Where does homology collide?

In comparative anatomy, two structures are homologous when they descend from the same structure in a shared ancestor, whatever their present form or function. Richard Owen's 1843 Lectures on the Comparative Anatomy and Physiology of the Invertebrate Animals coined the term, defining a homologue as the same organ in different animals under every variety of form and function, set against an analogue that merely shares a job. Wagner's 2007 The developmental genetics of homology recast the idea in terms of shared developmental and genetic origin. The referent is an inherited correspondence between body parts, such as the human arm and the bat wing, and it is not a group built from cycles in a space, a chemical family differing by a fixed unit, or a matching of structures across a society.[1][2]

Unit

A pair of structures judged to descend from one structure in a common ancestor

Recovery means

Not applicable

Measured by

Assessed by comparative anatomy, embryology, and molecular and genetic evidence of shared descent

In organic chemistry, a homologous series is a set of compounds that share one general formula and differ from each neighbour by a constant unit, the CH2 group. Charles Gerhardt's Précis de chimie organique (1844) grouped organic compounds into such series, whose members rise by a fixed increment and vary smoothly in their physical properties. The alkanes methane, ethane, and propane form one such series. The referent is a graded family of molecules ordered by a repeating addition, and it is not an inherited body part, a group built from cycles in a space, or a correspondence between social structures.[3]

Unit

One compound within a series set apart from its neighbours by one CH2 unit

Recovery means

Not applicable

Measured by

Identified by a shared general formula and the regular change in boiling point, melting point, and reactivity along the series

In algebraic topology, homology assigns to a space a sequence of groups that count its holes of each dimension, treating two loops as the same when together they bound a filled-in region. Henri Poincaré's 1895 Analysis situs introduced homologies and homologous cycles, building on the earlier counting of Enrico Betti, and later work turned these into the homology groups. Hatcher's 2002 Algebraic Topology gives the standard modern treatment. The referent is an algebraic invariant that distinguishes shapes, such as telling a sphere from a doughnut by their holes, and it is not an inherited body part, a chemical family, or a correspondence between social structures.[4][5]

Unit

One homology group per dimension, its rank counting the independent holes of that dimension

Recovery means

Not applicable

Measured by

Computed from a chain complex built on a triangulation or cell structure by taking cycles modulo boundaries

In cultural sociology, structural homology is a correspondence of form between two orders, so that the pattern of a group's tastes or cultural products matches the pattern of its position in society. Lucien Goldmann's 1964 Pour une sociologie du roman used homology for the fit between the structure of the novel and the structure of a market economy. Pierre Bourdieu's 1984 Distinction made it central, mapping the space of lifestyles onto the space of social positions, and Paul Willis's 1977 Learning to Labour traced a like fit between school and shop-floor culture. The referent is a matching of patterns across a society, read from surveys and ethnography, and it is not an inherited body part, a chemical family, or a group built from the holes of a space.[6][7][8]

Unit

One correspondence between a cultural pattern and a social-structural pattern

Recovery means

Not applicable

Measured by

Traced through survey mapping of tastes onto class positions and through ethnographic comparison of cultural forms