Etymology
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Dianthus (n.)

large genus of flowering plants including carnations, 1849, from Modern Latin (Linnaeus), literally "flower of Zeus," from Greek Dios, genitive of Zeus "Zeus" (see Zeus) + anthos "flower" (see anther).

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pink (n., adj.)

1570s, common name of Dianthus, a garden plant of various colors; a word of unknown origin. It is perhaps from pink (v.) via the notion of "perforated" (scalloped) petals. Or perhaps it is from Dutch pink "small, narrow" (see pinkie), itself obscure, via the term pinck oogen "half-closed eyes," literally "small eyes," which was borrowed into English (1570s) and may have been used as a name for Dianthus, which sometimes has small dots resembling eyes.

The noun meaning "pale red color, red color of low chroma but high luminosity" is recorded by 1733 (pink-coloured is recorded from 1680s), from one of the common colors of the flowers.  The adjective pink is attested by 1720. As an earlier name for such a color English had incarnation "flesh-color" (mid-14c.), and as an adjective incarnate (1530s), from Latin words for "flesh" (see incarnation) but these also had other associations and tended to drift in sense from "flesh-color, blush-color" toward "crimson, blood color."

The flower meaning led (by 1590s) to a figurative use for "the flower" or highest type or example of excellence of anything (as in Mercutio's "Nay, I am the very pinck of curtesie," Rom. & Jul. II.iv.61). Compare flour (n.). The political noun sense "person perceived as left of center but not entirely radical (i.e. red)" is attested by 1927, but the image dates to at least 1837. Pink slip "discharge notice" is attested by 1915; pink slips had various connotations in employment in the first decade of the 20th century, including a paper signed by a worker to testify he would leave the labor union or else be fired. To see pink elephants "hallucinate from alcoholism" is from 1913 in Jack London's "John Barleycorn."

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*dyeu- 

Proto-Indo-European root meaning "to shine," in derivatives "sky, heaven, god."

It forms all or part of: adieu; adios; adjourn; Asmodeus; circadian; deific; deify; deism; deity; deodand; deus ex machina; deva; dial; diary; Diana; Dianthus; diet (n.2) "assembly;" Dioscuri; Dis; dismal; diurnal; diva; Dives; divine; joss; journal; journalist; journey; Jove; jovial; Julia; Julius; July; Jupiter; meridian; Midi; per diem; psychedelic; quotidian; sojourn; Tuesday; Zeus.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit deva "god" (literally "shining one"); diva "by day;" Avestan dava- "spirit, demon;" Greek delos "clear;" Latin dies "day," deus "god;" Welsh diw, Breton deiz "day;" Armenian tiw "day;" Lithuanian dievas "god," diena "day;" Old Church Slavonic dini, Polish dzień, Russian den "day;" Old Norse tivar "gods;" Old English Tig, genitive Tiwes, name of a god.

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carnation (n.)

common name of the Dianthus Caryophyllus or "pink," a herbaceous perennial flowering plant; 1530s, a word of uncertain origin. The early forms are confused; perhaps (on evidence of spellings) it is a corruption of coronation, from the flower's being used in chaplets or from the toothed crown-like look of the petals.

Or it might be called for its pinkness and derive from French carnation "person's color or complexion" (15c.), which probably is from Italian dialectal carnagione "flesh color," from Late Latin carnationem (nominative carnatio) "fleshiness," from Latin caro "flesh" (originally "a piece of flesh," from PIE root *sker- (1) "to cut"). OED points out that not all the flowers are this color.

This French carnation had been borrowed separately into English as "color of human flesh" (1530s) and as an adjective meaning "flesh-colored" (1560s; the earliest use of the word in English was to mean "the incarnation of Christ," mid-14c.). It also was a term in painting for "representation of the flesh, nude or undraped parts of a figure" (1704).

The flowering plant is  native to southern Europe but was widely cultivated from ancient times for its fragrance and beauty, and was abundant in Normandy.

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