What is "homology"

Homology \Ho*mol"o*gy\, n. [Gr. ? agreement. See Homologous.]

1. The quality of being homologous; correspondence; relation; as, the homologyof similar polygons.

2. (Biol.) Correspondence or relation in type of structure in contradistinction to similarity of function; as, the relation in structure between the leg and arm of a man; or that between the arm of a man, the fore leg of a horse, the wing of a bird, and the fin of a fish, all these organs being modifications of one type of structure.

   Note: Homology indicates genetic relationship, and according to Haeckel special homology should be defined in terms of identity of embryonic origin. See Homotypy, and Homogeny.

3. (Chem.) The correspondence or resemblance of substances belonging to the same type or series; a similarity of composition varying by a small, regular difference, and usually attended by a regular variation in physical properties; as, there is an homology between methane, CH4, ethane, C2H6, propane, C3H8, etc., all members of the paraffin series. In an extended sense, the term is applied to the relation between chemical elements of the same group; as, chlorine, bromine, and iodine are said to be in homology with each other. Cf. Heterology.

   General homology (Biol.), the higher relation which a series of parts, or a single part, bears to the fundamental or general type on which the group is constituted.
   --Owen.

   Serial homology (Biol.), representative or repetitive relation in the segments of the same organism, -- as in the lobster, where the parts follow each other in a straight line or series.
   --Owen. See Homotypy.

   Special homology (Biol.), the correspondence of a part or organ with those of a different animal, as determined by relative position and connection.
   --Owen.

n. 1 A homologous relationship. 2 (context biology English) A correspondence of structures in two life forms with a common evolutionary origin, such as flippers and hands. 3 (context chemistry English) The relationship between the elements in the same group of the periodic table, or between organic compounds in a homologous series. 4 (context topology English) A theory associating a system of groups to each topological space. 5 (context algebra English) A certain system of groups associated to a chain complex. 6 (context genetics English) The presence of the same series of bases in related genes.

n. the quality of being similar or corresponding in position or value or structure or function

Homology may refer to:

• Homology (anthropology), analogy between human beliefs, practices or artifacts owing to genetic or historical connections
• Homology (biology), any characteristic of biological organisms that is derived from a common ancestor.
• Homology (chemistry), the relationship between compounds in a homologous series
• Homology (mathematics), a procedure to associate a sequence of abelian groups or modules with a given mathematical object
• Homology modeling, a method of protein structure prediction
• Homology (psychology), behavioral characteristics that have common origins in either evolution or development
• Homology (sociology), a structural 'resonance' between the different elements making up a socio-cultural whole

Homologous may refer to:

• Homologous chromosomes, chromosomes in a biological cell that pair up (synapse) during meiosis
• Homologous genes, DNA sequences or organs, biological features related by evolutionary ancestry; see Homology (biology)
• Homologous behaviors, behaviors typical of species that share a common ancestor that was characterized by that behavior OR behaviors in an individual that share common origins in development; see Homology (psychology)
• Homologous desensitization, a receptor decreases its response to a signalling molecule when that agonist is in high concentration
• Homologous recombination, genetic recombination in which nucleotide sequences are exchanged between molecules of DNA
• Homologous series (chemistry), a series of organic compounds having different quantities of a repeated unit
• Homologous temperature, the temperature of a material as a fraction of its absolute melting point

Homological may refer to:

• Homological word, a word expressing a property which it possesses itself
• Homological algebra, a branch of mathematics

Homologation may refer to:

• Homologation, from the ancient Greek "to agree", to indicate the approval of a sanctioning body
• Homologation (motorsport), the process in motorsports where the sanctioning body approves a racing model for official use
• Homologation reaction is a chemical reaction which produces the next logical member of a homologous series

In anthropology and archaeology, homology is a type of analogy whereby two human beliefs, practices or artifacts are separated by time but share similarities due to genetic or historical connections. Specifically in anthropology, a homology is a structure that is shared through descent from a common ancestor.

The concept was explored by the American archaeologist William Duncan Strong in his direct historical approach to archaeological theory.

