his last film, The Sacrifice, Tarkovsky worked with cinematographer Sven Nykvist, who had worked on many films with director Ingmar Bergman. (Nykvist was not alone: several people involved in the production had previously collaborated with Bergman, notably lead actor Erland Josephson, who had also acted for Tarkovsky in Nostalghia.) Nykvist complained that Tarkovsky would frequently look through the camera and even direct actors through it, but ultimately stated that choosing to work with Tarkovsky was one of the best choices he had ever made. |
Andrei Tarkovsky | 676 | Filmography | Tarkovsky is mainly known as a film director. During his career he directed seven feature films, as well as three shorts from his time at VGIK. His features are: |
Andrei Tarkovsky | 676 | Filmography | He also wrote several screenplays. Furthermore, he directed the play Hamlet for the stage in Moscow, directed the opera Boris Godunov in London, and he directed a radio production of the short story Turnabout by William Faulkner. He also wrote Sculpting in Time, a book on film theory. |
Andrei Tarkovsky | 676 | Filmography | Tarkovsky's first feature film was Ivan's Childhood in 1962. He then directed Andrei Rublev in 1966, Solaris in 1972, Mirror in 1975 and Stalker in 1979. The documentary Voyage in Time was produced in Italy in 1982, as was Nostalghia in 1983. His last film The Sacrifice was produced in Sweden in 1986. Tarkovsky was personally involved in writing the screenplays for all his films, sometimes with a cowriter. Tarkovsky once said that a director who realizes somebody else's screenplay without being involved in it becomes a mere illustrator, resulting in dead and monotonous films. |
Andrei Tarkovsky | 676 | Unproduced screenplays | Concentrate (Концентрат, Kontsentrat) is a never-filmed 1958 screenplay by Tarkovsky. The screenplay is based on Tarkovsky's year in the taiga as a member of a research expedition, prior to his enrollment in film school. It's about the leader of a geological expedition, who waits for the boat that brings back the concentrates collected by the expedition. The expedition is surrounded by mystery, and its purpose is a state secret. |
Andrei Tarkovsky | 676 | Unproduced screenplays | Although some authors claim that the screenplay was filmed, according to Marina Tarkovskaya, Tarkovsky's sister (and wife of Aleksandr Gordon, a fellow student of Tarkovsky during his film school years) the screenplay was never filmed. Tarkovsky wrote the screenplay during his entrance examination at the State Institute of Cinematography (VGIK) in a single sitting. He earned the highest possible grade, "excellent" (отлично) for this work. In 1994, fragments of Concentrate were filmed and used in the documentary Andrei Tarkovsky's Taiga Summer by Marina Tarkovskaya and Aleksandr Gordon. |
Andrei Tarkovsky | 676 | Unproduced screenplays | Hoffmanniana (Гофманиана) is a never-filmed 1974 screenplay by Tarkovsky. The screenplay is based on the life and work of German author E. T. A. Hoffmann. In 1974, an acquaintance from Tallinnfilm approached Tarkovsky to write a screenplay on a German theme. Tarkovsky considered Thomas Mann and E. T. A. Hoffmann, and also thought about Ibsen's Peer Gynt. In the end Tarkovsky signed a contract for a script based on the life and work of Hoffmann. He planned to write the script during the summer of 1974 at his dacha. Writing was not without difficulty, less than a month before the deadline he had not written a single page. He finally finished the project in late 1974 and submitted the final script to Tallinnfilm in October. |
Andrei Tarkovsky | 676 | Unproduced screenplays | Although the script was well received by the officials at Tallinnfilm, it was the consensus that no one but Tarkovsky would be able to direct it. The script was sent to Goskino in February 1976, and although approval was granted for proceeding with making the film, the screenplay was never realized. In 1984, during the time of his exile in the West, Tarkovsky revisited the screenplay and made a few changes. He also considered to finally direct a film based on the screenplay but ultimately dropped this idea. |
Andrei Tarkovsky | 676 | Awards and commemoration | Numerous awards were bestowed on Tarkovsky throughout his lifetime. |
Andrei Tarkovsky | 676 | Awards and commemoration | Under the influence of Glasnost and Perestroika, Tarkovsky was finally recognized in the Soviet Union in the Autumn of 1986, shortly before his death, by a retrospective of his films in Moscow. After his death, an entire issue of the film magazine Iskusstvo Kino was devoted to Tarkovsky. In their obituaries, the film committee of the Council of Ministers of the Soviet Union and the Union of Soviet Film Makers expressed their sorrow that Tarkovsky had to spend the last years of his life in exile. |
