A mixture or jumble of different languages, especially Greek mixed with other languages; nonsense or gibberish.
Likely a corruption or folk etymology of 'alligator' or a blend created by English speakers trying to describe incomprehensible multilingual speech; possibly influenced by 'Greeking' (using Greek as a sign of unintelligibility).
Medieval printers would use 'aligreek'—literally fake Greek letters—as placeholder text when they didn't have the real thing, which is why we still use Lorem Ipsum today!
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