In terms of Mesopotamian science, my only knowledge is from a book I read by Dick Teresi, Lost Discoveries: The Multicultural Roots of Modern Science from the Babylonians to the Maya. It's a "history lite" type of book which would definitely not pass muster as a textbook for this class, but it was very engaging to read, and I especially liked the way it exposed the real lack of interest by the Greeks (and also the Romans) in computational mathematics, something which the Egyptians and also the people of Babylonia were experts in apparently. If you asked Plato what six times eight is, he would have been baffled! So, from Dick Teresi I gained learned that the way the Greeks pursued mathematics was quite different from that of their ancient neighbors. I'm guessing that mathematics will be part of the astronomical story that we will learn about this week, so hopefully I will have something more than Dick Teresi to rely on for this bit of knowledge!
The image below is from the Memory-Alpha.org wiki page for Darmok:
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