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Ambiguity is the property of words, terms, notations and concepts (within a particular context) as being undefined, undefinable, or without an obvious definition and thus having an unclear meaning. Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... Words has several meanings: words in Unix. ... In linguistics, meaning is the content carried by the words or signs exchanged by people when communicating through language. ...

A word, phrase, sentence, or other communication is called “ambiguous” if it can be interpreted in more than one way. Ambiguity is distinct from vagueness, which arises when the boundaries of meaning are indistinct. Ambiguity is in contrast with definition, and typically refers to an unclear choice between standard definitions, as given by a dictionary, or else understood as common knowledge. Look up phrase in Wiktionary, the free dictionary. ... In linguistics, a sentence is a unit of language, characterized in most languages by the presence of a finite verb. ... Ambiguity is one way in which the meanings of words and phrases can be unclear, but there is another way, which is different from ambiguity: vagueness. ... Look up Contrast in Wiktionary, the free dictionary. ... For other uses, see Definition (disambiguation). ... For other uses, see Dictionary (disambiguation). ... Common knowledge is what everybody knows, usually with reference to the community in which the term is used. ...

Lexical ambiguity arises when context is insufficient to determine the sense of a single word that has more than one meaning. For example, the word “bank” has several meanings, including “financial institution” and “edge of a river,” but if someone says “I deposited \$100 in the bank,” the intended meaning is clear. More problematic are words whose senses 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” (He is a good person), and probably other similar things. “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 unlocked” or “impossible to lock”). Polysemy (from the Greek Ï€Î¿Î»Ï…ÏƒÎ·Î¼ÎµÎ¯Î± = multiple meaning) is the capacity for a sign to have multiple meanings. ... A prefix is the initial portion of some object or term (typically in text or speech) with a distinct and he base semantics for a word. ... Look up Suffix in Wiktionary, the free dictionary. ...

Syntactic ambiguity arises when a sentence can be parsed in more than one way. “He ate the cookies on the couch,” for example, could mean that he ate those cookies which 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. Spoken language can also contain such 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 based on the context. A mishearing of such based on incorrectly-resolved ambiguity is called a mondegreen. Syntactic ambiguity is a property of sentences which may be reasonably interpreted in more than one way, or reasonably interpreted to mean more than one thing. ... An example of parsing a mathematical expression. ... Spoken language is a language that people utter words of the language. ... A mondegreen is the mishearing (usually accidental) of a phrase as a homophone or near-homophone in such a way that it acquires a new meaning. ...

Semantic ambiguity arises when a word or concept has an inherently diffuse meaning based on widespread or informal usage. This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion. A non-linguistic meaning is an actual or possible derivation from sentience, which is not associated with signs that have any original or primary intent of communication. ...

For example, “You could do with a new automobile. How about a test drive?” The clause “You could do with” presents a statement with such wide possible interpretation as to be essentially meaningless. 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 is one way in which the meanings of words and phrases can be unclear, but there is another way, which is different from ambiguity: vagueness. ...

## Physics and mathematics

The mathematical notations, widely used in physics and other sciences, are supposed to avoid any ambiguity. However, the application of mathematics require all possible simplifications. This may lead to the lexical, syntactic and semantic ambiguities mentioned above. Mathematical notation is used in mathematics, and throughout the physical sciences, engineering, and economics. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... In the lexicon of a language, lexical words or nouns refer to things. ... In linguistics, syntax is the study of the rules, or patterned relations, that govern the way the words in a sentence come together. ... In general, semantics (from the Greek semantikos, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ...

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, $~f=f(x)~$. Then, if one sees $~g=f(y+1)~$, there is no way to distinguish, does it mean $~f=f(x)~$ multiplied by $~(y+1)~$, or function $~f~$ evaluated at argument equal to $~(y+1)~$. In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.

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. This diagram does not represent a true function, because the element 3 in X is associated with two elements, b and c, in Y. In mathematics, a multivalued function is a total relation; i. ...

Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages (C++, MATLAB, Fortran, Maple) require the character * as symbol of multiplication. The language 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) is qualified as an error. C++ (pronounced see plus plus, IPA: ) is a general-purpose programming language with high-level and low-level capabilities. ... Not to be confused with Matlab Upazila in Chandpur District, Bangladesh. ... Fortran (previously FORTRAN[1]) is a general-purpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ... For other uses, see Maple (disambiguation). ... For other uses, see Mathematica (disambiguation). ...

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, $~a/bc~$ is interpreted as $~a/(bc)~$; 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. Sometimes, one uses italics letters to denote elementary functions. In the scientific journal style, the expression $~ s i n alpha~$ means product of variables $~s~$, $~i~$, $~n~$ and $~alpha~$, although in a slideshow, it may mean $~sin[alpha]~$. A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. ... Nature, Science and PNAS In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. ...

Comma in subscripts and superscripts sometimes is omitted; it is also ambiguous notation. If it is written $~T_{mnk}~$, the reader should guess from the context, does it mean a single-index object, evaluated while the subscript is equal to product of variables $~m~$, $~n~$ and $~k~$, or it is indication to a three-valent tensor. The writing of $~T_{mnk}~$ instead of $~T_{m,n,k}~$ may mean that the writer either is stretched in space (for example, to reduce the publication fee), or aims to increase number of publications without considering readers. The same may apply to any other use of ambiguous notations.

## Examples of potentially confusing ambiguous expressions

$sin^2alpha/2,$, which could be understood to mean either $(sin(alpha/2))^2,$ or $(sin(alpha))^2/2,$.

$~sin^{-1} alpha$, which by convention means $~arcsin(alpha) ~$, though it might be thought to mean $(sin(alpha))^{-1},$ since $~sin^{n} alpha$ means $(sin(alpha))^{n},$.

$a/2b,$, which arguably should mean $(a/2)b,$ but would commonly be understood to mean $a/(2b),$

## Citations

Some scientific journals required that all the references are marked as if they would be exponential functions, for example: ..number of partial lasers does not exceed 109"(can you guess that it is reference number 9, not 1000000000 lasers?). Recently, OSA journals improved the style to avoid such ambiguity; since 2007, February 14, the cites appear in squared parentheses [1]. Nature, Science and PNAS In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. ...

## Pedagogic use of ambiguous expressions

Ambiguity can be used as a pedagogical trick, to force students to reproduce the deduction by themselves. Some textbooks [2] give the same name to the function and to its Fourier transform: In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...

$~f(omega)=int f(t) exp(iomega t) {rm d}t$.

Rigorously speaking, such an expression requires that $~ f=0 ~$; even if function $~ f ~$ is a self-Fourier function, the expression should be written as $~f(omega)=frac{1}{sqrt{2pi}}int f(t) exp(iomega t) {rm d}t$; however, it is assumed that the shape of the function (and even its norm $int |f(x)|^2 {rm d}x$) depend on the character used to denote its argument. If the Greek letter is used, it is assumed to be a Fourier transform of another function, The first function is assumed, if the expression in the argument contains more characters $~t~$ or $~tau~$, than characters $~omega~$, and the second function is assumed in the opposite case. Expressions like $~f(omega t)~$ or $~f(y)~$ contain symbols $~t~$ and $~omega~$ in equal amounts; they are ambiguous and should be avoided in serious deduction. In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...

## Ambiguity of notations in quantum optics and quantum mechanics

It is common to define the coherent states in quantum optics with $~|alpharangle~$ and states with fixed number of photons with $~|nrangle~$. Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and $~n~$photon state if the Latin characters dominate. The ambiguity becomes even worse, if $~|xrangle~$ is used for the states with certain value of the coordinate, and $~|prangle~$ means the state with certain value of the momentum, which may be used in books on quantum mechanics. Such ambiguities easy lead to confusions, especially if some normalized adimensional, dimensionless variables are used. Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resemble the oscillating behaviour of a classical harmonic oscillator system. ... Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement...

