Hi there,
I am very interested in how ancient astronomers had such precise calculations of certain measurements. Of particular interest to me is the ancient Hebrew calculation of the solar year and lunar month. It appears that their calculations of these measures were off by seconds (26 seconds for the calculations of a solar year) and fractions of a second (.5 seconds) for the lunar month (information gleaned from http://www.sciencedirect.com/science/article/pii/S0898122100001024). I am an ex-religious Jew, so this accuracy gets brought up to me constantly as proof of the divinity of the Talmudic sages. Though I feel confident debating most other claims, I'm looking for some information as to how this accuracy can be explained without resorting to divine means. Naturally, I invoke the god of the gaps refutation when they bring up said divinity (we don't know how they could have been so accurate, therefore it must have been god), but more concrete information would help.
All help is appreciated. Thanks in advance.
Err, you seem to have misread the article. The 26 seconds is the modern secular calendar, while the current Hebrew calendar, based off of the Greek Metonic cycle, is off by 6 minutes and 40 seconds, approximately.
I am not sure why taking eight hundred years to accept the superiority of Meton of Athens' math is a sign of divine inspiration, personally.
Ok, I'm glad that you are realizing how fraught this issue is. There is a lot of skewed and flat out incorrect information out there. The article you linked . . . well, it isn't very comprehensive, is it? A good place to start is Otto Neugebauer, who "wrote the book" on modern understanding of ancient astronomy and mathematics. He fled Europe and the Nazis in 1939 and came to Brown University in the US. In 1984 he moved to the very prestigious Institute for Advanced Study at Princeton. He was an awesome dude and I barely understand most of what he wrote (fair warning).
If you want a relatively basic discussion, see here starting on his page 42 (but you might want to back up and just read the whole article). You will see that the Jewish element of ancient astronomical calculation is just a footnote (sorry, and probably RIP my inbox). The basis is really about the Egyptians and Babylonians, and through them, the Greek contributions.
If that whets your interest, there is also a book of his collected essays:
Neugebauer, O. 1983. *Astronomy and History: Selected Essays.* New York: Springer Science+Business Media.
You might be especially interested in chapter 34 of that book: "The Astronomy of Maimonides and Its Sources" (p.381-424).
Articles written in the 40s and 50s are pretty dated, and normally I would try to find more recent material, but in this case I don't know it. I know of Neugebauer, but ancient science is not my field. If somebody could chime in with a more recent synthesis, that would be great.