Attempting to prove to me that Judaism is the only true religion, a friend of mine read to me from a book titled, The Coming Revolution, that the Zohar (a 2nd/3rd century CE commentary on the Torah allegedly written by Rabbi Simeon bar Yochai) uses a highly accurate value for the duration of the full moon cycle (29.530588853), centuries before this calculation could be made by modern calculators. How true is this claim?

My Google "skills" were unable to find who was the first person in history to come up with the calculation (NASA?). The only thing I could find, more or less related is this page using Gematria to calculate the moon cycle. But honestly, I'm not too sure what to make of it.

Note: Some people think the Zohar was written by Moses de León in the 13th century which, if true, would still be ages before NASA.

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    From a comment in the page linked above, "I would be very cautious (or rather selective) when citing Zamir Cohen. A lot of the material in his books is absolute nonsense, superstitious pseudoscience and has nothing to do with Torah. (And thus, raises the issue of דרכי האמורי)." – user7920 Mar 2 '15 at 19:43
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    A few seconds with Google (and some prior knowledge) will find multiple references to the Babylonians and others calculating the moon cycle, and much else, many centuries earlier. Here's a concise article on the precision question: thetruthiswrong.com/indeed/belief/argument-and-preaching/… In your place, I'd also ask how a calculation like this can prove religion. Maybe if the number was written down in some holy book or other... – jamesqf Mar 2 '15 at 19:44
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    One might suggest that confirmation bias and cherry picking could be coming into play here. If one has enough source material to work from, and a sufficiently vague, allegorical approach to interpreting it, then one can 'prove' anything at all. This is how numerology works. Also relevant: en.wikipedia.org/wiki/Bible_code – A E Mar 2 '15 at 20:01
  • 29.530588853 as far as I know, decimal fractions were not in use by any civilisation at that time – hdhondt Mar 2 '15 at 22:50
  • There is some doubt as to the dating of the Zohar and of Kabbalah in general, as there is no documentary evidence before the 2nd millennium (CE). But accurate lunar astronomy was possible well before this. – Henry Jan 11 '16 at 18:09

Maimonidies (12th Century) puts it at 29.530594. His source is the Talmud (Bavli RH 25a) (~7th century quoting a rabbi from the 2nd century).

(For the curious the precise number given is 29 days, 12 hours, and 793/1080 of an hour.)

However, lunar cycles can be calculated pretty accurately even in ancient times by counting between total solar eclipses. Consider (from here) the two solar eclipses from Portugal on July 19, 418 and December 23, 447. As long as someone remembered that there were 364 lunar months between them, they could easily calculate a lunar month length of 29.53021 (accurate to 3 decimal places). With a longer gap between eclipses and more accuracy of when during the day it occurred, even more places can be calculated. This is certainly something the Greeks were capable of doing.

(FWIW Maimonidies himself states that he got all his numbers from the Greeks (see Laws of New Moons 17:24 and Guide to the Perplexed 3:14)).

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    If I may, we should be careful not to fall for the fallacy fallacy here. – Double AA Mar 3 '15 at 19:30
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    The Babylonians had a pretty accurate measure of the length of lunar month (by keeping long timebase calendrical records) – Francis Davey Mar 4 '15 at 10:02
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    Please avoid assuming that the readers are Jewish or familiar with Judaism. Who is Maimonidies? What is this Kiddush Hachodesh thing? Is chabad.org a reputable source? How do we reliably know that he's a 7th century rabbi quoting a 2nd century one? Where on that page do we see 29.530594? 793/1080 units of what? Please flesh things out. Also, "something that the Greeks were capable of doing" doesn't mean that they did. This aside is a distraction. – user7920 Mar 5 '15 at 20:22
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    @coleopterist Maimonides is arguably the most famous non-biblical Jew ever. I state very clearly that it's 793/1080 of an hour. The OP asked "before this calculation could be made by modern calculators" and I answered that it certainly could have been made back then. A cursory look at Wikipedia on the Talmud will tell you that it can be very, very, very reliably assumed to predate the 13th century (and hence the OP's cited text as well). If you want to add +/- 4 centuries to my numbers here it wouldn't affect the answer in the slightest. – Double AA Mar 6 '15 at 1:15
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    @coleopterist: The answer also assumes that the reader is acquainted with the sun, moon, and eclipses. Is that also a problem, or should we be allowed to assume either a basic cultural knowledge, or the ability to use Google? As for reliability, what's more reliable than basic math applied to astronomical observations? – jamesqf Mar 9 '15 at 18:10