## Examples of ambiguous terms

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. 2-dimensional renderings (ie. ... In physics, atomic spectral lines are of two types: An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength. ...

A highly confusing term is gain. For example, the sentence "the gain of a system should be doubled", without context, means close to nothing.
It may mean that the ratio of the output voltage of an electric circuit to the input voltage should be doubled.
It may mean that the ratio of the output power of an electric or optical circuit to the input power should be doubled.
It may mean that the gain of the laser medium should be doubled, for example, doubling the population of the upper laser level in a quasi-two level system (assuming negligible absorption of the ground-state). In electronics, gain is usually taken as the mean ratio of the signal output of a system to the signal input of the system. ...

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 which still can be resolved at the background of statistical noise. See also Accuracy and precision and its talk. There are very few or no other articles that link to this one. ... A dopant, also called doping agent and dope, is an impurity element added to a semiconductor lattice in low concentrations in order to alter the optical/electrical properties of the semiconductor. ... The word resolution has several meanings, depending on context. ... Imaging is the action or process of producing images, animations, 3D computer graphics or any other spatial representation of a physical object. ... â€œAccuracyâ€ redirects here. ...

Many terms are ambiguous. Each use of an ambiguous term should be preceded by the definition, suitable for a specific case.

The Berry paradox arises as a result of systematic ambiguity. In various formulations of the Berry paradox, such as one that reads: The number not nameable in less than eleven syllables the term nameable is one that has this systematic ambiguity. Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, definable, true, false, function, property, class, relation, cardinal, and ordinal.[3] The Berry paradox is the apparent contradiction that arises from expressions such as the following: The smallest positive integer not nameable in under eleven words. ... Vicious Circle is an album released in 1995 by L.A. Guns. ...

## Psychology and Management

An increasing amount of research is concentrating on how people react and respond to ambiguous and uncertain situations. Much of this focuses on ambiguity tolerance. A number of correlations have been found between an individual’s reaction and tolerance to ambiguity and a range of factors. Ambiguity tolerance is the ability to perceive ambiguities (contradictory issues which may be difficult to understand) in social and cultural behaviors as well as information with equivocal (several) meanings in a neutral and open way. ...

Apter and Desselles (2001)[4] for example, found a strong correlation with such attributes and factors like a greater preference for safe as opposed to risk based sports, a preference for endurance type activities as opposed to explosive activities, a more organised and less casual lifestyle, greater care and precision in descriptions, a lower sensitivity to emotional and unpleasant words, a less acute sense of humour, engaging a smaller variety of sexual practices than their more risk comfortable colleagues, a lower likelihood of the use of drugs, pornography and drink, a greater likelihood of displaying obsessional behaviour.

In the field of leadership Wilkinson (2006) [5] found strong correlations between an individual leaders reaction to ambiguous situations and the Leadership modes they use, the type of creativity (Kirton (2003) [6] and how they relate to others. Leader redirects here. ... For other uses of Creativity, see Creativity (disambiguation). ...

## Applications

Philosophers (and other users of logic) spend a lot of time and effort searching for and removing 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.” Some will think he opposes taxes in general because they hinder economic growth; others will think he opposes only those taxes that he believes will hinder economic growth (although in writing, the correct insertion or omission of a comma after “taxes” removes ambiguity here - in addition, for the latter meaning, “that” is properly used in place of “which”). The politician hopes that each will interpret the statement in the way he wants, and both will think the politician is on his side. The logical fallacies of amphiboly and equivocation also rely on the use of ambiguous words and phrases. A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other uses, see Comma. ... Amphibology or amphiboly (from the Greek ampibolia) is, in logic, a verbal fallacy arising from ambiguity in the grammatical structure of a sentence. ... Equivocation, also known as amphibology, is classified as both a formal and informal fallacy. ...

