Tzippori was home to a flourishing mixed pagan, Christian and Jewish community during the 4th-7th centuries CE. In the third century CE, it was the seat of Rabbi Yehuda Hanasi, aka Judah the Prince, where he began compiling the Mishnah. There is no iconography on the wine presses and, according to National Parks Authority archaeologist Dr. Zvika Tzuk, in such a heterogeneous society, it would be impossible to know who made the wine at these two presses.On his e-mail list, Joseph Lauer has asked for more information about this "obscure Jewish law." I don't know the answer, but if you can help, please drop me a note.
However, he told The Times of Israel, based on an obscure Jewish law practiced during the Shmita year (every seventh year in the agricultural calendar when the fields are meant to “rest”), the size of the smaller wine press could be an indication that it was used by Jews of the era.
For past PaleoJudaica posts about discoveries at the site of Tzipori/Tzippori/Zippori/Sepphoris, see here and links (cf. here and here).
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