Andrei Tarkovsky | 676 | Awards and commemoration | Posthumously, he was awarded the Lenin Prize in 1990, one of the highest state honors in the Soviet Union. In 1989, the Andrei Tarkovsky Memorial Prize was established, with its first recipient being the Russian animator Yuri Norstein. In three consecutive events, the Moscow International Film Festival awarded the Andrei Tarkovsky Award in 1993, 1995, and 1997. |
Andrei Tarkovsky | 676 | Awards and commemoration | In 1996, the Andrei Tarkovsky Museum opened in Yuryevets, his childhood town. A minor planet, 3345 Tarkovskij, discovered by Soviet astronomer Lyudmila Karachkina in 1982, has been named after him. |
Andrei Tarkovsky | 676 | Awards and commemoration | Tarkovsky has been the subject of several documentaries. Most notable is the 1988 documentary Moscow Elegy, by Russian film director Alexander Sokurov. Sokurov's own work has been heavily influenced by Tarkovsky. The film consists mostly of narration over stock footage from Tarkovsky's films. Directed by Andrei Tarkovsky is a 1988 documentary film by Michal Leszczylowski, an editor of the film The Sacrifice. Film director Chris Marker produced the television documentary One Day in the Life of Andrei Arsenevich as an homage to Andrei Tarkovsky in 2000. |
Andrei Tarkovsky | 676 | Awards and commemoration | At the entrance to the Gerasimov Institute of Cinematography in Moscow, there is a monument that includes statues of Tarkovsky, Gennady Shpalikov and Vasily Shukshin. |
Andrei Tarkovsky | 676 | Reception and legacy | Andrei Tarkovsky and his works have received praise from many filmmakers, critics and thinkers. |
Andrei Tarkovsky | 676 | Reception and legacy | The Swedish filmmaker Ingmar Bergman was quoted as saying: "Tarkovsky for me is the greatest [of us all], the one who invented a new language, true to the nature of film, as it captures life as a reflection, life as a dream". |
Andrei Tarkovsky | 676 | Reception and legacy | The Japanese filmmaker Akira Kurosawa remarked on Tarkovsky's films as saying: "His unusual sensitivity is both overwhelming and astounding. It almost reaches a pathological intensity. Probably there is no equal among film directors alive now." Kurosawa also commented: "I love all of Tarkovsky's films. I love his personality and all his works. Every cut from his films is a marvelous image in itself. But the finished image is nothing more than the imperfect accomplishment of his idea. His ideas are only realized in part. And he had to make do with it." |
Andrei Tarkovsky | 676 | Reception and legacy | The Iranian filmmaker Abbas Kiarostami remarked that: "Tarkovsky's works separate me completely from physical life, and are the most spiritual films I have seen". |
Andrei Tarkovsky | 676 | Reception and legacy | The Polish filmmaker Krzysztof Kieślowski commented that: "Andrei Tarkovsky was one of the greatest directors of recent years," and regarded Tarkovsky's film Ivan's Childhood as an influence on his own work. |
Andrei Tarkovsky | 676 | Reception and legacy | The Turkish filmmaker Nuri Bilge Ceylan said that when he first discovered the films of Andrei Tarkovsky as a college student, unsure of what he wanted to do with his life, he was utterly baffled by the lauded Russian master. He walked out of a screening of Solaris at the halfway point, and stopped a VHS tape of Mirror at a similar juncture. Today, he considers the latter to be the greatest film ever made. "I've seen it maybe 20 times," he says. |
Andrei Tarkovsky | 676 | Reception and legacy | The Armenian filmmaker Sergei Parajanov remarked that watching Tarkovsky's film, Ivan's Childhood was his main inspiration to become a filmmaker by saying: "I did not know how to do anything and I would not have done anything if there had not been Ivan's Childhood". |
Andrei Tarkovsky | 676 | Reception and legacy | The Austrian filmmaker Michael Haneke voted for Mirror on his top 10 films in the 2002 Sight & Sound directors' poll and later said that he has seen the picture at least 25 times. |
Andrei Tarkovsky | 676 | Reception and legacy | The German filmmaker Wim Wenders dedicated his film Wings of Desire to Tarkovsky (along with François Truffaut and Yasujirō Ozu). |
Andrei Tarkovsky | 676 | Reception and legacy | The French filmmaker Chris Marker directed a documentary film as a homage to Tarkovsky called One Day in the Life of Andrei Arsenevich and used Tarkovsky's concept of "The Zone" (from the film, Stalker) for his 1983 film essay, Sans Soleil. |
Andrei Tarkovsky | 676 | Reception and legacy | The Greek filmmaker Theo Angelopoulos regarded Tarkovsky's film Stalker as one of the films that influenced him. |
Andrei Tarkovsky | 676 | Reception and legacy | The Polish filmmaker Andrzej Żuławski remarked that: "If anybody influenced anybody, it’s me being influenced by Tarkovsky, not the reverse", and called Tarkovsky's film Andrei Rublev a "masterpiece". |
Andrei Tarkovsky | 676 | Reception and legacy | The Greek-Australian filmmaker Alex Proyas was "extremely influenced" by Tarkovsky's work and cited Stalker as one of his favorite films. |
