Thursday, May 04, 2006

Daf Yomi Pesachim 103b-104a: No Less Than X, No More Than Y. What About Number In Between?

In Pesachim 103b, there is a very informative story. It it meant to teach us about the number of "divisions" one should make in havdalah, but it also seems to teach us the meaning of a specific construct of
__ הפוחת לא יפחות מ_ והמוסיף לא יוסיף על. Specifically, what about numbers in between? This has relevance to tzitzit, where we have such an instruction and we indeed do use numbers between the bounds.

First, the gemara in Pesachim.

Pesachim 103b:
פתח ואמר המבדיל בין קודש לחול בין אור לחשך בין ישראל לעמים בין יום השביעי לששת ימי המעשה
א"ל למה לך כולי האי? והאמר רב יהודה אמר רב המבדיל בין קודש לחול זו היא הבדלתו של רבי יהודה הנשיא
א"ל אנא כהא סבירא לי דאמר ר"א אמר רבי אושעיא הפוחת לא יפחות מג' והמוסיף לא יוסיף על ז'
אמר ליה

104a:
והא מר לא תלתא אמר ולא שבע אמר
א"ל איברא בין יום השביעי לששת ימי המעשה מעין חתימה היא
ואמר רב יהודה אמר שמואל המבדיל צריך שיאמר מעין חתימה סמוך לחתימתו ופומבדיתאי אמרי מעין פתיחתן סמוך לחתימתן

In English (as I translated for the Rif):
When they came to havdala, his {=Rava's} attendant arose to light a torch {avuka} from a candle.
He {=Rav Yaakov} said {Bach: to him = Rava}: Why does Master need all this? There is a candle resting before us!
He {Rava} said to him: so said Rav: a torch for havdala is the best fulfillment of the precept.
He began, saying, "who divides holy from profane, and between light and darkness, and between Israel and the nations, and between the seventh day and the six days of work."
He said to him: Why does Master need all this? Rav Yehuda cited Shmuel that "who divides between holy and profane" is the havdala of Rabbi Yehuda haNasi.
He said to him: This is what I hold - for Rabbi Eleazer cited Rabbi Hoshaya: he who decreases should not decrease to less than three, and he who increases should not increase more than seven.
He said to him: But Master did not say three and did not say seven! {but rather four!}
He said to him: The division between the seventh day and the six days of work are like the closing.
{Pesachim 104a}
For Rav Tachlifa bar Avdimi cited Shmuel: For all blessing must say something similar to their closing in proximity to their closing.
And those of Pumpedita say similar to the opening in proximity to its closing.
And we establish like Shmuel. Therefore, Yom Tov which occurs after Shabbat, one needs to say "between the holiness of Shabbat and the holiness of Yom Tov you have divided.

The Rif adds: And the halacha is that a torch for havdala is the best way of fulfilling the precept. And one who makes havdala should not decrease less than three nor increase more than seven. And even though Rav Yehuda cited Shmuel that "who divides between holy and profane" is the havdala of Rabbi Yehuda haNasi, and Ulla also conducted himself like him, and in perek Shoel Adam meChaveiro {Shabbat 150b, perek 23} Rav Ashi said, "when we were in the house of Rav Kahana we {our gemara: he} said "who divides between holy and profane," and then we chopped up logs, even so, the nation is accustomed to say three. And we establish in something like this that custom is relevant. Therefore, he needs to say three: "who divides between holy and profane, and between light and darkness, and between Israel and the nations." And "between the seventh day and the six days of work" is like the closing, and is not part of the count.
Thus, there is a statement that one should not decrease less than three nor increase more than seven, and an objection was raised when four, a number in between, seemed to be said. Why should this even be a question if any number within the bounds is acceptable?

Now, perhaps one can give an answer, but I am reluctant to offer the answer because I think that this may indeed be a valid point, and that one should not use numbers within the bounds. However, perhaps one can say that since the specific number was not specified, Rava could have either wanted to make the havdalah short or long. Rav Yaakov merely wanted to know what exactly caused Rava to use a number in the middle of the bounds, which of course would be perfectly acceptable had Rava indeed done so. Was there some other Rabbinic statement influencing Rava? As it turned out, that was not Rava's intention, and it was good Rav Yaakov asked this, so that we could understand the exact construction of this havdalah. But it would have been acceptable had there actually been four divisions.

I do not think that the aforementioned explanation is the simplest, but rather think that the question presupposes that a number in the middle of the two bounds is not acceptable, a somewhat surprising result.

