Editing Symmetry (section)

==In science and nature==
{{Further|Patterns in nature}}

===In physics===
{{Main|Symmetry in physics}}

Symmetry in physics has been generalized to mean [[Invariant (physics)|invariance]]—that is, lack of change—under any kind of transformation, for example [[General covariance|arbitrary coordinate transformations]].<ref>{{cite book |title = Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries |first1 = Giovanni |last1 = Costa |first2=Gianluigi |last2=Fogli| publisher = Springer Science & Business Media |year = 2012 |page = 112}}</ref> This concept has become one of the most powerful tools of [[theoretical physics]], as it has become evident that practically all laws of nature originate in symmetries. In fact, this role inspired the Nobel laureate [[Philip Warren Anderson|PW Anderson]] to write in his widely read 1972 article ''More is Different'' that "it is only slightly overstating the case to say that physics is the study of symmetry."<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=[[Science (journal)|Science]] | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 |bibcode = 1972Sci...177..393A | s2cid=34548824 }}</ref> See [[Noether's theorem]] (which, in greatly simplified form, states that for every continuous mathematical symmetry, there is a corresponding conserved quantity such as energy or momentum; a conserved current, in Noether's original language);<ref name=Noether>{{Cite book | last = Kosmann-Schwarzbach | first = Yvette | author-link = Yvette Kosmann-Schwarzbach | title = The Noether theorems: Invariance and conservation laws in the twentieth century | publisher = [[Springer Science+Business Media|Springer-Verlag]] | series = Sources and Studies in the History of Mathematics and Physical Sciences | year = 2010 | isbn = 978-0-387-87867-6}}</ref> and also, [[Wigner's classification]], which says that the symmetries of the laws of physics determine the properties of the particles found in nature.<ref>{{citation|first=E. P.|last=Wigner|author-link=Eugene Wigner|title=On unitary representations of the inhomogeneous Lorentz group|journal=[[Annals of Mathematics]]|issue=1|volume=40|pages=149–204|year=1939|doi=10.2307/1968551|mr=1503456 |bibcode = 1939AnMat..40..149W |jstor=1968551|s2cid=121773411 }}</ref>

Important symmetries in physics include [[continuous symmetry|continuous symmetries]] and [[discrete symmetry|discrete symmetries]] of [[spacetime]]; [[internal symmetry|internal symmetries]] of particles; and [[supersymmetry]] of physical theories.

===In biology===
{{Further|symmetry in biology|facial symmetry}}
[[File:Chance and a Half, Posing.jpg|thumb|upright=0.8|Many animals are approximately mirror-symmetric, though internal organs are often arranged asymmetrically.]]
In biology, the notion of symmetry is mostly used explicitly to describe body shapes. [[Bilateria|Bilateral animals]], including humans, are more or less symmetric with respect to the [[sagittal plane]] which divides the body into left and right halves.<ref>{{cite web |last=Valentine |first=James W. |title=Bilateria |url=http://www.accessscience.com/abstract.aspx?id=802620&referURL=http%3a%2f%2fwww.accessscience.com%2fcontent.aspx%3fid%3d802620 |publisher=AccessScience |access-date=29 May 2013 |url-status=dead |archive-url=https://web.archive.org/web/20080118213208/http://www.accessscience.com/abstract.aspx?id=802620&referURL=http%3A%2F%2Fwww.accessscience.com%2Fcontent.aspx%3Fid%3D802620 |archive-date=18 January 2008 }}</ref> Animals that move in one direction necessarily have upper and lower sides, head and tail ends, and therefore a left and a right. The [[cephalisation|head becomes specialized]] with a mouth and sense organs, and the body becomes bilaterally symmetric for the purpose of movement, with symmetrical pairs of muscles and skeletal elements, though internal organs often remain asymmetric.<ref>{{cite web | url=http://biocongroup.eu/DA/Calendario_files/Bilateria.pdf | title=Animal Diversity (Third Edition) | publisher=McGraw-Hill | work=Chapter 8: Acoelomate Bilateral Animals | year=2002 | access-date=October 25, 2012 | author1=Hickman, Cleveland P. | author2=Roberts, Larry S. | author3=Larson, Allan | page=139 | archive-date=May 17, 2016 | archive-url=http://arquivo.pt/wayback/20160517212058/http://biocongroup.eu/DA/Calendario_files/Bilateria.pdf | url-status=dead }}</ref>

Plants and sessile (attached) animals such as [[sea anemone]]s often have radial or [[rotational symmetry]], which suits them because food or threats may arrive from any direction. Fivefold symmetry is found in the [[echinoderms]], the group that includes [[starfish]], [[sea urchin]]s, and [[sea lilies]].<ref>{{cite book | title=What Shape is a Snowflake? Magical Numbers in Nature | publisher=Weidenfeld & Nicolson | author=Stewart, Ian | year=2001 | pages=64–65}}</ref>

In biology, the notion of symmetry is also used as in physics, that is to say to describe the properties of the objects studied, including their interactions. A remarkable property of biological evolution is the changes of symmetry corresponding to the appearance of new parts and dynamics.<ref>{{cite book |url=https://www.springer.com/la/book/9783642359378 |title=Perspectives on Organisms: Biological time, Symmetries and Singularities |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |date=2016 |publisher=Springer  |isbn=978-3-662-51229-6 |language=en}}</ref><ref>{{cite journal |last1=Montévil |first1=Maël |last2=Mossio |first2=Matteo |last3=Pocheville |first3=Arnaud |last4=Longo |first4=Giuseppe |date=2016 |title=Theoretical principles for biology: Variation |url=https://www.academia.edu/27942089 |journal=Progress in Biophysics and Molecular Biology |series=From the Century of the Genome to the Century of the Organism: New Theoretical Approaches |volume=122 |issue=1 |pages=36–50 |doi=10.1016/j.pbiomolbio.2016.08.005|pmid=27530930 |s2cid=3671068 }}</ref>

