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When Queen Vashti refused to entertain the men (was she an early feminist or a leper with a tail the commentators are divided) at Ahasueruss party, he consulted his advisers, who were versed in dat and precedent (Esther 1:13). Dat means law and appears 20 times in Megilat Esther. Haman, when making the case for the Jews destruction, tells the King that their dat is different from those of any other people (Esther 3:8).
Dat, as www.balashon.com explains, derives from the Persian word for law, data. ThroughMegilat Esther, dat has entered Hebrew and appears in later biblical works, such as Ezra and Daniel.
Dat can also mean custom. At Ahasueruss infamous party at the beginning of the Megilah, the alcohol was according to dat. The midrash explains that the King gave instructions that people could drink according to their individual cultural customs. (How a king with such sensitivity to ethnic diversity could later agree to wipe out an entire nation is rather baffling.)
Nowadays, dat does not mean law but rather religion. Someone who is dati is religious. The term dosim based on an Ashkenazi pronunciation is a deprecatory term for religious Jews. Many datiim (religious people) playfully use the term to refer to themselves, removing its sting.