Andrei Tarkovsky | 676 | Reception and legacy | The French philosopher Jean-Paul Sartre highly praised Tarkovsky's film Ivan's Childhood, saying that it was one of the most beautiful films he had ever seen. |
Andrei Tarkovsky | 676 | Reception and legacy | The Japanese anime filmmaker Mamoru Oshii, known for his works such as Ghost in the Shell, was influenced by Tarkovsky. |
Andrei Tarkovsky | 676 | Reception and legacy | The Indian-born British American novelist Salman Rushdie praised Tarkovsky and his work Solaris by calling it "a sci-fi masterpiece". |
Andrei Tarkovsky | 676 | Reception and legacy | Film historian Steven Dillon says that much of subsequent film was deeply influenced by the films of Tarkovsky. |
Andrei Tarkovsky | 676 | Reception and legacy | Mexican filmmaker Alejandro González Iñarritu is a huge fan of Tarkovsky. He once said in an interview: "Andrei Rublev is maybe my favorite film ever", and in another interview, he added: "I remember, the first time I saw a Tarkovsky film, I was shocked by it. I did not know what to do. I was shocked by it. I was fascinated, because suddenly I realized that film could have so many more layers to it than what I had imagined before". There are many direct references and hidden tributes to Tarkovsky's movies in Iñarritu's 2015 Oscar-winning drama The Revenant. |
Andrei Tarkovsky | 676 | Reception and legacy | Danish film director Lars von Trier is a fervent admirer of Tarkovsky. He dedicated his 2009 film Antichrist to him, and, while discussing it with critic David Jenkins, asked: "Have you seen Mirror? I was hypnotised! I've seen it 20 times. It's the closest thing I've got to a religion – to me he is a god". |
Andrei Tarkovsky | 676 | Reception and legacy | Two film festivals have been named in his honor: |
Andrei Tarkovsky | 676 | References | Notes |
Andrei Tarkovsky | 676 | References | Bibliography |
Ambiguity | 677 | Ambiguity is the type of meaning in which a phrase, statement, or resolution is not explicitly defined, making several interpretations, others describe it as a concept or statement that has no real reference. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved, according to a rule or process with a finite number of steps. (The prefix ambi- reflects the idea of "two", as in "two meanings".) |
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Ambiguity | 677 | The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity. |
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Ambiguity | 677 | Linguistic forms | Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning. This form of ambiguity is closely related to vagueness. |
Ambiguity | 677 | Linguistic forms | Ambiguity in human language is argued to reflect principles of efficient communication. Languages that communicate efficiently will avoid sending information that is redundant with information provided in the context. This can be shown mathematically to result in a system that is ambiguous when context is neglected. In this way, ambiguity is viewed as a generally useful feature of a linguistic system. |
Ambiguity | 677 | Linguistic forms | Linguistic ambiguity can be a problem in law, because the interpretation of written documents and oral agreements is often of paramount importance. |
Ambiguity | 677 | Linguistic forms | The lexical ambiguity of a word or phrase applies to it having more than one meaning in the language to which the word belongs. "Meaning" here refers to whatever should be represented by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "financial institution" and "edge of a river". Or consider "apothecary". One could say "I bought herbs from the apothecary". This could mean one actually spoke to the apothecary (pharmacist) or went to the apothecary (pharmacy). |
Ambiguity | 677 | Linguistic forms | The context in which an ambiguous word is used often makes it clearer which of the meanings is intended. If, for instance, someone says "I put $100 in the bank", most people would not think someone used a shovel to dig in the mud. However, some linguistic contexts do not provide sufficient information to make a used word clearer. |
Ambiguity | 677 | Linguistic forms | Lexical ambiguity can be addressed by algorithmic methods that automatically associate the appropriate meaning with a word in context, a task referred to as word-sense disambiguation. |
Ambiguity | 677 | Linguistic forms | The use of multi-defined words requires the author or speaker to clarify their context, and sometimes elaborate on their specific intended meaning (in which case, a less ambiguous term should have been used). The goal of clear concise communication is that the receiver(s) have no misunderstanding about what was meant to be conveyed. An exception to this could include a politician whose "weasel words" and obfuscation are necessary to gain support from multiple constituents with mutually exclusive conflicting desires from his or her candidate of choice. Ambiguity is a powerful tool of political science. |
