Torah tidbits
Rosh Hashana

STATS
LO AD”U ROSH says that (in our fixed calendar) Rosh HaShana (the first day) cannot fall on Sunday, Wednesday, or Friday. That means, of course, that it CAN fall on Monday, Tuesday, Thurs- day, or Shabbat. Rosh HaShana is Shabbat-Sunday 28.6% of the time. That’s an average of about twice in seven years.

During the current century (the 58th since Creation, that is - 5701-5800), RH is Shabbat 28 times. 5703, 06, 10, 13, 16, 20, 23, 30, 33, 36, 37, 40, 43, 47, 50, 57, 60, 61, 5763 (this year), 64, 67, 70, 81, 84, 87, 88, 91, 94. Notice that the time between one Shabbat-RH to the next is most often 3 or 4 years - 19 times in this century. Twice it was 7 years and once it will be 11. Four times, RH is Shabbat in two consecutive years, and once the gap is 2 years.

By the way, the condition necessary for two consecutive years matching in day of the week (e.g. the Seder was on Wednesday night last year and will be Wednesday night again this year; Yom Kippur is Monday this year and next; etc.) is that the year be M’uberet (13 months, 2 Adars) and that it be SHALEIM, i.e. Cheshvan & Kislev both having 30 days. Such a year has 385 days, exactly 55 weeks. That’s why the day of the week repeats. All other years are not a whole number of weeks. M’uberet-Shaleim years occur 16% of the time, about once in six years on average.

Two consecutive Shabbat-RHs occur less than 5% of the time, so four times during the 58th century is within range.

More interesting is the question as to how often do we get 4 Shabbat-RHs in a five-year span. We’re in one now, 5760-5764. The last such span was 5689-5693, 71 years earlier. The time before that was 5513-5517 - that’s 176 years earlier, in the lifetime of the Vilna Gaon (and his contemporary, George Washington). The time before that was 71 years earlier still, 5442-5446 (in the 1680s). The next time such a span is scheduled is 176 years from now, 5936-5940.

So within a 500 year period, there is a pattern of 71 years, 176 years, 71 years, 176 years.

Nice pattern, but does it hold? And so we continue to travel back in time with the old Hebrew Calendar DOS program (written back in 1985) until we find another 5 year span with 4 Shab-RHs. And here it is - only 27 years earlier, 5415-5419. So much for patterns. And before that? 5266-5270, 149 years earlier. Pattern shot? Not really. 27+149=176. 71 years earlier? Yes. 5195-5199. Shall we keep going back a little longer? Okay. 5168-5172. 27 years again. Then 5019-5023. 149 years again. So the pattern continues with a little glitch. Or is the glitch part of a more complex pattern? Perhaps. Enough. We covered the whole sixth millennium, during which there are 10 five-year spans with 4 Shabbat-RHs.

If you are reading these words, you probably enjoyed the excursion into calendar statistics. This page was written for you. Those who gave up towards the beginning or were scared away by the imposing title STATS, don’t know what they’re missing. :)


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