ambiguity

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Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is
uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially ...
. 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 '' ambi-'' part of the term reflects an idea of " two", as in "two meanings".) The concept of ambiguity is generally contrasted with
vagueness In linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and s ...
. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with information that is vague, it is difficult to form any interpretation at the desired level of specificity.

# Linguistic forms

Lexical ambiguity is contrasted with
semantic ambiguity In linguistics, an expression is semantically ambiguous when it can have multiple meanings. The higher the amount of synonyms a word has, the higher the degree of ambiguity. Like other kinds of ambiguity, semantic ambiguities are often clarified by ...
. The former represents a choice between a finite number of known and meaningful
context Context may refer to: * Context (language use), the relevant constraints of the communicative situation that influence language use, language variation, and discourse summary Computing * Context (computing), the virtual environment required to su ...
-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 In linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and s ...
. Linguistic ambiguity can be a problem in law, because the interpretation of written documents and oral agreements is often of paramount importance.

## Lexical ambiguity

The lexical ambiguity of a word or phrase pertains to its having more than one meaning in the language to which the word belongs. "Meaning" here refers to whatever should be captured by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "
financial institution Financial institutions, sometimes called banking institutions, are business entities that provide services as intermediaries for different types of financial monetary transactions. Broadly speaking, there are three major types of financial insti ...
" and " edge of a river". Or consider "
apothecary ''Apothecary'' () is a mostly archaic term for a medicine, medical professional who formulates and dispenses ''materia medica'' (medicine) to physicians, surgeons, and patients. The modern chemist (British English) or pharmacist (British and Nor ...
". One could say "I bought herbs from the apothecary". This could mean one actually spoke to the apothecary (
pharmacist A pharmacist, also known as a chemist (English in the Commonwealth of Nations, Commonwealth English) or a druggist (North American and, archaically, Commonwealth English), is a healthcare professional who prepares, controls and distributes med ...
) or went to the apothecary (
pharmacy Pharmacy is the science and practice of discovering, producing, preparing, dispensing, reviewing and monitoring medications, aiming to ensure the safe, effective, and affordable use of medication, medicines. It is a miscellaneous science as it ...
). The context in which an ambiguous word is used often makes it evident which of the meanings is intended. If, for instance, someone says "I buried $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 disambiguate a used word. 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 Word-sense disambiguation (WSD) is the process of identifying which word sense, sense of a word is meant in a sentence (linguistics), sentence or other segment of context (language use), context. In human language processing in the brain, languag ... . 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 word A weasel word, or anonymous authority, is an slang, informal term for words and phrases aimed at creating an impression that something specific and meaningful has been said, when in fact only a vague or ambiguous claim has been communicated. Exa ... s" and obfuscation Obfuscation is the wikt:obscure#Verb, obscuring of the intended meaning (linguistics), meaning of communication by making the message difficult to understand, usually with mental confusion, confusing and ambiguity, ambiguous language. The obfuscat ... are necessary to gain support from multiple constituents with mutually exclusive In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails ... conflicting desires from their candidate of choice. Ambiguity is a powerful tool of political science Political science is the science, scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of politics, political activities, political thought, political behavior, and associated c ... . 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" (''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 prefix A prefix is an affix which is placed before the Word stem, stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy'' ... es and suffix In linguistics, a suffix is an affix which is placed after the Stem (linguistics), stem of a word. Common examples are case endings, which indicate the grammatical case of nouns, adjectives, and verb endings, which form the Grammatical conjugation ... es can also create ambiguity ("unlockable" can mean "capable of being unlocked" or "impossible to lock"). ## Semantic and syntactic ambiguity Semantic ambiguity In linguistics, an expression is semantically ambiguous when it can have multiple meanings. The higher the amount of synonyms a word has, the higher the degree of ambiguity. Like other kinds of ambiguity, semantic ambiguities are often clarified by ... 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 # to the person's bird (the noun "duck", modified by the possessive pronoun "her"), or # to a motion she made (the verb "duck", the subject of which is the objective pronoun "her", object of the verb "saw"). Syntactic ambiguity Syntactic ambiguity, also called structural ambiguity, amphiboly or amphibology, is a situation where a Sentence (linguistics), sentence may be interpreted in more than one way due to ambiguous syntax, sentence structure. Syntactic ambiguity aris ... 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.Critical Thinking, 10th ed., Ch 3, Moore, Brooke N. and Parker, Richard. McGraw-Hill, 2012 For the notion of, and theoretic results about, syntactic ambiguity in artificial, formal languages (such as computer
programming language A programming language is a system of notation for writing computer program, computer programs. Most programming languages are text-based formal languages, but they may also be visual programming language, graphical. They are a kind of computer ...
s), see
Ambiguous grammar In computer science, an ambiguous grammar is a context-free grammar for which there exists a string (computer science), string that can have more than one leftmost derivation or parse tree, while an unambiguous grammar is a context-free grammar for ...
. 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?"
Spoken language A spoken language is a language produced by articulate sounds or (depending on one's definition) manual gestures, as opposed to a written language. An oral language or vocal language is a language produced with the vocal tract in contrast with a si ...
can contain many more types of ambiguities which 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 A mondegreen () is a mishearing or misinterpretation of a phrase in a way that gives it a new meaning. Mondegreens are most often created by a person listening to a poem or a song; the listener, being unable to hear a lyric clearly, substitutes w ...
.