Ambiguity | 677 | Linguistic forms | More problematic are words whose multiple meanings express closely related concepts. "Good", for example, can mean "useful" or "functional" (That's a good hammer), "exemplary" (She's a good student), "pleasing" (This is good soup), "moral" (a good person versus the lesson to be learned from a story), "righteous", etc. "I have a good daughter" is not clear about which sense is intended. The various ways to apply prefixes and suffixes can also create ambiguity ("unlockable" can mean "capable of being opened" or "impossible to lock"). |
Ambiguity | 677 | Linguistic forms | Semantic ambiguity occurs when a word, phrase or sentence, taken out of context, has more than one interpretation. In "We saw her duck" (example due to Richard Nordquist), the words "her duck" can refer either |
Ambiguity | 677 | Linguistic forms | Syntactic ambiguity arises when a sentence can have two (or more) different meanings because of the structure of the sentence—its syntax. This is often due to a modifying expression, such as a prepositional phrase, the application of which is unclear. "He ate the cookies on the couch", for example, could mean that he ate those cookies that were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies. "To get in, you will need an entrance fee of $10 or your voucher and your drivers' license." This could mean that you need EITHER ten dollars OR BOTH your voucher and your license. Or it could mean that you need your license AND you need EITHER ten dollars OR a voucher. Only rewriting the sentence, or placing appropriate punctuation can resolve a syntactic ambiguity. For the notion of, and theoretic results about, syntactic ambiguity in artificial, formal languages (such as computer programming languages), see Ambiguous grammar. |
Ambiguity | 677 | Linguistic forms | Usually, semantic and syntactic ambiguity go hand in hand. The sentence "We saw her duck" is also syntactically ambiguous. Conversely, a sentence like "He ate the cookies on the couch" is also semantically ambiguous. Rarely, but occasionally, the different parsings of a syntactically ambiguous phrase result in the same meaning. For example, the command "Cook, cook!" can be parsed as "Cook (noun used as vocative), cook (imperative verb form)!", but also as "Cook (imperative verb form), cook (noun used as vocative)!". It is more common that a syntactically unambiguous phrase has a semantic ambiguity; for example, the lexical ambiguity in "Your boss is a funny man" is purely semantic, leading to the response "Funny ha-ha or funny peculiar?" |
Ambiguity | 677 | Linguistic forms | Spoken language can contain many more types of ambiguities that are called phonological ambiguities, where there is more than one way to compose a set of sounds into words. For example, "ice cream" and "I scream". Such ambiguity is generally resolved according to the context. A mishearing of such, based on incorrectly resolved ambiguity, is called a mondegreen. |
Ambiguity | 677 | Philosophy | Philosophers (and other users of logic) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments. For example, a politician might say, "I oppose taxes which hinder economic growth", an example of a glittering generality. Some will think they oppose taxes in general because they hinder economic growth. Others may think they oppose only those taxes that they believe will hinder economic growth. In writing, the sentence can be rewritten to reduce possible misinterpretation, either by adding a comma after "taxes" (to convey the first sense) or by changing "which" to "that" (to convey the second sense) or by rewriting it in other ways. The devious politician hopes that each constituent will interpret the statement in the most desirable way, and think the politician supports everyone's opinion. However, the opposite can also be true—an opponent can turn a positive statement into a bad one if the speaker uses ambiguity (intentionally or not). The logical fallacies of amphiboly and equivocation rely heavily on the use of ambiguous words and phrases. |
Ambiguity | 677 | Philosophy | In continental philosophy (particularly phenomenology and existentialism), there is much greater tolerance of ambiguity, as it is generally seen as an integral part of the human condition. Martin Heidegger argued that the relation between the subject and object is ambiguous, as is the relation of mind and body, and part and whole. In Heidegger's phenomenology, Dasein is always in a meaningful world, but there is always an underlying background for every instance of signification. Thus, although some things may be certain, they have little to do with Dasein's sense of care and existential anxiety, e.g., in the face of death. In calling his work Being and Nothingness an "essay in phenomenological ontology" Jean-Paul Sartre follows Heidegger in defining the human essence as ambiguous, or relating fundamentally to such ambiguity. Simone de Beauvoir tries to base an ethics on Heidegger's and Sartre's writings (The Ethics of Ambiguity), where she highlights the need to grapple with ambiguity: "as long as there have been philosophers and they have thought, most of them have tried to mask it ... And the ethics which they have proposed to their disciples has always pursued the same goal. It has been a matter of eliminating the ambiguity by making oneself pure inwardness or pure externality, by escaping from the sensible world or being engulfed by it, by yielding to eternity or enclosing oneself in the pure moment." Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science. She states: "Since we do not succeed in fleeing it, let us, therefore, try to look the truth in the face. Let us try to assume our fundamental ambiguity. It is in the knowledge of the genuine conditions of our life that we must draw our strength to live and our reason for acting". Other continental philosophers suggest that concepts such as life, nature, and sex are ambiguous. Corey Anton has argued that we cannot be certain what is separate from or unified with something else: language, he asserts, divides what is not, in fact, separate. Following Ernest Becker, he argues that the desire to 'authoritatively disambiguate' the world and existence has led to numerous ideologies and historical events such as genocide. On this basis, he argues that ethics must focus on 'dialectically integrating opposites' and balancing tension, rather than seeking a priori validation or certainty. Like the existentialists and phenomenologists, he sees the ambiguity of life as the basis of creativity. |
Ambiguity | 677 | Literature and rhetoric | In literature and rhetoric, ambiguity can be a useful tool. Groucho Marx's classic joke depends on a grammatical ambiguity for its humor, for example: "Last night I shot an elephant in my pajamas. How he got in my pajamas, I'll never know". Songs and poetry often rely on ambiguous words for artistic effect, as in the song title "Don't It Make My Brown Eyes Blue" (where "blue" can refer to the color, or to sadness). |
Ambiguity | 677 | Literature and rhetoric | In the narrative, ambiguity can be introduced in several ways: motive, plot, character. F. Scott Fitzgerald uses the latter type of ambiguity with notable effect in his novel The Great Gatsby. |
Ambiguity | 677 | Mathematical notation | Mathematical notation is a helpful tool that eliminates a lot of misunderstandings associated with natural language in physics and other sciences. Nonetheless, there are still some inherent ambiguities due to lexical, syntactic, and semantic reasons that persist in mathematical notation. |
Ambiguity | 677 | Mathematical notation | The ambiguity in the style of writing a function should not be confused with a multivalued function, which can (and should) be defined in a deterministic and unambiguous way. Several special functions still do not have established notations. Usually, the conversion to another notation requires to scale the argument or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions: |
Ambiguity | 677 | Mathematical notation | Ambiguous expressions often appear in physical and mathematical texts. It is common practice to omit multiplication signs in mathematical expressions. Also, it is common to give the same name to a variable and a function, for example, f = f ( x ) {\displaystyle f=f(x)} . Then, if one sees f = f ( y + 1 ) {\displaystyle f=f(y+1)} , there is no way to distinguish whether it means f = f ( x ) {\displaystyle f=f(x)} multiplied by ( y + 1 ) {\displaystyle (y+1)} , or function f {\displaystyle f} evaluated at argument equal to ( y + 1 ) {\displaystyle (y+1)} . In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning. |
Ambiguity | 677 | Mathematical notation | Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages (C++ and Fortran) require the character * as symbol of multiplication. The Wolfram Language used in Mathematica allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions. Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression f = f ( x ) {\displaystyle f=f(x)} is qualified as an error. |
Ambiguity | 677 | Mathematical notation | The order of operations may depend on the context. In most programming languages, the operations of division and multiplication have equal priority and are executed from left to right. Until the last century, many editorials assumed that multiplication is performed first, for example, a / b c {\displaystyle a/bc} is interpreted as a / ( b c ) {\displaystyle a/(bc)} ; in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language. In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity. In the scientific journal style, one uses roman letters to denote elementary functions, whereas variables are written using italics. For example, in mathematical journals the expression s i n {\displaystyle sin} does not denote the sine function, but the product of the three variables s {\displaystyle s} , i {\displaystyle i} , n {\displaystyle n} , although in the informal notation of a slide presentation it may stand for sin {\displaystyle \sin } . |
