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Asymmetry is the absence of, or a violation of,
symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
(the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. The absence of or violation of symmetry that are either expected or desired can have important consequences for a system.


In organisms

Due to how
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
divide in
organism In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells ( cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and ...
s, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension. Louis Pasteur proposed that biological molecules are asymmetric because the cosmic .e. physicalforces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time.


Asymmetry in biology

Asymmetry is an important and widespread trait, having evolved numerous times in many organisms and at many levels of organisation (ranging from individual cells, through organs, to entire body-shapes). Benefits of asymmetry sometimes have to do with improved spatial arrangements, such as the left
human Humans (''Homo sapiens'') are the most abundant and widespread species of primate, characterized by bipedalism and exceptional cognitive skills due to a large and complex brain. This has enabled the development of advanced tools, culture, ...
lung The lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side ...
being smaller, and having one fewer lobes than the right lung to make room for the asymmetrical
heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to ...
. In other examples, division of function between the right and left half may have been beneficial and has driven the asymmetry to become stronger. Such an explanation is usually given for mammal hand or paw preference ( handedness), an asymmetry in skill development in mammals. Training the neural pathways in a skill with one hand (or paw) may take less effort than doing the same with both hands. Nature also provides several examples of handedness in traits that are usually symmetric. The following are examples of animals with obvious left-right asymmetries: *Most
snail A snail is, in loose terms, a shelled gastropod. The name is most often applied to land snails, terrestrial pulmonate gastropod molluscs. However, the common name ''snail'' is also used for most of the members of the molluscan class Ga ...
s, because of torsion during development, show remarkable asymmetry in the shell and in the internal organs. *
Fiddler crab The fiddler crab or calling crab may be any of more than one hundred species of semiterrestrial marine crabs in the family Ocypodidae, well known for their sexually dimorphic claws; the males' major claw is much larger than the minor claw, while ...
s have one big claw and one small claw. *The
narwhal The narwhal, also known as a narwhale (''Monodon monoceros''), is a medium-sized toothed whale that possesses a large " tusk" from a protruding canine tooth. It lives year-round in the Arctic waters around Greenland, Canada and Russia. It is ...
's tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix. *
Flatfish A flatfish is a member of the ray-finned demersal fish order Pleuronectiformes, also called the Heterosomata, sometimes classified as a suborder of Perciformes. In many species, both eyes lie on one side of the head, one or the other migratin ...
have evolved to swim with one side upward, and as a result have both eyes on one side of their heads. *Several species of
owl Owls are birds from the order Strigiformes (), which includes over 200 species of mostly solitary and nocturnal birds of prey typified by an upright stance, a large, broad head, binocular vision, binaural hearing, sharp talons, and feathers a ...
s exhibit asymmetries in the size and positioning of their ears, which is thought to help locate prey. *Many animals (ranging from insects to mammals) have asymmetric male
genitalia A sex organ (or reproductive organ) is any part of an animal or plant that is involved in sexual reproduction. The reproductive organs together constitute the reproductive system. In animals, the testis in the male, and the ovary in the female, ...
. The evolutionary cause behind this is, in most cases, still a mystery.


As an indicator of unfitness

*Certain disturbances during the development of the organism, resulting in
birth defect A birth defect, also known as a congenital disorder, is an abnormal condition that is present at birth regardless of its cause. Birth defects may result in disabilities that may be physical, intellectual, or developmental. The disabilities can ...
s. *Injuries after cell division that cannot be biologically repaired, such as a lost
limb Limb may refer to: Science and technology *Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, t ...
from an accident. Since birth defects and injuries are likely to indicate poor health of the organism, defects resulting in asymmetry often put an animal at a disadvantage when it comes to finding a mate. For example, a greater degree of
facial symmetry Facial symmetry is one specific measure of bodily symmetry. Along with traits such as averageness and youthfulness it influences judgments of aesthetic traits of physical attractiveness and beauty. For instance, in mate selection, people have b ...
is seen as more attractive in humans, especially in the context of mate selection. In general, there is a correlation between symmetry and fitness-related traits such as growth rate, fecundity and survivability for many species. This means that, through
sexual selection Sexual selection is a mode of natural selection in which members of one biological sex choose mates of the other sex to mate with (intersexual selection), and compete with members of the same sex for access to members of the opposite sex (int ...
, individuals with greater symmetry (and therefore fitness) tend to be preferred as mates, as they are more likely to produce healthy offspring.


