Monday, November 3, 2008

Rebbi Abahu's Calculation

At the end of Yerushalmi Sukkah, there is a puzzling Gemara.  There is a discussion regarding the 24 watches of Kohanim.  Every week, the work in the Beit HaMikdash was taken care of by one watch.  The watch of Bilgah is treated negatively, for reasons stated in the Gemara.  The question arises, why not mix Bilgah in with another watch?  And then it is asked, why not just eliminate the watch altogether and leave it with just 23 watches?

We can't do that, as it is written "They were established by David and Shmuel the seer, with their faith" (Divrei HaYamim 1 chapter 9)  Great skill (a slight change to the word for faith) is here, that one watch does not take and take again from the Ancestral Field until the others take.  Rebbi Abahu said: I calculated them and one watch does not take and take again from the Ancestral Field until the others take.
The basic idea with the Ancestral Fields is that if a person sanctifies his field, he has until the Yovel year to redeem it.  If he does not, then the watch which serves at the time that the Yovel begins receives that field.  Therefore, there are mefarshim that say that this means that over 24 Yovel cycles, each watch will serve exactly once at the beginning of the Yovel.

The problem with that is obvious: Yovel was never observed for 1200 consecutive years (50 * 24), so what is the great skill used?

The P'nei Moshe says that in the Yovel year, during the first 48 weeks, the fields which were sanctified throughout the 48 years of the Yovel cycle (the years in which people sanctify their fields, since for the most part this is not done in the 49th year) are given out in that order.  If so, why would Rebbi Abahu have to say that he did any calculations?

Comments and speculation are welcome.


  1. Dear Gilui n�y,

    I hope the following make sense:

    �The watch which serves at the time that the Yovel begins receives that field.�

    The problem, of the possibility of one watch taking once and then again until the others take, arises because the watches were apportioned according to complete weeks, whereas the years would repeat in irregular cycles not divisible by 7. Furthermore, the Yovel cycle is not divisible by 19, which is the cycle for a repeat of extra months for years of Ibbur. The addition of the extra days for the 1st Tishri in years of Dehiyyah further complicates the issue.

    In addition the shortest calendar year has just over 50 weeks and the longest has just under 55 weeks, but the watches are apportioned weekly between 24 watches, meaning that in any one year all the watches will serve at least twice and between 2 to 7 watches will serve three times in that year, and the watches cycles do not match that of the calendar. (I am assuming that the Chagim, when all the watches served jointly, did not push aside the regular watch).

    Therefore, it could happen that by the time one watch took its share one or more of the others had already taken once and then again.

    Taking an average solar year, one year of 52/53 weeks would allow for all 24 watches to serve twice, plus another 4/5 watches. Therefore, over a Yovel cycle, the beginning of the next cycle of watches would be multiples of 5 nominal calendar weeks out of sync as follows:

    Yovel X+1: Watch No.1
    Yovel X+2: Watch No.6
    Yovel X+3: Watch No.11
    Yovel X+4: Watch No.16
    Yovel X+5: Watch No.21
    Yovel X+6: Watch No.2
    Yovel X+7: Watch No.7
    Yovel X+8: Watch No.12
    Yovel X+9: Watch No.17
    Yovel X+10: Watch No.22
    Yovel X+11: Watch No.3
    Yovel X+12: Watch No.8
    Yovel X+13: Watch No.13
    Yovel X+14: Watch No.18
    Yovel X+15: Watch No.23
    Yovel X+16: Watch No.4
    Yovel X+17: Watch No.9
    Yovel X+18: Watch No.14
    Yovel X+19: Watch No.19
    Yovel X+20: Watch No.24
    Yovel X+21: Watch No.5
    Yovel X+22: Watch No.10
    Yovel X+23: Watch No.15
    Yovel X+24: Watch No.20

    With the above simplified application there is no watch that would take once and again before all the other watches have taken their share. If the same exercise were done with 23 watches instead of 24 it would not work.

    The above exercise would need to be fine-tuned to verify whether it matches actual calendar dates, taking Ibburing and Dehiyyot into account. That would require the working out of all the permutations as per R� Hillel�s calendar counts.

    R� Abahu belonged to one generation of Amoraim before R� Hillel. It seems that he would have had to work it out from basic principles, something that was previously known to David Hamelech and Shemuel Hanavi.

    You comment that �Yovel was never observed for 1200 consecutive years, so what is the great skill used�. But is that not Rambam�s view? Does he not state afterwards (Hilchot Shemitah veYovel 10:5) that according to the Geonim Shemittah only was counted between the destruction of the 1st Bayit and the building of the 2nd Bayit, and again after the destruction of the 2nd Bayit, implying that during the 2nd Bayit they did count Yovel?

    I am no mathematician, but perhaps someone with more mathematical knowledge could put all the above into a simple mathematical/calendrical formula that is intelligible to all of us.

    Shalom uBrachah.

  2. Thank you for your comment. Regarding the last section, the Rambam held that Yovel was in effect from the time of Yehoshua until the time of Galut Reuven/Gad/half of Menashe, and therefore less than 1000 years. The Rambam further brings that Yovel was counted consecutively (if not observed always) from 2504-3339, also less than 1000 years. After the 70 years, it resumed for under 420 years (3416-3829).

  3. Gilui, I am sorry, I misunderstood the meaning of your original comment about the 1200 consecutive years.
    I should clarify that, because of the watches being out of sync with the yearly calendar, the problem of unfair sharing would arise before the full 24 Yovel cycles are complete, although the exercise would still need to be applied to the complete 24 Yovel cycles. In the example I gave above the possibility could have arisen as early on as the 6th Yovel.