Etymology
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Midi 

"southern France," 1883, from French midi "south," literally "midday" (12c.), from mi "middle" (from Latin medius "middle;" see medial (adj.)) + di "day" (from Latin dies, from PIE root *dyeu- "to shine"). At midday in the northern hemisphere the sun is in the south of the sky. Compare Latin meridianus "of midday, of noon;" also "southerly, to the south" (see meridian), and Middle English mid-dai in its secondary sense "south, to the south" (late 14c.).

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MIDI 

"device for connecting computers and electronic musical instruments," 1983, acronym for Musical Instrument Digital Interface.

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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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ivory tower (n.)

symbol of artistic or intellectual aloofness, by 1889, from French tour d'ivoire, used in 1837 by critic Charles-Augustin Sainte-Beuve (1804-1869) with reference to the poet Alfred de Vigny (1797-1863), whom he accused of excessive aloofness.

Et Vigny, plus secret, comme en sa tour d'ivoire, avant midi rentrait. [Sainte-Beuve, "Pensées d'Août, à M. Villemain," 1837]

Used earlier as a type of a wonder or a symbol of "the ideal." The literal image is perhaps from Song of Solomon [vii:4]:

Thy neck is as a tower of ivory; thine eyes like the fishpools in Heshbon, by the gate of Bathrabbim: thy nose is as the tower of Lebanon which looketh toward Damascus. [KJV]
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