===In chemistry===
{{Main|Molecular symmetry}}

Symmetry is important to [[chemistry]] because it undergirds essentially all ''specific'' interactions between molecules in nature (i.e.,  via the interaction of natural and human-made [[chiral (chemistry)|chiral]] molecules with inherently chiral biological systems). The control of the [[molecular symmetry|symmetry]] of molecules produced in modern [[chemical synthesis]] contributes to the ability of scientists to offer [[drug|therapeutic]] interventions with minimal [[side effects]]. A rigorous understanding of symmetry explains fundamental observations in [[quantum chemistry]], and in the applied areas of [[spectroscopy]] and [[crystallography]]. The theory and application of symmetry to these areas of [[physical science]] draws heavily on the mathematical area of [[group theory]].<ref>{{cite book |author1=Lowe, John P |author2=Peterson, Kirk | title=Quantum Chemistry | publisher=Academic Press| edition=Third | year=2005 | isbn=0-12-457551-X}}</ref>

===In psychology and neuroscience===
{{Further|Visual perception}}

For a human observer, some symmetry types are more salient than others, in particular the most salient is a reflection with a vertical axis, like that present in the human face. [[Ernst Mach]] made this observation in his book "The analysis of sensations" (1897),<ref>{{cite book |title = Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries | first1 = Ernst |last1 = Mach | publisher = Open Court Publishing House |year = 1897}}</ref> and this implies that perception of symmetry is not a general response to all types of regularities. Both behavioural and neurophysiological studies have confirmed the special sensitivity to reflection symmetry in humans and also in other animals.<ref>{{cite journal|author1=Wagemans, J.|title=Characteristics and models of human symmetry detection|journal=[[Trends in Cognitive Sciences]]|volume=1|issue=9|pages=346–352| year=1997|doi= 10.1016/S1364-6613(97)01105-4|pmid=21223945|s2cid=2143353|url=https://lirias.kuleuven.be/handle/123456789/207060}}</ref> Early studies within the [[Gestalt psychology|Gestalt]] tradition suggested that bilateral symmetry was one of the key factors in perceptual [[Principles of grouping|grouping]]. This is known as the [[Gestalt psychology#Law of Symmetry|Law of Symmetry]]. The role of symmetry in grouping and figure/ground organization has been confirmed in many studies. For instance, detection of reflectional symmetry is faster when this is a property of a single object.<ref>{{cite journal | author1=Bertamini, M.| title=Sensitivity to reflection and translation is modulated by objectness | journal=[[Perception (journal)|Perception]]| volume=39|pages=27–40| year=2010| issue=1 | doi=10.1068/p6393| pmid=20301844 | s2cid=22451173 }}</ref> Studies of human perception and psychophysics have shown that detection of symmetry is fast, efficient and robust to perturbations. For example, symmetry can be detected with presentations between 100 and 150 milliseconds.<ref>{{cite journal|author1=Barlow, H.B.|author2=Reeves, B.C.|title=The versatility and absolute efficiency of detecting mirror symmetry in random dot displays|journal=[[Vision Research]]|volume=19|issue=7|pages=783–793|year=1979|doi= 10.1016/0042-6989(79)90154-8|pmid=483597|s2cid=41530752}}</ref>

More recent neuroimaging studies have documented which brain regions are active during perception of symmetry. Sasaki et al.<ref>{{cite journal |author1=Sasaki, Y.|author2=Vanduffel, W.|author3=Knutsen, T.|author4=Tyler, C.W.|author5=Tootell, R.|title=Symmetry activates extrastriate visual cortex in human and nonhuman primates |journal=[[Proceedings of the National Academy of Sciences of the USA]]|volume=102|issue=8|pages=3159–3163|year=2005|doi= 10.1073/pnas.0500319102|pmid=15710884|pmc=549500|bibcode=2005PNAS..102.3159S|doi-access=free}}</ref> used functional magnetic resonance imaging (fMRI) to compare responses for patterns with symmetrical or random dots. A strong activity was present in extrastriate regions of the occipital cortex but not in the primary visual cortex. The extrastriate regions included V3A, V4, V7, and the lateral occipital complex (LOC). Electrophysiological studies have found a late posterior negativity that originates from the same areas.<ref>{{cite journal |author1=Makin, A.D.J. |author2=Rampone, G. |author3= Pecchinenda, A. |author4= Bertamini, M. |title= Electrophysiological responses to visuospatial regularity |journal=[[Psychophysiology]]| volume=50| pages= 1045–1055|year=2013|issue=10 |doi=10.1111/psyp.12082|pmid=23941638 }}</ref> In general, a large part of the visual system seems to be involved in processing visual symmetry, and these areas involve similar networks to those responsible for detecting and recognising objects.<ref>{{cite journal |author1=Bertamini, M.|author2=Silvanto, J. |author3=Norcia, A.M. |author4=Makin, A.D.J. |author5= Wagemans, J. |title=The neural basis of visual symmetry and its role in middle and high-level visual processing |journal=[[Annals of the New York Academy of Sciences]]|volume=132|pages=280–293|year=2018|issue=1 |doi=10.1111/nyas.13667|pmid=29604083 |bibcode=2018NYASA1426..111B |doi-access=free|hdl=11577/3289328 |hdl-access=free }}</ref>