Asymmetry is the absence of, or a violation of, symmetry

Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...

.

In organisms

Due to how cell

Cell (biology)

The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....

s divide in organism

Organism

In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

s, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry

Symmetry (biology)

Symmetry in biology is the balanced distribution of duplicate body parts or shapes. The body plans of most multicellular organisms exhibit some form of symmetry, either radial symmetry or bilateral symmetry or "spherical symmetry". A small minority exhibit no symmetry .In nature and biology,...

 also being common in at least one dimension.

Louis Pasteur proposed that biological molecules are asymmetric because the cosmic [i.e. physical] forces 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. Further, truly fundamental left-right symmetry violation is now known in particle physics (see Parity violation below).

Phylum Porifera consisting of sponges in largely known to be asymmetrical.

Usefulness to organisms

Asymmetry and important evolutionary traits, such as the left human

Human

Humans are the only living species in the Homo genus...

 lung

Lung

The lung is the essential respiration organ in many air-breathing animals, including most tetrapods, a few fish and a few snails. In mammals and the more complex life forms, the two lungs are located near the backbone on either side of the heart...

 being smaller, and having one fewer lobes than the right lung to make room for the asymmetrical heart

Heart

The heart is a myogenic muscular organ found in all animals with a circulatory system , that is responsible for pumping blood throughout the blood vessels by repeated, rhythmic contractions...

.

• Handedness
  Handedness
  Handedness is a human attribute defined by unequal distribution of fine motor skills between the left and right hands. An individual who is more dexterous with the right hand is called right-handed and one who is more skilled with the left is said to be left-handed...
  
   is an asymmetry in skill development in people and animals. Training the neural pathways in a skill with one hand (or paw) takes 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:

• Fiddler crab
  Fiddler crab
  A fiddler crab, sometimes known as a calling crab, may be any of approximately 100 species of semi-terrestrial marine crabs which make up the genus Uca. As members of the family Ocypodidae, fiddler crabs are most closely related to the ghost crabs of the genus Ocypode. This entire group is composed...
  
  s have one big claw and one small claw.
• The narwhal
  Narwhal
  The narwhal, Monodon monoceros, is a medium-sized toothed whale that lives year-round in the Arctic. One of two living species of whale in the Monodontidae family, along with the beluga whale, the narwhal males are distinguished by a characteristic long, straight, helical tusk extending from their...
  
  's tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix.
• Flatfish
  Flatfish
  The flatfish are an order of ray-finned fish, 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 migrating through and around the head during development...
  
   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
  Owl
  Owls are a group of birds that belong to the order Strigiformes, constituting 200 bird of prey species. Most are solitary and nocturnal, with some exceptions . Owls hunt mostly small mammals, insects, and other birds, although a few species specialize in hunting fish...
  
  s exhibit asymmetries in the size and positioning of their ears, which is thought to help locate prey.

As an indicator of unfitness

• Certain disturbances during the development of the organism, resulting in birth defects.
• Injuries after cell division that cannot be biologically repaired, such as a lost limb
  Limb (anatomy)
  A limb is a jointed, or prehensile , appendage of the human or other animal body....
  
   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. In particular, a degree of facial symmetry

Facial symmetry

Facial symmetry, is one element of bodily symmetry, including fluctuating asymmetry. Along with traits such as averageness and youthfulness it influences judgements of aesthetic traits of physical attractiveness and beauty, and is associated with fitness-linked traits including health, It is also...

 is associated with physical attractiveness, but complete symmetry is both impossible and probably unattractive.

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 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

In chemistry

Certain molecules are chiral

Chirality (chemistry)

A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....

; that is, they cannot be superposed upon their mirror image.

Thermodynamics

The original non-statistical formulation of thermodynamics

Thermodynamics

Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

 was asymmetrical in time

Entropy (arrow of time)

Entropy is the only quantity in the physical sciences that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase...

: it claimed that the entropy

Entropy

Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 in a closed system can only increase with time. A consequence of this is Clausius' Second Law, which states that there is no thermodynamic process whose sole effect is to extract a quantity of heat from a colder reservoir and deliver it to a hotter reservoir. 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 in physics

In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...

 is one of the most powerful tools in particle physics

Particle physics

Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, 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

Parity (physics)

In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

. Although parity is conserved in electromagnetism

Electromagnetism

Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

, strong interactions and gravity, it turns out to be violated in weak interactions. The Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

 incorporates parity violation by expressing the weak interaction as a chiral

Chirality (physics)

A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...

 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 have only been observed as left-handed particles (and antineutrinos as right-handed particles).

In 1956-1957 Chien-Shiung Wu

Chien-Shiung Wu

Chien-Shiung Wu was a Chinese-American physicist with expertise in the techniques of experimental physics and radioactivity. Wu worked on the Manhattan Project...