# 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. In
continental philosophy Continental philosophy is a term used to describe some philosophers and philosophical traditions that do not fall under the umbrella of analytic philosophy. However, there is no academic consensus on the definition of continental philosophy. Pri ...
(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 Martin Heidegger (; ; 26 September 188926 May 1976) was a German philosopher who is best known for contributions to Phenomenology (philosophy), phenomenology, hermeneutics, and existentialism. He is among the most important and influential phi ...
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 Jean-Paul Charles Aymard Sartre (, ; ; 21 June 1905 – 15 April 1980) was one of the key figures in the philosophy of existentialist, existentialism (and Phenomenology (philosophy), phenomenology), a French playwright, novelist, screenwriter ...
follows Heidegger in defining the human essence as ambiguous, or relating fundamentally to such ambiguity.
Simone de Beauvoir Simone Lucie Ernestine Marie Bertrand de Beauvoir (, ; ; 9 January 1908 – 14 April 1986) was a French Existentialism, existentialist philosopher, writer, social theorist, and Feminism, feminist activist. Though she did not consider herself ...
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.

# 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). 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''.

# Mathematical notation

Mathematical notation Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations and any other mathematical objects, and assembling the ...
, widely used in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
and other
science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
s, avoids many ambiguities compared to expression in natural language. However, for various reasons, several
lexical Lexical may refer to: Linguistics * Lexical corpus or lexis, a complete set of all words in a language * Lexical item, a basic unit of lexicographical classification * Lexicon, the vocabulary of a person, language, or branch of knowledge * Lexical ...
,
syntactic In linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature an ...
and
semantic Semantics (from grc, wikt:σημαντικός, σημαντικός ''sēmantikós'', "significant") is the study of reference, Meaning (philosophy), meaning, or truth. The term can be used to refer to subfields of several distinct discipline ...
ambiguities remain.

## Names of functions

The ambiguity in the style of writing a function should not be confused with a
multivalued function In mathematics, a multivalued function, also called multifunction, many-valued function, set-valued function, is similar to a function (mathematics), function, but may associate several values to each input. More precisely, a multivalued funct ...
, which can (and should) be defined in a deterministic and unambiguous way. Several
special function Special functions are particular function (mathematics), mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. ...
s 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: * Sinc function * Elliptic integral of the third kind; translating elliptic integral form
MAPLE ''Acer'' () is a genus of trees and shrubs commonly known as maples. The genus is placed in the family Sapindaceae.Stevens, P. F. (2001 onwards). Angiosperm Phylogeny Website. Version 9, June 2008 nd more or less continuously updated since h ...
to
Mathematica Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, Computer algebra, symbolic computation, data manipulation, network analysis, time series analysi ...
, one should replace the second argument to its square, see Talk:Elliptic integral#List of notations; dealing with complex values, this may cause problems. *
Exponential integral In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument of a function, argument. Definitions For real ...

