Degeneracy, degenerate, or degeneration may refer to:

Arts and entertainment

* ''Degenerate'' (album), a 2010 album by the British band Trigger the Bloodshed * Degenerate art, a term adopted in the 1920s by the Nazi Party in Germany to describe modern art **

Decadent movement The Decadent movement (from the French language, French ''décadence'', ) was a late 19th-century Art movement, artistic and literary movement, literary movement, centered in Western Europe, that followed an aesthetic ideology of excess and artif ...

, often associated with degeneracy * Dégénération, a single by Mylène Farmer * ''Degeneration'' (Nordau), an 1892 book by Max Nordau * '' Resident Evil: Degeneration'', a 2008 film * "Degenerate", a song by Blink-182 from the album ''

Dude Ranch A guest ranch, also known as a dude ranch, is a type of ranch oriented towards visitors or tourism. It is considered a form of agrotourism. History Guest ranches arose in response to the romanticization of the American West that began to occur ...

'' * "Degenerates", a song by A Day to Remember from the album '' You're Welcome'' * "DEGENERATE", a 2024 song by

Starset Starset is an American Rock music, rock band from Columbus, Ohio, formed by Dustin Bates in 2013. They released their debut album, ''Transmissions (Starset album), Transmissions'', in 2014 and their second album, ''Vessels (Starset album), Vesse ...

Science, mathematics, and medicine

Mathematics

Degeneracy (mathematics) In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; "degeneracy" is the condition of being a degenerate case. The definiti ...

, a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class *

Degeneracy (graph theory) In graph theory, a -degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree (graph theory), degree at most k. That is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degener ...

, a measure of the sparseness of a graph *

Degeneration (algebraic geometry) In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism :\pi: \mathcal \to C, of a variety (or a scheme) to a curve ''C'' with origin 0 (e.g., affine or projective ...

, the act of taking a limit of a family of varieties * Degenerate bilinear form, a bilinear form on a vector space ''V'' whose induced map from ''V'' to the dual space of ''V'' is not an isomorphism *

Degenerate distribution In probability theory, a degenerate distribution on a measure space (E, \mathcal, \mu) is a probability distribution whose support is a null set with respect to \mu. For instance, in the -dimensional space endowed with the Lebesgue measure, an ...

, the probability distribution of a random variable which only takes a single value *

Degenerate conic In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the complex numbers (or more ...

, a conic (a second-degree plane curve, the points of which satisfy an equation that is quadratic in one or the other or both variables) that fails to be an irreducible curve *

Degenerate dimension According to Ralph Kimball, in a data warehouse, a degenerate dimension is a dimension key (primary key for a dimension table) in the fact table that does not have its own dimension table, because all the interesting attributes have been placed in ...

, a dimension key in the fact table that does not have its own dimension table, because all the interesting attributes have been placed in analytic dimensions. The term "degenerate dimension" was originated by Ralph Kimball

Quantum mechanics

Degenerate energy levels In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give th ...

, different arrangements of a physical system which have the same energy *

Degenerate matter Degenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal press ...

, a very highly compressed phase of matter which resists further compression because of quantum mechanical effects *

Degenerate semiconductor A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than a semiconductor. Unlike non-degenerate semiconductors, these kinds of semiconductor do not obey the law of mass a ...

, a semiconductor with such a high doping-level that the material starts to act more like a metal than as a semiconductor

Other uses in science and medicine

Degeneracy (biology) Within biological systems, degeneracy occurs when structurally dissimilar components/pathways can perform similar functions (i.e. are effectively interchangeable) under certain conditions, but perform distinct functions in other conditions. Degener ...

, the ability of elements that are structurally different to perform the same function or yield the same output **

Codon degeneracy Degeneracy or redundancy of codons is the redundancy of the genetic code, exhibited as the multiplicity of three-base pair codon combinations that specify an amino acid. The degeneracy of the genetic code is what accounts for the existence of syno ...

, in genetics *

Degeneration (medicine) Degeneration is deterioration in the medical sense. Generally, it is the change from a higher to a lower form. More specifically, it is the change of tissue to a lower or less functionally active form. * True degeneration: when there is actual ...

Degenerative disease Degenerative disease is the result of a continuous process based on degenerative cell changes, affecting tissues or organs, which will increasingly deteriorate over time. In neurodegenerative diseases, cells of the central nervous system stop wo ...

, a disease that causes deterioration over time *

Social degeneration Social degeneration was a widely influential concept at the interface of the social and biological sciences in the 18th and 19th centuries. During the 18th century, scientific thinkers including Georges-Louis Leclerc, Comte de Buffon, Johann Fri ...

, a late 19th–early 20th century sociological concept

Other uses

* Degeneration, a type of