Tuesday, September 06, 2005

The Molad

I don't know if you've ever heard that the Gemara's calculation of the molad, the time of the astronomical new moon, is proof of the scientific wisdom of the sages of the Talmud, but I have. I can't seem to find it on any kiruv website, but I'm sure I've heard it somewhere. Anyway, it turns out it's not.

I have some irrational phobia of the intricate calculations of the Jewish calendar. You'd think I wouldn't, since I majored in math and have made a good living from my math skills. But so it is. I even have a cousin through marriage who is a world expert on this subject and occasionally e-mails me articles that intimidate me into saving them and pretending that I might read them some day.

In the most recent issue of Tradition (Fall 2004), there is an article about this titled "A 5765 Anomaly," by Sheldon Epstein, Bernard Dickman and Yonah Wilamowsky. I forced myself to start reading it, despite (or perhaps to spite) my aforementioned phobia, and to my great surprise I found it fascinating. I even saw my cousin quoted in a few endnotes!

The article contains the following (pp. 42-43) -- trust me, read through this despite its intimdating numbers:

As cited previously, the Gemara presents 29.5 days and 793 halakim (29.530594138 days to the nearest 10 decimal places) as a lower limit for lunation. Rambam (KH 6:3) says that this figure refers to the mean lunation, i.e., the length of any individual month can show considerable variability. The actual time between two successive true conjunctions ranges in the 20th and 21st centuries between approximately 29 days 6.5 hours, and 29 days 20 hours, and for the period 1000 BCE until 4000 CE, it ranges from a low of 29 days, 6 hours and 26 minutes (in 302 BCE) to a high of 29 days, 20 hours and 6 minutes (in 400 BCE).

Just as the range of lunation has changed with time, so has the mean lunation changed with the passage of time. The current most accurate estimate of the mean lunation value is given by NASA to 10 decimal places as 29.5305888531 days. Thus the Gemara's 2000 year-old value overestimates the current best scientific calculation by 5.2827E-06 days, or a little less than 1/2 a second (i.e., .4564 seconds). The fact fact that the Gemara's lunation value is an overestimate of the mean and R. Gamliel indicated that it was an underestimate is not problematic. The mean lunation has been decreasing with the passing of time. Thus, in the Gemara's time the actual mean lunation was more than NASA's current figure. By some estimates the mean lunation was actually 29.5 days and 793 halakim somewhere around the beginning of the Common Era. Thus, when R. Gamliel, first century tanna, asserts having received information from the house of his grandfather, he is apparently citing from an old tradition that had been in his family for a very long time. As evidence of the ancient origins of the mean lunation being 29.5 days and 793 halakim, we note that some attribute the value to Cidenas who lived about 383 BCE, i.e., 500 years before R. Gamliel. At that point in time over 2500 years ago the actual mean lunation may very well have exceeded 29.5 days and 793 halakim
This is interesting on a number of levels. First, the length of a lunar month was slightly overestimated by R. Gamliel, who said that it was an underestimation. But this can be explained if he was only relaying a tradition that was correct at the time it was originally taught.

Furthermore, it seems that the Babylonian astronomer Cidenas had arrived at such a calculation about 500 years before R. Gamliel.

More than that, though, this value is actually changing over time. We can state about this with full scientific backing that nishtaneh ha-teva -- nature has changed. The length of a lunar month was once exactly 29.5 days and 793 halakim but it has now changed.

The bulk of the article is about the practical problems that this growing discrepancy is causing (pp. 43-44):
Although our estimate of the mean lunation differs insignificantly from the true mean lunation, over long periods of time the cumulative sum of these monthly differences results in significant differences between the molad based on 29.5 days and 793 halakim and the true mean conjunction based on the true mean lunation
Because of this two-hour difference, it seems that the date of Rosh Hashanah last year was pushed off by two days, which it would not have been had we used the astronomical calculation of the molad. Fascinating. Who would have thought?

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