Asymmetry is the absence of, or a violation of, symmetry. 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 violation of symmetry that are either expected or desired
can have important consequences for a system.
In organisms Due to how cells divide in organisms, 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 [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. Usefulness to organisms
Asymmetry and important evolutionary traits, such as the left human lung being smaller,
and having one fewer lobes than the right lung to make room for the asymmetrical heart.
Handedness is an asymmetry in skill development in people and animals. Training the neural
pathways in a skill with one hand 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 crabs have one big claw and one small claw.
The narwhal's tusk is a left incisor which can grow up to 10 feet in length and forms
a left-handed helix. Flatfish have evolved to swim with one side
upward, and as a result have both eyes on one side of their heads.
Several species of owls exhibit asymmetries in the size and positioning of their ears,
which is thought to help locate prey. Phylum Porifera consisting of sponges are
part of a small minority of species demonstrating almost no body symmetry. They are instead
evolved for maximal efficiency of water flow through their central cavity.
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 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 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 mathematics There are no a and b such that a < b and b
< a. This form of asymmetry is an asymmetrical relation
In chemistry Certain molecules are chiral; 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 was asymmetrical in time: it claimed that the entropy in a closed system
can only increase with time. This was derived from the Second Law and using the Clausius'
Theorem. 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 is one of the most powerful tools in particle physics, 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,
strong interactions and gravity, it turns out to be violated in weak interactions. The
Standard Model incorporates parity violation by expressing the weak interaction as a chiral
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.
In 1956-1957 Chien-Shiung Wu, 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, 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 and simultaneous charge conjugation, 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 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 produces a combined symmetry
called CPT symmetry. CPT symmetry must be preserved in any Lorentz invariant local quantum
field theory with a Hermitian Hamiltonian. As of 2006, no violations of CPT symmetry
have been observed. Baryon asymmetry of the universe
The baryons observed in the universe are overwhelmingly matter as opposed to anti-matter. This asymmetry
is called the baryon asymmetry of the universe. Isospin violation
Isospin is the symmetry transformation of the weak interactions. The concept was first
introduced by Werner Heisenberg in nuclear physics based on the observations that the
masses of the neutron and the proton are almost identical and that the strength of the strong
interaction 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 quarks. 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
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 interactions violate parity,
collider 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, 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 of protons at the Tevatron 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 and anti-B meson
production at the BaBar and Belle experiments. Lexical
Asymmetry is also relevant to grammar and linguistics, especially in the contexts of
lexical analysis and transformational grammar. Enumeration example: In English, there are
grammatical rules for specifying coordinate items in an enumeration or series. Similar
rules exist for programming languages and mathematical notation. 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. ### in-line symmetric and grammatical
We sell domesticated animals. ### in-line symmetric and ungrammatical
We sell domesticated animals: ### outline symmetric and grammatical
- cats - dogs
- goldfish
Other uses Asymmetric gameplay is a form of multiplayer
in video games, in which multiple players can play the same game simultaneously in different
ways. A strong example of this is Nintendo's Wii U console, which offers asymmetric gameplay
experiences via its Wii U GamePad. For example, in Rayman Legends, a player using a standard
controller can control the on-screen character, whilst a second player using the Wii U GamePad's
touchscreen can control an extra character that can manipulate the environment. Another
good example is the upcoming multiplayer game Evolve, which pits a team of four player-controlled
Hunters against a fifth player, who controls a giant Monster character.
See also Information asymmetry
Asymmetric multiprocessing References
^ Introduction to Set Theory, Third Edition, Revised and Expanded: Hrbacek, Jech.
Further reading Gardner, Martin, The New Ambidextrous Universe:
Symmetry and Asymmetry from Mirror Reflections to Superstrings, 3rd edition, W.H.Freeman
& Co Ltd. Yuh-Nung Jan and Lily Yeh Jan, 1999. Asymmetry
across species. Nature Cell Biology 1, E42 - E44 PMID 10559895