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The solution to the apparent paradox lies in a distinction between two concepts of "perfection": that of regularity, and that of utility.Imperfection is perfect in technology, in the sense that irregularity is useful.The Greek equivalent of the Latin "perfectus" was "teleos." The latter Greek expression generally had concrete referents, such as a perfect physician or flutist, a perfect comedy or a perfect social system.Hence the Greek "teleiotes" was not yet so fraught with abstract and superlative associations as would be the Latin "perfectio" or the modern "perfection." To avoid the latter associations, the Greek term has generally been translated as "completeness" rather than "perfection." The oldest definition of "perfection", fairly precise and distinguishing the shades of the concept, goes back to Aristotle.Perfection is, broadly, a state of completeness and flawlessness.The term perfection is used to designate a range of diverse, if often kindred, concepts.The perfection of the number 3 actually became proverbial: "omne trinum perfectum" (Latin: ).
This was formulated by Lucilio Vanini (1585–1619), who had a precursor in the 16th-century writer Joseph Juste Scaliger, and they in turn referred to the ancient philosopher Empedocles.
The ancients also considered 6 a perfect number because the human foot constituted one-sixth the height of a man, hence the number 6 determined the height of the human body.
Belief in the "perfection" of certain numbers survived antiquity, but this quality came to be ascribed to other numbers as well.
The paradox of perfection—that imperfection is perfect—applies not only to human affairs, but to technology.
Thus, irregularity in semiconductor crystals (an imperfection, in the form of contaminants) is requisite for the production of semiconductors.
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These concepts have historically been addressed in a number of discrete disciplines, notably mathematics, physics, chemistry, ethics, aesthetics, ontology, and theology.