Editing Emergence (section)

==In science==
In [[physics]], emergence is used to describe a property, law, or phenomenon which occurs at macroscopic scales (in space or time) but not at microscopic scales, despite the fact that a macroscopic system can be viewed as a very large ensemble of microscopic systems.<ref>{{Cite book|last=Anderson|first=Philip W.|url=https://books.google.com/books?id=9HhQDwAAQBAJ|title=Basic Notions Of Condensed Matter Physics|date=2018-03-09|publisher=CRC Press|isbn=978-0-429-97374-1|language=en}}</ref><ref>{{Cite book|last1=Girvin|first1=Steven M.|url=https://books.google.com/books?id=2ESIDwAAQBAJ|title=Modern Condensed Matter Physics|last2=Yang|first2=Kun|date=2019-02-28|publisher=Cambridge University Press|isbn=978-1-108-57347-4|language=en}}</ref>

<blockquote>
An emergent behavior of a physical system is a qualitative property that can only occur in the limit that the number of microscopic constituents tends to infinity.<ref>{{cite journal |last1=Kivelson |first1=Sophia |last2=Kivelson |first2=Steve |title=Defining Emergence in Physics |journal=npj Quantum Materials |volume=1 |publisher=Nature Research |doi=10.1038/npjquantmats.2016.24 |year=2016 |issue=1 |page=16024 |doi-access=free |bibcode=2016npjQM...116024K }}</ref>
</blockquote>

According to [[Robert Laughlin]],{{sfn|Laughlin|2005}} for many-particle systems, nothing can be calculated exactly from the microscopic equations, and macroscopic systems are characterised by broken symmetry: the symmetry present in the microscopic equations is not present in the macroscopic system, due to phase transitions. As a result, these macroscopic systems are described in their own terminology, and have properties that do not depend on many microscopic details.

Novelist [[Arthur Koestler]] used the metaphor of [[Janus]] (a symbol of the unity underlying complements like open/shut, peace/war) to illustrate how the two perspectives (strong vs. weak or [[holistic]] vs. [[reductionistic]]) should be treated as non-exclusive, and should work together to address the issues of emergence.{{sfn|Koestler|1969}} Theoretical physicist [[Philip W. Anderson]] states it this way:

{{blockquote|The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.{{sfn|Anderson|1972}}}}

Meanwhile, others have worked towards developing analytical evidence of strong emergence. [[Renormalization group|Renormalization]] methods in theoretical physics enable physicists to study critical phenomena that are not tractable as the combination of their parts.<ref>{{Cite journal|last1= Longo|first1= Giuseppe|last2= Montévil|first2= Maël|last3= Pocheville|first3= Arnaud|date= 2012-01-01|title= From bottom-up approaches to levels of organization and extended critical transitions|journal= Frontiers in Physiology|volume= 3|page= 232|doi= 10.3389/fphys.2012.00232|pmc= 3429021|pmid= 22934001|doi-access= free}}</ref> In 2009, Gu ''et al.'' presented a class of infinite physical systems that exhibits non-computable macroscopic properties.<ref name="morereally">{{cite journal | last1 = Gu | first1 = Mile | display-authors = etal  | year = 2009 | title = More really is different | journal = Physica D: Nonlinear Phenomena | volume = 238 | issue = 9| pages = 835–39 | doi=10.1016/j.physd.2008.12.016| arxiv = 0809.0151 | bibcode = 2009PhyD..238..835G | s2cid = 61197980 }}</ref><ref name="binder">{{cite journal | last1 = Binder | first1 = P-M | year = 2009 | title = Computation: The edge of reductionism | journal = Nature | volume = 459 | issue = 7245| pages = 332–34 | doi=10.1038/459332a| pmid = 19458701 | bibcode = 2009Natur.459..332B| s2cid = 205046586 }}</ref> More precisely, if one could compute certain macroscopic properties of these systems from the microscopic description of these systems, then one would be able to solve computational problems known to be undecidable in computer science. These results concern infinite systems, finite systems being considered computable. However, macroscopic concepts which only apply in the limit of infinite systems, such as [[phase transition]]s and the [[renormalization group]], are important for understanding and modeling real, finite physical systems. Gu ''et al.'' concluded that

{{blockquote|Although macroscopic concepts are essential for understanding our world, much of fundamental physics has been devoted to the search for a 'theory of everything', a set of equations that perfectly describe the behavior of all fundamental particles. The view that this is the goal of science rests in part on the rationale that such a theory would allow us to derive the behavior of all macroscopic concepts, at least in principle. The evidence we have presented suggests that this view may be overly optimistic. A 'theory of everything' is one of many components necessary for complete understanding of the universe, but is not necessarily the only one. The development of macroscopic laws from first principles may involve more than just systematic logic, and could require conjectures suggested by experiments, simulations or insight.<ref name="morereally" />}}