In structures

Pre-modern architectural styles tended to place an emphasis on symmetry, except where extreme site conditions or historical developments lead away from this classical ideal. To the contrary,
modernist Modernism is both a philosophy, philosophical and arts movement that arose from broad transformations in Western world, Western society during the late 19th and early 20th centuries. The movement reflected a desire for the creation of new fo ...
and postmodern architects became much more free to use asymmetry as a design element. While most bridges employ a symmetrical form due to intrinsic simplicities of design, analysis and fabrication and economical use of materials, a number of modern bridges have deliberately departed from this, either in response to site-specific considerations or to create a dramatic design statement. Some asymmetrical structures File:ProposedSFOBBEasternSpan.jpg,
Eastern span replacement of the San Francisco – Oakland Bay Bridge Eastern may refer to: Transportation *China Eastern Airlines, a current Chinese airline based in Shanghai * Eastern Air, former name of Zambia Skyways * Eastern Air Lines, a defunct American airline that operated from 1926 to 1991 * Eastern Air ...
File:MujeresBridgeCropped IMG 5968.jpg,
Puente de la Mujer The Puente de la Mujer ( Spanish for "Woman's Bridge") is a rotating footbridge for Dock 3 of the Puerto Madero commercial district of Buenos Aires, Argentina. It is of the cantilever spar cable-stayed bridge type and is also a swing bridge, but ...
File:Auditorio de Tenerife Pano.jpg,
Auditorio de Tenerife The Auditorio de Tenerife "Adán Martín" (commonly referred to as the Auditorio de Tenerife) is an auditorium in Santa Cruz de Tenerife, Canary Islands, Spain. Designed by architect Santiago Calatrava, it is located on the Avenue of the Constitu ...
File:Bundesarchiv Bild 146-1980-117-01, Aufklärungsflugzeug Blohm - Voß BV 141.jpg,
Blohm & Voss BV 141 The Blohm & Voss BV 141 was a World War II German tactical reconnaissance aircraft, notable for its uncommon structural asymmetry. Although the Blohm & Voss BV 141 performed well, it was never ordered into full-scale production, for reasons th ...
aircraft File:Munroe 1900 proa.jpg, A
proa Proas are various types of multi-hull outrigger sailboats of the Austronesian peoples. The terms were used for native Austronesian ships in European records during the Colonial era indiscriminately, and thus can confusingly refer to the ...
, a form of
outrigger canoe Outrigger boats are various watercraft featuring one or more lateral support floats known as outriggers, which are fastened to one or both sides of the main hull. They can range from small dugout canoes to large plank-built vessels. Outrigger ...


In fire protection

In fire-resistance rated wall assemblies, used in
passive fire protection Passive fire protection (PFP) is components or systems of a building or structure that slows or impedes the spread of the effects of fire or smoke without system activation, and usually without movement. Examples of passive systems include floor- ...
, including, but not limited to,
high-voltage transformer fire barriers High-voltage transformer fire barriers, or transformer firewalls, transformer ballistic firewalls, transformer blast walls, are outdoor countermeasures against cascading failures in a national electric grid. The purpose of these barriers, like co ...
, asymmetry is a crucial aspect of design. When designing a facility, it is not always certain, that in the event of
fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction Product (chemistry), products. At a certain point in the combustion reaction, called the ignition ...
, which ''side'' a fire may come from. Therefore, many building codes and fire test standards outline, that a symmetrical assembly, need only be
tested ''Tested'' is a live album by punk rock band Bad Religion. It was recorded in the USA, Canada, Germany, Estonia, Denmark, Italy and Austria, in 1996, and released in 1997. It is Bad Religion's second live album. Instead of using crowd microp ...
from one side, because both sides are the same. However, as soon as an assembly is asymmetrical, both sides must be tested and the test report is required to state the results for each side. In practical use, the lowest result achieved is the one that turns up in
certification listing A certification listing is a document used to guide installations of certified products, against which a field installation is compared to make sure that it complies with a regulation (e.g., a building code). Typically, products or items are req ...
s. Neither the test sponsor, nor the laboratory can go by an opinion or deduction as to which side was in more peril as a result of contemplated testing and then test only one side. Both must be tested in order to be compliant with test standards and
building code A building code (also building control or building regulations) is a set of rules that specify the standards for constructed objects such as buildings and non-building structures. Buildings must conform to the code to obtain planning permiss ...
s.


In mathematics

There are no ''a'' and ''b'' such that ''a'' < ''b'' and ''b'' < ''a''.''Introduction to Set Theory'', Third Edition, Revised and Expanded: Hrbacek, Jech. This form of asymmetry is an asymmetrical relation.


