HOMOLOGY
What is homology?
"Homologous" is a technical term, defined by Webster's New World Dictionary as meaning agreeing, matching in structure, position, etc. The concise way to say this, is that things are "equivalent instances" - but that immediately raises complications. No two (or more) things can ever be "exactly the same" because each is composed of its own individual elements. What "homologous" identifies, therefore, is the sharing of certain features, which means that the members of the category display certain characteristics or patterns. Conceivably a number of things with a dozen features might only share one of them in common, but that one shared feature could be the basis for categorizing them as homologous ("equivalent instances") for some particular purpose.
Since things (or sets, or patterns, or structures, or situations) may display a multitude of features, the categorization process is more credible IF the criteria for the grouping is identified, and the rationale for the grouping is plausible (i.e., does it make sense, and does it [really] serve the purpose?). The possibility of a feature being shared only makes sense if the feature itself has a range of acceptable variation - blue things, even those of the "same" hue, are rarely all of precisely the same wavelength in Angstrom units - so this range of acceptable variation also needs to be specified. Inclusion on the basis of some variable also implies exclusion in the absence of the same variable.
How is homology used?
Homology is most often used to "qualify" something (in the sense that the term is used in marketing). To "qualify" as a good prospect, a customer must possess certain characteristics: sufficient disposable income to afford the product, an intrinsic or induced need for the product, etc. During categorization, those entities that qualify as homologous are equivalent enough to serve as the plausible basis for grouping together. Pose the questions: Why is this categorization necessary? and What will the grouping achieve? Problems often occur because the basis of categories is not clearly defined, nor their implications sufficiently thought through.
One of the maxims of mensuration (the act, process, or art of measuring) also serves for categorization: Let the degree of exactness reflect the purpose of the task. Measuring for the tolerance of components in a piece of precision machinery may require calipers or even electronic measuring devices. Estimating the length of one's stride while out walking does not require specification at the level of centimeters. Categorization should be practiced in the same pragmatic way. If the attribute for grouping is an important one, define it as exactly as needed for the grouping that is contemplated. If "close" is close enough, it may be best to keep the boundaries variable.