Ambiguity | 677 | Mathematical notation | Commas in multi-component subscripts and superscripts are sometimes omitted; this is also potentially ambiguous notation. For example, in the notation T m n k {\displaystyle T_{mnk}} , the reader can only infer from the context whether it means a single-index object, taken with the subscript equal to product of variables m {\displaystyle m} , n {\displaystyle n} and k {\displaystyle k} , or it is an indication to a trivalent tensor. |
Ambiguity | 677 | Mathematical notation | An expression such as sin 2 α / 2 {\displaystyle \sin ^{2}\alpha /2} can be understood to mean either ( sin ( α / 2 ) ) 2 {\displaystyle (\sin(\alpha /2))^{2}} or ( sin α ) 2 / 2 {\displaystyle (\sin \alpha )^{2}/2} . Often the author's intention can be understood from the context, in cases where only one of the two makes sense, but an ambiguity like this should be avoided, for example by writing sin 2 ( α / 2 ) {\displaystyle \sin ^{2}(\alpha /2)} or 1 2 sin 2 α {\textstyle {\frac {1}{2}}\sin ^{2}\alpha } . |
Ambiguity | 677 | Mathematical notation | The expression sin − 1 α {\displaystyle \sin ^{-1}\alpha } means arcsin ( α ) {\displaystyle \arcsin(\alpha )} in several texts, though it might be thought to mean ( sin α ) − 1 {\displaystyle (\sin \alpha )^{-1}} , since sin n α {\displaystyle \sin ^{n}\alpha } commonly means ( sin α ) n {\displaystyle (\sin \alpha )^{n}} . Conversely, sin 2 α {\displaystyle \sin ^{2}\alpha } might seem to mean sin ( sin α ) {\displaystyle \sin(\sin \alpha )} , as this exponentiation notation usually denotes function iteration: in general, f 2 ( x ) {\displaystyle f^{2}(x)} means f ( f ( x ) ) {\displaystyle f(f(x))} . However, for trigonometric and hyperbolic functions, this notation conventionally means exponentiation of the result of function application. |
Ambiguity | 677 | Mathematical notation | The expression a / 2 b {\displaystyle a/2b} can be interpreted as meaning ( a / 2 ) b {\displaystyle (a/2)b} ; however, it is more commonly understood to mean a / ( 2 b ) {\displaystyle a/(2b)} . |
Ambiguity | 677 | Mathematical notation | It is common to define the coherent states in quantum optics with | α ⟩ {\displaystyle ~|\alpha \rangle ~} and states with fixed number of photons with | n ⟩ {\displaystyle ~|n\rangle ~} . Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and n {\displaystyle n} -photon state if the Latin characters dominate. The ambiguity becomes even worse, if | x ⟩ {\displaystyle ~|x\rangle ~} is used for the states with certain value of the coordinate, and | p ⟩ {\displaystyle ~|p\rangle ~} means the state with certain value of the momentum, which may be used in books on quantum mechanics. Such ambiguities easily lead to confusions, especially if some normalized adimensional, dimensionless variables are used. Expression | 1 ⟩ {\displaystyle |1\rangle } may mean a state with single photon, or the coherent state with mean amplitude equal to 1, or state with momentum equal to unity, and so on. The reader is supposed to guess from the context. |
Ambiguity | 677 | Mathematical notation | Some physical quantities do not yet have established notations; their value (and sometimes even dimension, as in the case of the Einstein coefficients), depends on the system of notations. Many terms are ambiguous. Each use of an ambiguous term should be preceded by the definition, suitable for a specific case. Just like Ludwig Wittgenstein states in Tractatus Logico-Philosophicus: "... Only in the context of a proposition has a name meaning." |
Ambiguity | 677 | Mathematical notation | A highly confusing term is gain. For example, the sentence "the gain of a system should be doubled", without context, means close to nothing. |
Ambiguity | 677 | Mathematical notation | The term intensity is ambiguous when applied to light. The term can refer to any of irradiance, luminous intensity, radiant intensity, or radiance, depending on the background of the person using the term. |
Ambiguity | 677 | Mathematical notation | Also, confusions may be related with the use of atomic percent as measure of concentration of a dopant, or resolution of an imaging system, as measure of the size of the smallest detail that still can be resolved at the background of statistical noise. See also Accuracy and precision. |
Ambiguity | 677 | Mathematical notation | The Berry paradox arises as a result of systematic ambiguity in the meaning of terms such as "definable" or "nameable". Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal. |
Ambiguity | 677 | Mathematical interpretation of ambiguity | In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, X = Y {\displaystyle X=Y} leaves open what the value of X {\displaystyle X} is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system—such as X = 2 , X = 3 {\displaystyle X=2,X=3} , which has no solution. |
Ambiguity | 677 | Mathematical interpretation of ambiguity | Logical ambiguity and self-contradiction is analogous to visual ambiguity and impossible objects, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher. |