There is a middle ground, which I think is the correct answer. That is, this is not a matter of personal preference, but rather there is a bare minimum, a maximum imposed by certain circumstances, and perhaps middle grounds also imposed by specific circumstance. But one is not free to choose how many on a whim. We shall see this by analyzing how this construction is used in other sugyot.

Another, related construction appears in the fourth perek of Rosh Hashana, 32a:
רבי יוחנן בן נורי אומר אם אמר שלש שלש מכולן יצא: איבעיא להו היכי קתני שלש מן התורה שלש מן הנביאים ושלש מן הכתובים דהוו תשע ואיכא בינייהו חדא או דלמא אחד מן התורה ואחד מן הנביאים ואחד מן הכתובים דהויין להו שלש ואיכא בינייהו טובא ת"ש דתניא אין פוחתין מעשרה מלכיות מעשרה זכרונות מעשרה שופרות ואם אמר שבע מכולן יצא כנגד שבעה רקיעים רבי יוחנן בן נורי אמר הפוחת לא יפחות משבע ואם אמר שלש מכולן יצא כנגד תורה נביאים וכתובים ואמרי לה כנגד כהנים לוים וישראלים אמר רב הונא אמר שמואל הלכה כר' יוחנן בן נורי:
in terms of the number of pesukim which should be cited relevant to Malchiyot, Zichronot, and Shofarot in Shemoneh Esrei. But an upper bound is not given within this construct, so we will not discuss this case further.

In Succah 53b, in the Mishna:

דף נג, ב משנה אין פוחתין מעשרים ואחת תקיעות במקדש ואין מוסיפין על ארבעים ושמנה בכל יום היו שם עשרים ואחת תקיעות במקדש שלש לפתיחת שערים ותשע לתמיד של שחר ותשע לתמיד של בין הערבים ובמוספין היו מוסיפין עוד תשע ובערב שבת היו מוסיפין שש שלש להבטיל את העם ממלאכה ושלש להבדיל בין קדש לחול ערב שבת שבתוך החג היו שם ארבעים ושמנה שלש לפתיחת שערים שלש לשער העליון ושלש לשער התחתון ושלש למילוי המים ושלש על גבי מזבח תשע לתמיד של שחר ותשע לתמיד של בין הערבים ותשע למוספין שלש להבטיל את העם מן המלאכה ושלש להבדיל בין קודש לחול:
In the Temple they never blew the trumpet less than twenty-one times a day, nor oftener than forty-eight times. They daily blew the trumpet twenty-one times: thrice at opening the gates, nine times at the daily morning offering, and nine times at the daily evening offering. When additional offerings were brought, they blew nine times more. On the eve of the Sabbath, they blew six times more: thrice to interdict the people from doing work, and thrice to separate the holy day from the work day. But on the eve of the Sabbath, during the festival (of Tabernacles) they blew forty-eight times: thrice at the opening of the gates, thrice at the upper gate, thrice at the lower gate, thrice at the drawing of water, thrice over the altar, nine times at the daily morning offering, nine times at the daily evening offering, nine times at the additional offerings, thrice to interdict the people from doing work, and thrice to separate the holy day from the work day.
This is also not exactly the same construction, but it is close -- אין פוחתין מעשרים ואחת תקיעות במקדש ואין מוסיפין על ארבעים ושמנה. Yet, there are clearly situations described in the Mishna in which value between the two bounds occur.

Further, in the gemara we see a brayta which makes clear that the two constructions are identical, for Rabbi Yehuda says the same thing, but divided by a third, because he maintains that a set of tekia terua tekia are considered one rather than three separate ones like the Tanna of our Mishna. Thus:
מתניתין דלא כרבי יהודה דתניא ר"י אומר הפוחת לא יפחות משבע והמוסיף לא יוסיף על שש עשרה במאי קא מיפלגי ר"י סבר תקיעה תרועה תקיעה אחת היא ורבנן סברי תקיעה לחוד ותרועה לחוד
Our Mishna is not in accordance with R. Jehudah of the following Boraitha: According to those who say they were few, they were not less than seven; and according to those who say that they were many, they were not more than sixteen.

What is the point on which they differ? R. Jehudah holds that blowing and alarming are one and the same thing, while the sages hold that they are two separate things.