In literature and rhetoric, on the other hand, 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. What he was doing in my pajamas I’ll never know.” Ambiguity can also be used as a comic device through a genuine intention to confuse, such as Magic: The Gathering's Unhinged © Ambiguity, which makes puns with homophones, mispunctuation, and run-ons: “Whenever a player plays a spell that counters a spell that has been played[,] or a player plays a spell that comes into play with counters, that player may counter the next spell played[,] or put an additional counter on a permanent that has already been played, but not countered.” 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). For other uses, see Literature (disambiguation). ... Rhetoric (from Greek , rhÃªtÃ´r, orator, teacher) is generally understood to be the art or technique of persuasion through the use of oral, visual, or written language; however, this definition of rhetoric has expanded greatly since rhetoric emerged as a field of study in universities. ... Groucho redirects here. ... Look up Humour in Wiktionary, the free dictionary. ... Sadness is a mood that displays feeling of disadvantage and loss. ...

In 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. Francis Scott Key Fitzgerald (September 24, 1896 â€“ December 21, 1940) was an American Jazz Age author of novels and short stories. ... This article is about the novel. ...

All religions debate the orthodoxy or heterodoxy of ambiguity. Christianity and Judaism employ the concept of paradox synonymously with 'ambiguity'. Ambiguity within Christianity [7](and other religions) is resisted by the conservatives and fundamentalists, who regard the concept as equating with 'contradicition'. Non-fundamentalist Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans. â€œOrthodoxâ€ redirects here. ... Heterodoxy includes any opinions or doctrines at variance with an official or orthodox position.[1] As an adjective, heterodox is used to describe a subject as characterized by departure from accepted beliefs or standards (status quo). ... Topics in Christianity Movements Â· Denominations Â· Other religions Ecumenism Â· Preaching Â· Prayer Music Â· Liturgy Â· Calendar Symbols Â· Art Â· Criticism Important figures Apostle Paul Â· Church Fathers Constantine Â· Athanasius Â· Augustine Anselm Â· Aquinas Â· Palamas Â· Luther Calvin Â· Wesley Arius Â· Marcion of Sinope Archbishop of Canterbury Â· Catholic Pope Coptic Pope Â· Ecumenical Patriarch Christianity Portal This box:      Christianity is... This article or section does not cite its references or sources. ... Look up paradox in Wiktionary, the free dictionary. ... Rudolf Otto (September 25, 1869 - 6 March 1937) was an eminent German protestant theologian and scholar of comparative religion. ...

### Constructed language

Some languages have been created with the intention of avoiding ambiguity, especially lexical ambiguity. Lojban and Loglan are two related languages which have been created with this in mind. The languages can be both spoken and written. These languages are intended to provide a greater technical precision over natural languages, although historically, such attempts at language improvement have been criticized. An artificial or constructed language (known colloquially as a conlang among aficionados), is a language whose vocabulary and grammar were specifically devised by an individual or small group, rather than having naturally evolved as part of a culture as with natural languages. ... Lojban (IPA ) is a constructed human language based on predicate logic. ... Loglan is a constructed language originally designed for linguistic research, particularly for investigating the Sapir-Whorf Hypothesis. ... The chief of the numerous works of John Wilkins was An Essay towards a Real Character and a Philosophical Language (London, 1668), in which he expounds a new universal language for the use of philosophers. ...

### Music

In music pieces or sections which 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.” For other uses, see Music (disambiguation). ... The musical use of more than one key simultaneously is polytonality. ... Metre is the measurement of a musical line into measures of stressed and unstressed beats, indicated in Western notation by a symbol called a time signature. ... This article is about the unit of length. ... Rhythm (Greek = flow, or in Modern Greek, style) is the variation of the length and accentuation of a series of sounds or other events. ... In music a phrase (Greek Ï†ÏÎ¬ÏƒÎ·, sentence, expression, see also strophe) is a section of music that is relatively self contained and coherent over a medium time scale. ... An aspect of music is any characteristic, dimension, or element taken as a part or component of music. ... Hand drumming is significant throughtout Africa The music of Africa is as vast and varied as the continents many regions, nations and ethnic groups. ... Wikisource has original works written by or about: Donald Francis Tovey Sir Donald Francis Tovey (July 17, 1875 â€“ July 10, 1940) was a British musical analyst, musicologist, writer on music, composer and pianist. ...

