Department of Mathematics, Temple University, Philadelphia, PA 19122, USA.
Preface: This was my annual April Fool's `joke' for 1999 that was complicated by the fact that this very important secular holiday coincided this year with the first day of the very important religious holiday called Passover. While the existence of the Pan-Judaic synod and the calendar reform might have to wait for the arrival of the Messiah, all the astronomical figures, and all the math is sound, and the proposal is a very good idea!
Important Note: This report was written on Nissan 14, 5759, but E-mailed by euclid to DZ's E-mailing list on Nissan 15, 5759, (4/1/99), following an `at' command, for batch jobs, that was entered well before sundown, on Nissan 14. Since the computer who did the mailing (euclid), is not Jewish, everything is Kosher for Passover.
Whenever there are two Jews, there are [at least] three opinions ----Anon.Abstract: I describe briefly the mathematical ideas behind the proposed adjustments to the Hebrew calendar, recommended by the technical advisory committee to the Pan-Judaic Synod, and that is expected to be approved unanimously, G-d willing, by its seventy learned and venerable members.
More than a hundred years ago, it was pointed out by Rabbi Dr. Isidore Loeb, that the Jewish year exceeds the Gregorian by 6 minutes and 39.37 seconds. He warned that, insignificant as this difference may appear, it will cause a considerable divergence in the relations between Nissan and spring as time goes on, and may require a Pan-Judaic Synod to adjust.
Although Jews are known for their diversity of opinions (see the quote above), no Jew, be he (or she) Hasidic, Ultra Orthodox, Orthodox, Conservative, Reform, or even Deconstructionist, or whether he or she are Ashkenazi or Sefardic, and regardless whether he or she eats Glatt Kosher, Kosher, Kosher-style, or Taref, no one wants to have a `white Passover' in ten thousand years!
When I suggested, a few years ago, a reform of the Hebrew calendar to the leadership of the main branches of contemporary Judaism, I was gratified to receive very enthusiastic responses from almost all Jewish spiritual leaders. I was authorized to organize a committee of ten (minyan) Jewish mathematicians, computer scientists and astronomers, including Eliyahu (Ilya) Korea, D. Nachum, R. Edward, V. Ilan, W. Herbert, and one (token(?)) Gentile (K. Donald), who served as an observer. Our 248-page report, containing 613 articles, will be soon officially submitted to the Pan-Judaic Synod, that was formed specifically for that purpose, and is expected to be approved. In this informal account I would like to state our most important suggestions, and to share with you the highly non-trivial math involved.
But, perhaps of more immediate concern are the updated dates of Passover starting next year (5760 to the creation of the world, 2000 to the Common Era). These are: May 18, 2000 (sic!), (instead of April 20), followed by: May 6, 2001 (instead of April 8) , and April 25, 2002 (instead of March 28). There will soon be a revised on-line Hebrew Calendar.
Now let's go to the math behind our proposal. The current Hebrew
Calendar is a brilliant application of Diophantine Approximation.
The Solar Year has Y:=365+5/24+48/24/60+46.069/24/60^2 days,
while the Lunar Month has
J:=29+12/24+44/24/60+2.481/24/60^2 days; It follows that
the Solar yeas has an excess of (Y-12*J)/J Lunar months.
Converting this to a continued fraction, we get:
[0, 2, 1, 2, 1, 1, 17, 1, 1, 2, 19, 1, 5, 3, 2, 1, 1, 1, 6, 2, 2, 3, 1, 2, ...];
(i.e. 0+1/(2+1/(2+1/...)), with its convergents:
[0, 1/2, 1/3, 3/8, 4/11, 7/19, 123/334, 130/353, 253/687, 636/1727, 12337/33500 , 12973/35227];
The current Hebrew calendar picked the convergent 7/19, and thus has a cycle of 19 years, with 7 of them (3,6,8,11,14,17,19) acronymed goakh adzat (gimel, vav, khet, [yod] alef, [yod] dalet, [yod] zayin [yod] tet), being leap years, in which a second month of Adar, Adar bet, is added.
Our committee suggested to first make up for the existing retardation, and the regrettable fact that Tu BiShvat, the `Birthday of trees' is often celebrated in the bitter cold of January. Unlike Pope Gregory, who had the option of erasing any number of days, we were restricted by units of the Lunar month (for obvious reasons, Passover needs a full moon, Rosh Hashana needs a new moon, etc.). Hence we decided, ONLY in the next year, to add yet another month of Adar, Adar Gimel, to once and for all, make Tu-Bishavt (and often Purim!), milder.
Having corrected this, from now we suggested to take the much superior 10th convergent, 636/1727, rather than 7/19, and to have a cycle of 1727 years, with 636 of them being leap years (where a 13th month, Adar bet, is inserted before Nissan). The most optimal arrangement turned out to be as given in the appendix below.
All the nice features of the current version of the Hebrew calendar have been preserved (e.g. Conway's formula for the date of Rosh Hashana, and the alef-tav, bet-shin method for finding the day of the week of the major holidays from the day of the week of the days of Passover). We were told by Professor Korea that 636 (in its Hebrew letters version: tav resh lamed vav) appears in 1727 ESLs in the Torah, which proved to us that we were only interpreting the Divine Will, and that our `new' reform was known to the almighty all along.