Here, the construct used is הפוחת לא יפחות משבע והמוסיף לא יוסיף על שש עשרה, the same construction used by Rabbi Eleazar (the Amora) citing Rabbi Hoshaya (who arranged braytot). Yet, there are clearly situations described in the Mishna in which value between the two bounds occur, and Rabbi Yehuda would agree in these situations.

At the same time, these are clearly defined situations. The construction is such that it is clear this is not a matter of reshut, personal preference. Rather, there is a base case in the Mishna of 21. There is a maximum, caused by various other requirements. And, there are middle cases, also caused by specific circumstances. Absent these special circumstances, it would be improper to make use of one of the middle numbers. For example, one would look askance if on a normal day they blew 24, or 48. We will return to our sugya in Pesachim later to see how this works out.

In the fourth perek of Menachot, 39a:
תאנא הפוחת לא יפחות משבע והמוסיף לא יוסיף על שלש עשרה הפוחת לא יפחות משבע כנגד שבעה רקיעים והמוסיף לא יוסיף על שלש עשרה כנגד שבעה רקיעין וששה אוירין שביניהם
One who decreases should not decrease less than 7 and one who increases should not increase more than 13. One who decreases should not decrease less than 7 - corresponding to the 7 firmaments (heavens). And one who increases should not increase more than 13 - corresponding to the 7 firmaments and the 6 sections of airspace between them.

This is a discussion of the number of sets of coils, though at various point people thought this referred to the number of coils in a set. A bit of explanation is in order first. Here is a picture -- a scan of my talit katan, which does not have techelet:

Thus, there are coils. A coil is a single winding around. There are also sets of coils. A single set of coils occurs between two knots on the tzitzit.

The true meaning of the aforementioned statement (as understood by Rishonim) is regarding the sets of coils. When one makes tzitzit, one might make few sets of coils or many sets of coils. One who decreases should not have less than seven sets of coils. This would mean that there are seven sets of coils, between 8 knots. One who chooses to increase should not increase more than thirteen. That would be thirteen sets of coils, between fourteen knots.

There is a separate statement concerning how many coils should be in a set, at a minimum:
וכמה שיעור חוליא תניא רבי אומר כדי שיכרוך וישנה וישלש
that there should be at least three coils in a set.

Now, looking at the picture above, this is clearly not the case. Rather, there are four sets of coils, between five knots. Meanwhile, in each set, there are clearly more than three coils - between 7 and 13.

The minhag which the above picture depicts is one in which there are four sets of coils, and the coils count up from 7 to 13. Namely, 7-8-11-13. This is called (Ashkenazic - there is also Sefardic) Tal, because Tal = 9 + 30 = 39, the total number of coils. There is another, apparently Sefardic custom, of 10-5-6-5, in which the number of coils in each set in turn is equal to the letters of the Tetragrammaton, the Divine 4-letter name.

(You can buy both of these options here, at haSofer.com.)

Now, the "Tal" option is at least based on the gemara. Alas, it misinterprets the statement referring to sets of coils and believes it to be discussing coils in a set. This is perhaps not such a big deal, since this is on a pair of tzitzit which does not contain techelet anyway. However, once we have techelet, we really should tie it appropriately (so Rav Schachter says), which means that there should be between 7 and 13 sets of coils. Each set should have no less than 3 coils. Indeed, this is how I tie the tzitzis on my tallis godol, which has techeles, except that I add more than 3 coils per set, so that it looks more normal. (Perhaps I'll post a scan of my
talis gadol later.)

The 10-5-6-5 seems not to correspond to the gemara at all - for the set of coils are not between 7 and 13 (but are rather 4, just like the "Tal"), and the number of coils in each set is once between 7 and 13 (that is, the 10), but otherwise is less than 7!

Even if we were to assume the "Tal" interpretation is correct, should we include some number between 7 and 13? The gemara gives cause for 7 and gives cause for 13, but does not give cause for 8 or 11! Presumably there are other, post-Talmudic reasons given for the 8 and 11.

What about when I tie my tzitzit with techelet, and want to tie it correctly, where the statement refers to sets of coils. Obviously I cannot count up from 7 to 13, since this is the number of sets on a given corner (and it would be strange to make differences between different corners). I tied mine with 7. I could have increased to 13. Could I have done 8, 9, 10, 11, or 12 sets?

I would think not, because after all, there is significance given to 7 and 13, but no number in between. This would work well with the interpretation of "he who increases" and "he who decreases" given above, not lending credence to numbers in the middle unless there is specific cause.

To be continued in another post, where I hope to return to the sugya in Pesachim and give further analysis.

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