Ambiguity | 677 | Constructed language | Some languages have been created with the intention of avoiding ambiguity, especially lexical ambiguity. Lojban and Loglan are two related languages that have been created for this, focusing chiefly on syntactic ambiguity as well. The languages can be both spoken and written. These languages are intended to provide a greater technical precision over big natural languages, although historically, such attempts at language improvement have been criticized. Languages composed from many diverse sources contain much ambiguity and inconsistency. The many exceptions to syntax and semantic rules are time-consuming and difficult to learn. |
Ambiguity | 677 | Biology | In structural biology, ambiguity has been recognized as a problem for studying protein conformations. The analysis of a protein three-dimensional structure consists in dividing the macromolecule into subunits called domains. The difficulty of this task arises from the fact that different definitions of what a domain is can be used (e.g. folding autonomy, function, thermodynamic stability, or domain motions), which sometimes results in a single protein having different—yet equally valid—domain assignments. |
Ambiguity | 677 | Christianity and Judaism | Christianity and Judaism employ the concept of paradox synonymously with "ambiguity". Many Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery that fascinates humans. The apocryphal Book of Judith is noted for the "ingenious ambiguity" expressed by its heroine; for example, she says to the villain of the story, Holofernes, "my lord will not fail to achieve his purposes", without specifying whether my lord refers to the villain or to God. |
Ambiguity | 677 | Christianity and Judaism | The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts that he found ambiguous or to reveal meaning often overlooked or forgotten in common phrases: the title of one of his most famous books, Orthodoxy (1908), itself employed such a paradox. |
Ambiguity | 677 | Music | In music, pieces or sections that confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some polytonality, polymeter, other ambiguous meters or rhythms, and ambiguous phrasing, or (Stein 2005, p. 79) any aspect of music. The music of Africa is often purposely ambiguous. To quote Sir Donald Francis Tovey (1935, p. 195), "Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value." |
Ambiguity | 677 | Visual art | In visual art, certain images are visually ambiguous, such as the Necker cube, which can be interpreted in two ways. Perceptions of such objects remain stable for a time, then may flip, a phenomenon called multistable perception. The opposite of such ambiguous images are impossible objects. |
Ambiguity | 677 | Visual art | Pictures or photographs may also be ambiguous at the semantic level: the visual image is unambiguous, but the meaning and narrative may be ambiguous: is a certain facial expression one of excitement or fear, for instance? |
Ambiguity | 677 | Social psychology and the bystander effect | In social psychology, ambiguity is a factor used in determining peoples' responses to various situations. High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for help) elicit more consistent intervention and assistance. With regard to the bystander effect, studies have shown that emergencies deemed ambiguous trigger the appearance of the classic bystander effect (wherein more witnesses decrease the likelihood of any of them helping) far more than non-ambiguous emergencies. |
Ambiguity | 677 | Computer science | In computer science, the SI prefixes kilo-, mega- and giga- were historically used in certain contexts to mean either the first three powers of 1024 (1024, 1024 and 1024) contrary to the metric system in which these units unambiguously mean one thousand, one million, and one billion. This usage is particularly prevalent with electronic memory devices (e.g. DRAM) addressed directly by a binary machine register where a decimal interpretation makes no practical sense. |
Ambiguity | 677 | Computer science | Subsequently, the Ki, Mi, and Gi prefixes were introduced so that binary prefixes could be written explicitly, also rendering k, M, and G unambiguous in texts conforming to the new standard—this led to a new ambiguity in engineering documents lacking outward trace of the binary prefixes (necessarily indicating the new style) as to whether the usage of k, M, and G remains ambiguous (old style) or not (new style). 1 M (where M is ambiguously 1000000 or 1048576) is less uncertain than the engineering value 1.0×10 (defined to designate the interval 950000 to 1050000). As non-volatile storage devices begin to exceed 1 GB in capacity (where the ambiguity begins to routinely impact the second significant digit), GB and TB almost always mean 10 and 10 bytes. |