In chemistry

Certain molecules are
chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
; that is, they cannot be superposed upon their mirror image. Chemically identical molecules with different chirality are called ''enantiomers''; this difference in orientation can lead to different properties in the way they react with biological systems.


In physics

Asymmetry arises in physics in a number of different realms.


Thermodynamics

The original non-statistical formulation of
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
was asymmetrical in time: it claimed that the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
in a closed system can only increase with time. This was derived from the Second Law (any of the two,
Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's princip ...
' or
Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...
's statement can be used since they are equivalent) and using the Clausius' Theorem (see Kerson Huang ). The later theory of statistical mechanics, however, is symmetric in time. Although it states that a system significantly below maximum entropy is very likely to evolve ''towards'' higher entropy, it also states that such a system is very likely to have evolved ''from'' higher entropy.


Particle physics

Symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
is one of the most powerful tools in
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, because it has become evident that practically all laws of nature originate in symmetries. Violations of symmetry therefore present theoretical and experimental puzzles that lead to a deeper understanding of nature. Asymmetries in experimental measurements also provide powerful handles that are often relatively free from background or systematic uncertainties.


Parity violation

Until the 1950s, it was believed that fundamental physics was left-right symmetric; i.e., that interactions were invariant under parity. Although parity is conserved in
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
, strong interactions and
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
, it turns out to be violated in weak interactions. The
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
incorporates parity violation by expressing the weak interaction as a
chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model. A consequence of parity violation in particle physics is that
neutrinos A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass i ...
have only been observed as left-handed particles (and antineutrinos as right-handed particles). In 1956–1957
Chien-Shiung Wu ) , spouse = , residence = , nationality = ChineseAmerican , field = Physics , work_institutions = Institute of Physics, Academia SinicaUniversity of California at BerkeleySmith CollegePrinceton UniversityColumbia UniversityZhejiang Unive ...
, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson found a clear violation of parity conservation in the beta decay of cobalt-60. Simultaneously, R. L. Garwin,
Leon Lederman Leon, Léon (French) or León (Spanish) may refer to: Places Europe * León, Spain, capital city of the Province of León * Province of León, Spain * Kingdom of León, an independent state in the Iberian Peninsula from 910 to 1230 and again fr ...
, and R. Weinrich modified an existing cyclotron experiment and immediately verified parity violation.


CP violation

After the discovery of the violation of parity in 1956–57, it was believed that the combined symmetry of parity (P) and simultaneous
charge conjugation In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
(C), called ''CP'', was preserved. For example, CP transforms a left-handed neutrino into a right-handed antineutrino. In 1964, however, James Cronin and
Val Fitch Val Logsdon Fitch (March 10, 1923 – February 5, 2015) was an American nuclear physicist who, with co-researcher James Cronin, was awarded the 1980 Nobel Prize in Physics for a 1964 experiment using the Alternating Gradient Synchrotron at Broo ...
provided clear evidence that CP symmetry was also violated in an experiment with neutral kaons. CP violation is one of the necessary conditions for the generation of a baryon asymmetry in the early universe. Combining the CP symmetry with simultaneous time reversal (T) produces a combined symmetry called
CPT symmetry Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and ...
. CPT symmetry must be preserved in any
Lorentz invariant In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of v ...
local
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
with a
Hermitian {{Short description, none Numerous things are named after the French mathematician Charles Hermite (1822–1901): Hermite * Cubic Hermite spline, a type of third-degree spline * Gauss–Hermite quadrature, an extension of Gaussian quadrature me ...
Hamiltonian. As of 2006, no violations of CPT symmetry have been observed.


Baryon asymmetry of the universe

The baryons (i.e., the
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
and
neutrons The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave ...
and the atoms that they comprise) observed so far in the universe are overwhelmingly
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic parti ...
as opposed to
anti-matter In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioact ...
. This asymmetry is called the
baryon asymmetry In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem, is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antib ...
of the universe.


Isospin violation

Isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
is the symmetry transformation of the weak interactions. The concept was first introduced by
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a Über quantentheoretische Umdeutung kinematis ...
in
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies t ...
based on the observations that the masses of the
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beha ...
and the
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
are almost identical and that the strength of the
strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the ...
between any pair of nucleons is the same, independent of whether they are protons or neutrons. This symmetry arises at a more fundamental level as a symmetry between up-type and down-type
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
s. Isospin symmetry in the strong interactions can be considered as a subset of a larger flavor symmetry group, in which the strong interactions are invariant under interchange of different types of quarks. Including the
strange quark The strange quark or s quark (from its symbol, s) is the third lightest of all quarks, a type of elementary particle. Strange quarks are found in subatomic particles called hadrons. Examples of hadrons containing strange quarks include kaons (), ...
in this scheme gives rise to the Eightfold Way scheme for classifying mesons and baryons. Isospin is violated by the fact that the masses of the up and down quarks are different, as well as by their different electric charges. Because this violation is only a small effect in most processes that involve the strong interactions, isospin symmetry remains a useful calculational tool, and its violation introduces corrections to the isospin-symmetric results.