The measurement of the mean lunar month as 29 days, 12 hours, and 793/1080 of an hour is (in this notation) first found in Treatise on the Computation of the Chronology of the Jews and their Festivals by the Muslim astronomer al-Khwarizmi in the 9th century, then by the Muslim al-Biruni in the 10th/11th century, then by the Jewish scholar Bar Hiyya in the 11th century, and by Maimonides in the 12th century.

The equivalent value in base-sixty notation is given already by Ptolemy (2nd century AD), quoting Hipparchus (2nd century BC), who had it from the ancient Babylonians, so it goes back a long way. The passage in the Talmud (B. RH 25a) quoting Gamaliel as putting the measurement of the month at 29 days, and half a day, and two thirds of an hour, and 73 parts is now generally considered to be an interpolation. See Sacha Stern, Calendar and community. A history of the Jewish calendar second century BCE – tenth century CE, Oxford, 2001, p. 201.

  • Can you add appropriate links to the sources you mention? We would like the evidence to be easily reached for verification. – Sklivvz Mar 9 '15 at 12:46
  • The book by Stern is in copyright, but you should be able to find it in a good library. – fdb Mar 9 '15 at 12:50
  • An amazon link or google books link will suffice then – Sklivvz Mar 9 '15 at 12:51
  • books.google.co.uk/books/about/… – fdb Mar 9 '15 at 12:53
  • For the Arabic sources there also chapter 4 in this book: books.google.co.uk/… – fdb Mar 9 '15 at 12:58

It is written in the Talmud (Rosh Hashanah p.25), which is dated 200-500 CE, and attributed of Gamlial (a Jewish leader early in the first century CE), who claimed to have learnt it from his grandparents.

Here is an English Translation of the passage:

Our Rabbis taught: Once the heavens were covered with clouds and the likeness of the moon was seen on the twenty-ninth of the month. The public were minded to declare New Moon, and the Beth din wanted to sanctify it, but Rabban Gamaliel said to them: I have it on the authority of the house of my father's father that the renewal of the moon takes place after not less than twenty-nine days and a half and two-thirds of an hour and seventy-three halakin.

The footnotes explain that a halakin is 1/1080th of an hour.

Note that the quote provides a minimum time, not an exact time.

Assuming 24 hours a day, 60 minutes per hour, then 29 days + 0.5 day + 2/3 hour + 78/1080 hour = 29.530787 days.

For comparison, a Synodic Month is actually 29.530588853 days - i.e. slightly less than the minimum time provided.

  • Please provide a citation (preferably in English, or translate your self) from the source backing your answer. (hint) – SIMEL Mar 30 '16 at 21:27
  • Welcome to Skeptics! Please provide some references to support your claims. – Oddthinking Mar 31 '16 at 9:10
  • @IlyaMelamed I have originally added a reference to the Talmud directly, but if you want a English language based reference I have now added based on your hint. – yoel halb Apr 4 '16 at 15:30
  • You edited away the context that explained how this was an answer. The result is misleading, and deserves downvoting again. :-( In particular. When you actually translate the term halakin (1/1080th of an hour) you see it does NOT exactly match the true value. It also is only claimed to be a lower bound. Omitting the errors makes this propaganda, not an answer. – Oddthinking Apr 8 '16 at 3:10
  • Did you read my answer from 2 years ago? – fdb Sep 29 '16 at 16:03

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