Abel | 678 | Abel is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepherd who offered his firstborn flock up to God as an offering. God accepted his offering but not his brother's. Cain then killed Abel out of jealousy. |
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Abel | 678 | According to Genesis, this was the first murder in the history of mankind. |
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Abel | 678 | Life and death | And the human knew Eve his woman and she conceived and bore Cain, and she said, "I have got me a man with the Lord." And she bore as well his brother Abel, and Abel became a herder of sheep while Cain was a tiller of the soil. And it happened in the course of time that Cain brought from the fruit of the soil an offering to the Lord. And Abel too had brought from the choice firstlings of his flock, and the Lord regarded Abel and his offering but did not regard Cain and his offering. And Cain was very incensed, and his face fell. And the Lord said to Cain, |
Abel | 678 | Life and death | "Why are you incensed, and why is your face fallen? For whether you offer well, or whether you do not, at the tent flap sin crouches and for you is its longing, but you will rule over it." |
Abel | 678 | Life and death | And Cain said to Abel his brother, "Let us go out to the field," and when they were in the field Cain rose against Abel his brother and killed him. And the Lord said to Cain, "Where is Abel your brother? And he said, "I do not know: am I my brother's keeper?" And He said, "What have you done? Listen! Your brother's blood cries out to me from the soil. And so, cursed shall you be by the soil that gaped with its mouth to take your brother's blood from your hand. If you till the soil, it will no longer give you strength. A restless wanderer shall you be on the earth." And Cain said to the Lord, "My punishment is too great to bear. Now that You have driven me this day from the soil I must hide from Your presence, I shall be a restless wanderer on the earth and whoever finds me will kill me." And the Lord said to him, "Therefore whoever kills Cain shall suffer sevenfold vengeance." And the Lord set a mark upon Cain so that whoever found him would not slay him. |
Abel | 678 | Life and death | And Cain went out from the Lord's presence and dwelled in the land of Nod east of Eden. And Cain knew his wife and she conceived and bore Enoch. Then he became the builder of a city and he called the name of the city like his son's name, Enoch. |
Abel | 678 | Interpretations | According to the narrative in Genesis, Abel (Hebrew: הֶבֶל Hébel, in pausa הָבֶל Hā́ḇel; Biblical Greek: Ἅβελ Hábel; Arabic: هابيل, Hābēl) is Eve's second son. His name in Hebrew is composed of the same three consonants as a root meaning "breath". Julius Wellhausen has proposed that the name is independent of the root. Eberhard Schrader had previously put forward the Akkadian (Old Assyrian dialect) ablu ("son") as a more likely etymology. |
Abel | 678 | Interpretations | In Christianity, comparisons are sometimes made between the death of Abel and that of Jesus, the former thus seen as being the first martyr. In Matthew 23:35 Jesus speaks of Abel as "righteous", and the Epistle to the Hebrews states that "The blood of sprinkling ... [speaks] better things than that of Abel" (Hebrews 12:24). The blood of Jesus is interpreted as bringing mercy; but that of Abel as demanding vengeance (hence the curse and mark). |
Abel | 678 | Interpretations | Abel is invoked in the litany for the dying in the Roman Catholic Church, and his sacrifice is mentioned in the Canon of the Mass along with those of Abraham and Melchizedek. The Alexandrian Rite commemorates him with a feast day on December 28. |
Abel | 678 | Interpretations | According to the Coptic Book of Adam and Eve (at 2:1–15), and the Syriac Cave of Treasures, Abel's body, after many days of mourning, was placed in the Cave of Treasures, before which Adam and Eve, and descendants, offered their prayers. In addition, the Sethite line of the Generations of Adam swear by Abel's blood to segregate themselves from the unrighteous. |
Abel | 678 | Interpretations | In the Book of Enoch (22:7), regarded by most Christian and Jewish traditions as extra-biblical, the soul of Abel is described as having been appointed as the chief of martyrs, crying for vengeance, for the destruction of the seed of Cain. A similar view is later shown in the Testament of Abraham (A:13 / B:11), where Abel has been raised to the position as the judge of the souls. |
Abel | 678 | Interpretations | In Bereshit Rabbah (22:2), a discussion of Gen. 4:1 ff. has Rabbi Yehoshua ben Korcha mentioning that Cain was born with a twin sister, and Abel with two twin sisters. This is based on the principle that the otherwise superfluous accusative article "et" always conveys some additional teaching (Pesachim 22b). The "et"'s are parsed slightly differently in Yebamot 62a where the two "et"'s in Gen. 4:2 indicate Cain and his sister, and Abel and his (one) sister. |
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