* Hermite polynomial

## Expressions

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, $f=f\left(x\right)$. Then, if one sees $f=f\left(y+1\right)$, there is no way to distinguish whether it means $f=f\left(x\right)$ multiplied by $\left(y+1\right)$, or function $f$ evaluated at argument equal to $\left(y+1\right)$. In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning. Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages ( and ) require the character * as symbol of multiplication. The
Wolfram Language The Wolfram Language ( ) is a general multi-paradigm programming language developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming and can employ arbitrary data structure, structures ...
used in
Mathematica Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, Computer algebra, symbolic computation, data manipulation, network analysis, time series analysi ...
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. The order of operations may depend on the context. In most
programming language A programming language is a system of notation for writing computer program, computer programs. Most programming languages are text-based formal languages, but they may also be visual programming language, graphical. They are a kind of computer ...
s, 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 $a/\left(bc\right)$; 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 In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in scientific journals are mostly written by active scientists such ...
style, one uses roman letters to denote elementary functions, whereas variables are written using italics. For example, in mathematical journals the expression $s i n$ does not denote the , but the product of the three variables $s$, $i$, $n$, although in the informal notation of a slide presentation it may stand for $\sin$. Commas in multi-component subscripts and superscripts are sometimes omitted; this is also potentially ambiguous notation. For example, in the notation $T_$, the reader can only infer from the context whether it means a single-index object, taken with the subscript equal to product of variables $m$, $n$ and $k$, or it is an indication to a trivalent
tensor In mathematics, a tensor is an mathematical object, algebraic object that describes a Multilinear map, multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as Vect ...

.

## Examples of potentially confusing ambiguous mathematical expressions

An expression such as $\sin^2\alpha/2$ can be understood to mean either $\left(\sin\left(\alpha/2\right)\right)^2$ or $\left(\sin \alpha\right)^2/2$. 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 $\sin^2\left(\alpha/2\right)$ or $\frac\sin^2\alpha$. The expression $\sin^\alpha$ means $\arcsin\left(\alpha\right)$ in several texts, though it might be thought to mean $\left(\sin \alpha\right)^$, since $\sin^ \alpha$ commonly means $\left(\sin \alpha\right)^$. Conversely, $\sin^2 \alpha$ might seem to mean $\sin\left(\sin \alpha\right)$, as this
exponentiation Exponentiation is a mathematics, mathematical operation (mathematics), operation, written as , involving two numbers, the ''Base (exponentiation), base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". W ...
notation usually denotes function iteration: in general, $f^2\left(x\right)$ means $f\left(f\left(x\right)\right)$. However, for
trigonometric Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic period, Hellenistic world during the 3rd century BC from applications of geometry to Astr ...
and
hyperbolic functions In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a unit circle, circle with a unit radius, the points form the right ha ...

, this notation conventionally means exponentiation of the result of function application. The expression $a/2b$ can be interpreted as meaning $\left(a/2\right)b$; however, it is more commonly understood to mean $a/\left(2b\right)$.

## Notations in quantum optics and quantum mechanics

It is common to define the coherent states in
quantum optics Quantum optics is a branch of Atomic, molecular, and optical physics, atomic, molecular, and optical physics dealing with how individual quanta of light, known as Photon, photons, interact with atoms and molecules. It includes the study of the par ...
with $~, \alpha\rangle~$ and states with fixed number of photons with $~, n\rangle~$. Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and $~n~$photon state if the Latin characters dominate. The ambiguity becomes even worse, if $~, x\rangle~$ is used for the states with certain value of the coordinate, and $~, p\rangle~$ means the state with certain value of the momentum, which may be used in books on
quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
. Such ambiguities easily lead to confusions, especially if some normalized adimensional,
dimensionless A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...
variables are used. Expression $, 1\rangle$ 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.