In collider experiments

Because the
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
s violate parity,
collider A collider is a type of particle accelerator which brings two opposing particle beams together such that the particles collide. Colliders may either be ring accelerators or linear accelerators. Colliders are used as a research tool in particle ...
processes that can involve the weak interactions typically exhibit asymmetries in the distributions of the final-state particles. These asymmetries are typically sensitive to the ''difference'' in the interaction between particles and antiparticles, or between left-handed and right-handed particles. They can thus be used as a sensitive measurement of differences in interaction strength and/or to distinguish a small asymmetric signal from a large but symmetric background. *A forward-backward asymmetry is defined as AFB=(NF-NB)/(NF+NB), where NF is the number of events in which some particular final-state particle is moving "forward" with respect to some chosen direction (e.g., a final-state electron moving in the same direction as the initial-state electron beam in electron-positron collisions), while NB is the number of events with the final-state particle moving "backward". Forward-backward asymmetries were used by the LEP experiments to measure the difference in the interaction strength of the Z boson between left-handed and right-handed fermions, which provides a precision measurement of the weak mixing angle. *A left-right asymmetry is defined as ALR=(NL-NR)/(NL+NR), where NL is the number of events in which some initial- or final-state particle is left-polarized, while NR is the corresponding number of right-polarized events. Left-right asymmetries in Z boson production and decay were measured at the Stanford Linear Collider using the event rates obtained with left-polarized versus right-polarized initial electron beams. Left-right asymmetries can also be defined as asymmetries in the polarization of final-state particles whose polarizations can be measured; e.g., tau leptons. *A charge asymmetry or particle-antiparticle asymmetry is defined in a similar way. This type of asymmetry has been used to constrain the
parton distribution functions In particle physics, the parton model is a model of hadrons, such as protons and neutrons, proposed by Richard Feynman. It is useful for interpreting the cascades of radiation (a parton shower) produced from quantum chromodynamics (QCD) processes a ...
of protons at the
Tevatron The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collide ...
from events in which a produced
W boson In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and ...
decays to a charged lepton. The asymmetry between positively and negatively charged leptons as a function of the direction of the W boson relative to the proton beam provides information on the relative distributions of up and down quarks in the proton. Particle-antiparticle asymmetries are also used to extract measurements of CP violation from B meson and anti-B meson production at the
BaBar Babar ( ur, ), also variously spelled as Baber, Babur, and Babor is a male given name of Pashto, and Persian origin, and a popular male given name in Pakistan. It is generally taken in reference to the Persian ''babr'' ( Persian: ببر), meani ...
and Belle experiments.


Lexical

Asymmetry is also relevant to
grammar In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes domain ...
and
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 structure. Ling ...
, especially in the contexts of
lexical analysis In computer science, lexical analysis, lexing or tokenization is the process of converting a sequence of characters (such as in a computer program or web page) into a sequence of ''lexical tokens'' ( strings with an assigned and thus identified ...
and transformational grammar. Enumeration example: In
English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...
, there are grammatical rules for specifying coordinate items in an enumeration or series. Similar rules exist for
programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...
s and
mathematical notation Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathem ...
. These rules vary, and some require lexical asymmetry to be considered grammatically correct. For example, in standard written English: We sell domesticated cats, dogs, and goldfish. ### in-line asymmetric and grammatical We sell domesticated animals (cats, dogs, goldfish). ### in-line symmetric and grammatical We sell domesticated animals (cats, dogs, goldfish,). ### in-line symmetric and ungrammatical We sell domesticated animals: ### outline symmetric and grammatical - cats - dogs - goldfish


See also

*
Information asymmetry In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. Information asymmetry creates an imbalance of power in transactions, which can ...
*
Asymmetric multiprocessing An asymmetric multiprocessing (AMP or ASMP) system is a multiprocessor computer system where not all of the multiple interconnected central processing units (CPUs) are treated equally. For example, a system might allow (either at the hardware or op ...


References


Further reading

* Gardner, Martin (1990), '' The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings, 3rd edition'', W.H.Freeman & Co Ltd. * {{Authority control * Passive fire protection