Length of the Year

I was asked to explain Avi Goldstein's point about the length of the year in his recent letter to The Jewish Press. The following is from R. Yehudah Levi, Facing Current Challenges, pp. 319-321 [note that the Hebrew edition has approbations from R. Ovadiah Yosef and R. Zalman Nechemiah Goldberg]:
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The length of the tropical year, meaning the year as counted from the beginning of the spring equinox until the beginning of the following spring, is quite close to 365 ¼ days. This is the commonly accepted length. The seasons based on this approximation are associated with the amora Shemuel (“tekufath Shemuel”); the Christian Julian calendar is also based on it. For most popular purposes this approximation is good for hundreds of years, because the degree of inaccuracy which accumulates in one hundred years is less than a day... According to this accounting (of a year consisting of 365 ¼ days or 52 weeks plus a day and a quarter)... [a]fter 28 years, the remainders accumulate to 35 days, that is, five entire weeks, and the beginning of spring returns to the same point in the week... On the day, which is always a Wednesday, “Whoever sees the sun in its cycle... says the blessing ‘Blessed is He... Who does the act of Creation,’” implying that even today God is performing the act of creation...

But here is the problem: the length of the true solar year is actually eleven minutes shorter. This means that at the end of 28 actual years, when the blessing is pronounced, spring has not returned precisely to the original point in the week. This error has accumulated over the years and now adds up to about thirteen days.

Our detractors, both from within and from without, have tried to conclude from the imprecision in Shemuel’s approximation, which accumulates to about seven and a half days every thousand years, that our Sages were deficient in their knowledge of astronomy… In light of all this, it is difficult to accept the claim that the Sages erred to such a great extent in so basic an astronomical constant as the length of the solar year. The mystery is cleared up, however, if we realize that exactness in the calculation of the time of the blessing of the sun is not all that important. At issue here is a symbol which comes to remind us of the wondrous stability of the laws of nature, which, in turn, points to the awesome Operator behind them. This type of symbol does not demand precision, but rather something which can be understood by the general public and be easily calculated. Hence it is readily understood why the aforementioned cycle of 28 years was chosen, a cycle based on a simple approximation. A more exact basis for calculation would demand a much longer cycle, which would not only greatly complicate the calculations, but also effectively prevent the blessing of the sun from serving as a reminder to us.