In chemistry, homology refers to the appearance of homologues. A homologue (also spelled as homolog) is a compound belonging to a series of compounds differing from each other by a repeating unit, such as a methylene bridge −−, a peptide residue, etc. A homolog is a special case of an analog. Examples are alkanes and compounds with alkyl side chains of different length (the repeating unit being a methylene group -CH-).

In the context of biology, homology is the existence of shared ancestry between a pair of structures, or genes, in different taxa. A common example of homologous structures in evolutionary biology are the wings of bats and the arms of primates. Evolutionary theory explains the existence of homologous structures adapted to different purposes as the result of descent with modification from a common ancestor.

In the context of sexual differentiation—the process of development of the differences between males and females from an undifferentiated fertilized egg — the male and female organs are homologous if they develop from the same embryonic tissue. A typical example is the ovaries of female humans and the testicles of male humans.

In the context of morphological differentiation, organs that developed in the same embryological manner from similar origins, such as from matching primordia in successive segments of the same organism, may be said to be homologous. Examples include the legs of a centipede, the maxillary palp and labial palp of an insect, and the spinous processes of successive vertebrae in a vertebral column. In contrast, a sesamoid bone such as the patella would not in any usual sense be regarded as homologous to a neighbouring skeletal bone such as the femur.

In mathematics (especially algebraic topology and abstract algebra), homology (in part from Greek ὁμός homos "identical") is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. However, similar constructions are available in a wide variety of other contexts, such as groups, Lie algebras, Galois theory, and algebraic geometry.

The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defining and categorizing holes in a manifold. Loosely speaking, a cycle is a closed submanifold, a boundary is the boundary of a submanifold with boundary, and a homology class (which represents a hole) is an equivalence class of cycles modulo boundaries.

There are many different homology theories. A particular type of mathematical object, such as a topological space or a group, may have one or more associated homology theories. When the underlying object has a geometric interpretation like topological spaces do, the nth homology group represents behavior unique to dimension n. In general, most homology groups or modules arise as derived functors on appropriate abelian categories. They provide concrete descriptions of the failure of a functor to be exact. From this abstract perspective, homology groups are determined by objects of a derived category.

Homologies are "structural 'resonances'...between the different elements making up a socio-cultural whole." (Middleton 1990, p. 9)

Examples include Alan Lomax's cantometrics, which:

Distinguishes ten musical styles, dealing most fully with Eurasian and Old European styles. These are correlated with sexual permissiveness, status of women, and treatment of children as the principal formative social influences. The musical styles are at the same time symbolic or expressive of such social influences, especially in the various musical communities of Spain and Italy, and are stable, persistent. Lomax states his expectation that further study and refinement of methods of measurement will increase our understanding of the relationships of musical style and culture in a way that Western European musical notation cannot adequately accomplish.

Richard Middleton (1990, p. 9-10) argues that "such theories always end up in some kind of reductionism - 'upwards', into an idealist cultural spirit, 'downwards', into economism, sociologism or technologism, or by 'circumnavigation', in a functionalist holism." However, he "would like to hang on to the notion of homology in a qualified sense. For it seems likely that some signifying structures are more easily articulated to the interests of one group than are some others; similarly, that they are more easily articulated to the interests of one group than to those of another. This is because, owing to the existence of what Paul Willis calls the ' objective possibilities' (and limitations) of material and ideological structures, it is easier to find links and analogies between them in some cases than in others (Willis 1978: 198-201)."

Homology in psychology, like homology in biology, refers to a relationship between characteristics that reflects the characteristics' origins in either evolution or development. Homologous behaviors can theoretically be of at least two different varieties. As with homologous anatomical characteristics, behaviors present in different species can be considered homologous if they are likely present in those species because the behaviors were present in a common ancestor of the two species. Alternatively, in much the same way as reproductive structures (e.g., the penis and the clitoris) are considered homologous because they share a common origin in embryonic tissues, behaviors—or the neural substrates associated with those behaviors—can also be considered homologous if they share common origins in development.

Behavioral homologies have drawn the attention of theorists at least since 1958 when the Nobel Prize-winning ethologist Konrad Lorenz concerned himself with the evolution of behavior. More recently, the question of behavioral homologies has been addressed by philosophers of science such as Marc Ereshefsky, psychologists such as Drew Rendall, and neuroscientists such as Georg Striedter and Glenn Northcutt.