, 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

Richard Garwin

Richard Lawrence Garwin , is an American physicist. He received his bachelor's degree from the Case Institute of Technology in 1947 and obtained his Doctor of Philosophy from the University of Chicago in 1949, where he worked in the lab of Enrico Fermi.Garwin is IBM Fellow Emeritus at the Thomas J...

, Leon Lederman, 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 (C), called CP, was preserved. For example, CP transforms a left-handed neutrino into a right-handed antineutrino. In 1964, however, James Cronin

James Cronin

James Watson Cronin is an American nuclear physicist.Cronin was born in Chicago, Illinois and attended Southern Methodist University in Dallas, Texas. Cronin and co-researcher Val Logsdon Fitch were awarded the 1980 Nobel Prize in Physics for a 1964 experiment that proved that certain subatomic...

 and Val Fitch 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 universe.

Combining the CP symmetry with simultaneous time reversal

T-symmetry

T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

 (T) produces a combined symmetry called CPT symmetry

CPT symmetry

CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

. CPT symmetry must be preserved in any Lorentz invariant local quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

 with a Hermitian

Self-adjoint operator

In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is an operator that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose...

 Hamiltonian

Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...

. As of 2006, no violations of CPT symmetry have been observed.

Baryon asymmetry of the universe

The baryons (i.e., the protons and neutrons and the atoms that they comprise) observed in the universe are overwhelmingly matter

Matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

 as opposed to anti-matter. This asymmetry is called the baryon asymmetry

Baryon asymmetry

The baryon asymmetry problem in physics refers to the apparent fact that there is an imbalance in baryonic matter and antibaryonic matter in the universe. Neither the standard model of particle physics, nor the theory of general relativity provide an obvious explanation for why this should be so;...

 of the universe.

Isospin violation

Isospin

Isospin

In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...

 is the symmetry transformation of the weak interactions. The concept was first introduced by Werner Heisenberg

Werner Heisenberg

Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

 in nuclear physics

Nuclear physics

Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

 based on the observations that the masses of the neutron

Neutron

The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 and the proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 are almost identical and that the strength of the strong interaction

Strong interaction

In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...

 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

Quark

A quark is an 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. Due to a phenomenon known as color confinement, quarks are never directly...

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

Strange quark

The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...

 in this scheme gives rise to the Eightfold Way

Eightfold way (physics)

In physics, the Eightfold Way is a term coined by American physicist Murray Gell-Mann for a theory organizing subatomic baryons and mesons into octets...

 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

Weak interaction

Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

s violate parity, collider

Collider

A collider is a type of a particle accelerator involving directed beams of particles.Colliders may either be ring accelerators or linear accelerators.-Explanation:...

 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 A_FB=(N_F-N_B)/(N_F+N_B), where N_F 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 N_B 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 A_LR=(N_L-N_R)/(N_L+N_R), where N_L is the number of events in which some initial- or final-state particle is left-polarized, while N_R 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 lepton
  Tau lepton
  The tau , also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Together with the electron, the muon, and the three neutrinos, it is classified as a lepton...
  
  s.
• 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
  Parton (particle physics)
  In particle physics, the parton model was proposed by Richard Feynman in 1969 as a way to analyze high-energy hadron collisions. It was later recognized that partons describe the same objects now more commonly referred to as quarks and gluons...
  
   of protons at the Tevatron
  Tevatron
  The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
  
   from events in which a produced W boson 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
  Meson
  In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
  
   and anti-B meson production at the BaBar
  BaBar experiment
  The BaBar experiment, or simply BaBar, is an international collaboration of more than 500 physicists and engineers studying the subatomic world at energies of approximately ten times the rest mass of a proton . Its design was motivated by the investigation of CP violation...
  
   and Belle
  Belle experiment
  The Belle experiment is a particle physics experiment conducted by the Belle Collaboration, an international collaboration of more than 400 physicists and engineers investigating CP-violation effects at the High Energy Accelerator Research Organisation in Tsukuba, Ibaraki Prefecture, Japan.The...
  
   experiments.

Lexical

Asymmetry is also relevant to grammar

Grammar

In linguistics, grammar is the set of structural rules that govern the composition of clauses, phrases, and words in any given natural language. The term refers also to the study of such rules, and this field includes morphology, syntax, and phonology, often complemented by phonetics, semantics,...

 and linguistics

Linguistics

Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

, especially in the contexts of lexical analysis

Lexical analysis

In computer science, lexical analysis is the process of converting a sequence of characters into a sequence of tokens. A program or function which performs lexical analysis is called a lexical analyzer, lexer or scanner...

 and transformational grammar

Transformational grammar

In linguistics, a transformational grammar or transformational-generative grammar is a generative grammar, especially of a natural language, that has been developed in the Chomskyan tradition of phrase structure grammars...

.

Enumeration example:
In English

English language

English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

, there are grammatical rules for specifying coordinate items in an enumeration or series. Similar rules exist for programming language

Programming language

A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....

s and mathematical notation

Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...

. 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