## Ambiguous terms in physics and mathematics

Some physical quantities do not yet have established notations; their value (and sometimes even
dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

, 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 Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy o ...

states in
Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and Citation, cited as TLP) is a book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein which deals with the relationship between language and reality and aims to ...
: "...Only in the context of a proposition has a name meaning." 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). The term ''intensity'' is ambiguous when applied to light. The term can refer to any of
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The International System of Units, SI unit of irradiance is the watt per square metre (W⋅m−2). The Centimetre–gram–second system of units, CGS unit e ...

,
luminous intensity In Photometry (optics), photometry, luminous intensity is a measure of the wavelength-weighted Power (physics), power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model ...
radiance In radiometry Radiometry is a set of techniques for measuring electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space ...
, depending on the background of the person using the term. Also, confusions may be related with the use of as measure of concentration of a
dopant A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optics, optical properties. The amount of dopant necessary to cause changes is typically very l ...
, 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 Accuracy and precision are two measures of '' observational error''. ''Accuracy'' is how close a given set of measurements ( observations or readings) are to their '' true value'', while ''precision'' is how close the measurements are to each o ...

and its talk. 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 A vicious circle (or cycle) is a complex chain of events that reinforces itself through a feedback loop, with detrimental results. It is a system with no tendency toward List of types of equilibrium, equilibrium (social equilibrium, social, Eco ...
fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal.

# Mathematical interpretation of ambiguity

In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of
underdetermination In the philosophy of science, underdetermination or the underdetermination of theory by data (sometimes abbreviated UTD) is the idea that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in re ...
—for example, $X=Y$ leaves open what the value of ''X'' is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or
oxymoron An oxymoron (usual plural oxymorons, more rarely oxymora) is a figure of speech that Juxtaposition, juxtaposes concepts with opposing meanings within a word or phrase that creates an ostensible self-contradiction (disambiguation), self-contradic ...
, or in mathematics an inconsistent system—such as $X=2, X=3$, which has no solution. Logical ambiguity and self-contradiction is analogous to visual ambiguity and s, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher.

# 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 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 In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentence (linguistics), sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence st ...

and
semantic Semantics (from grc, wikt:σημαντικός, σημαντικός ''sēmantikós'', "significant") is the study of reference, Meaning (philosophy), meaning, or truth. The term can be used to refer to subfields of several distinct discipline ...
rules are time-consuming and difficult to learn.

# Biology

In
structural biology Structural biology is a field that is many centuries old which, and as defined by the Journal of Structural Biology, deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every le ...
, ambiguity has been recognized as a problem for studying . 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.

# Christianity and Judaism

Christianity Christianity is an Abrahamic religions, Abrahamic Monotheism, monotheistic religion based on the Life of Jesus in the New Testament, life and Teachings of Jesus, teachings of Jesus, Jesus of Nazareth. It is the Major religious groups, world's ...

and
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic religions, Abrahamic, monotheism, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots ...
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 which fascinates humans. The
apocrypha Apocrypha are works, usually written, of unknown authorship or of doubtful origin. The word ''apocryphal'' (ἀπόκρυφος) was first applied to writings which were kept secret because they were the vehicles of esoteric knowledge considered ...
l Book of Judith is noted for the "ingenious ambiguity" expressed by its heroine e.g. she says to the villain of the story, Holofernes, "my lord will not fail to achieve his purposes". The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts which 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.

# 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 metre, meters or rhythms, and ambiguous phrase (music), phrasing, or (Stein 2005, p.79) any aspect of music. The music of Africa is often purposely ambiguous. To quote Donald Francis Tovey, 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."

# 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 s. 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?

# 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.

# 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, 10242 and 10243) 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. Subsequently, the Ki, Mi, and Gi prefixes were introduced so that metric prefix#Binary prefixes, 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 1,000,000 or 1,048,576) is ''less'' uncertain than the engineering value 1.0e6 (defined to designate the interval 950,000 to 1,050,000). 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 109 and 1012 bytes.