I just saw this Ostracon with Demotic Inscription and wondered whether Demotic script has anything to do with the written Arabic language today?
The two scripts are indirectly related. The root alphabet that many Western and Near Eastern scripts can be traced back to is known as Proto-Canaanite or Proto-Sinaitic. This alphabet is directly based on a dramatically simplified version of ancient Egyptian hieroglyphs; Demotic is a cursive form of hieroglyphs.
Modern Arabic comes from Nabataean, which is based on Aramaic, which is based on Phoenician, which comes directly from Proto-Canaanite.
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Scholars use the word ostrakon to described scraps of stone or pottery that have been written on drawn on. These materials, in the ancient Mediterranean, functioned much like we use scrap paper today.
They were often used for quick records, like this prayer that was likely written down to archived in a temple to Amun.