## Abbreviations

Abbreviations form, perhaps, the richest field of ambiguiguity, see List of classical abbreviations, which is still far from complete. For example, AU may mean Atomic Unit, Astronomical unit, as well as Arbitrary Unit, American University, and a lot of other things. Simple transmutation of the same letters gives University of Arizona (which is 200 km away from the Arizona State University), United Airlines, Unidad Administrativa (Spanish) and so on. This article does not cite any references or sources. ... The following list contains a selection from the latin abbreviations that occur in the writings and inscriptions of the Romans. ... Look up Au, au in Wiktionary, the free dictionary. ... The atomic mass unit (amu), unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic masses and molecular masses. ... The astronomical unit (AU or au or a. ... For other universities known as American University, see American University (disambiguation). ... The University of Arizona (UA or U of A) is a land-grant and space-grant public institution of higher education and research located in Tucson, Arizona, United States. ... Arizona State University (ASU) is a public research institution of higher education and research with campuses located in the Phoenix Metropolitan Area. ... United Airlines, also known as United Air Lines, Inc. ...

Sometimes, an abbreviation, which looks pretty innocent in one language, allows sexual or dirty interpretation in other language; especially if an abbreviation constructed of several words is used as URL. The interpretation of ambiguous abbreviation should be extremely careful. Better to say, that interpretation of ANY abbreviation should be careful: one never knows, how many meanings may have an apparently obvious abbreviation. A Uniform Resource Locator, URL (spelled out as an acronym, not pronounced as earl), or Web address, is a standardized address name layout for resources (such as documents or images) on the Internet (or elsewhere). ...

Examples:

• http://www.opticsexpress.org; how an automatic filter can guess, that it does not refer to some editorial publishing materials about some kind of optic sex?
• http://xxx.lanl.gov; (one system manager condemned one "investigador" for intents to access this URL, and the director also was pretty sure that this site refers to an adult material, he neither clicked this link, nor discussed it with the researcher.)

## References

1. ^ A %; C (2007). "[http://josab.osa.org/submit/templates/decault.cftm % OSA journals manuscript submission template]". Journal.
2. ^ H. Haug, S. Koch. Quantum Theory of the Optical and Electronic Properties of Semiconductors, http://www.allbookstores.com/book/9812387560
4. ^ in Motivational Styles in Everyday life: A guide to reversal Theory. M.J. Apter (ed) (2001) APA Books
5. ^ Wilkinson, D.J. (2006) The Ambiguity Advantage: What great leaders are great at. New York Palgrave Macmillan.
6. ^ Kirton, M.J. (2003)Adaption-Innovation: In the Context of Diversity and Change. Routledge.
7. ^ [1]

Results from FactBites:

 Ambiguity (2494 words) Part of the answer consists in identifying phenomena with which ambiguity may be confused, such as vagueness, unclarity, inexplicitness and indexicality. Structural ambiguity occurs when a phrase or sentence has more than one underlying structure, such as the phrases 'Tibetan history teacher', 'a student of high moral principles' and 'short men and women', and the sentences 'The girl hit the boy with a book' and 'Visiting relatives can be boring'. Philosophers sometimes lament the prevalence of ambiguity in natural languages and yearn for an ideal language in which it is absent.
 Ambiguity - LoveToKnow 1911 (245 words) In law an ambiguity as to the meaning of the words of a written instrument may be of considerable importance. (1) Patent ambiguity is that ambiguity which is apparent on the face of an instrument to any one perusing it, even if he be unacquainted with the circumstances of the parties. A latent ambiguity may be explained by parol evidence, for, as the ambiguity has been brought about by circumstances extraneous to the instrument, the explanation must necessarily be sought for from such circumstances.
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