SOME SERIOUS NUMBER GAMES

This Mishnah deals with groupings of people by number and offers us a first chance to get a concentrated impression of Maharal’s thoughts about numbers. The Mishnah says that if ten people are discussing Torah matters, the Divine Presence joins their midst, proving it with a verse from Scripture (while some of the verses will be important for Maharal, this one is not, so I will not cite it). The Mishnah then says, in paraphrase, how do we know that even five are the same way, and offers a verse that reads ve’agudato `al ‘erets yesadah, presumably with an agudah referring to five in some way. Interestingly, though, there are two versions of this Mishnah; in the other version, the prooftext for five is the verse we have for three, with an agudah being taken as a reference to three, not five. After five comes three, then two, with the same prooftext for two as we saw in the earlier Mishnah in this pereq, "’az nidberu yir’ei Hashem, etc." For one, however, the Mishnah does not use the verse in the earlier Mishnah, but rather cites "be-khol hamaqom asher azkir et shemi avo elekha u-verakhtikha, in every place that My Name is mentioned [or, probably, that I cause My Name to be mentioned], I will come and bless you."

THE OBVIOUS QUESTIONS

Maharal raises numerous questions about this Mishnah, most of them obvious to any attentive reader. He wonders why, if one person merits a visitation of the Divine Presence, the Mishnah starts with ten and works its way down. Granted that the Mishnah was going to do that, why were these the stages it chose (what about 4, 6, etc.)? He does not immediately understand how the verse of va’agudato refers to five—other commentators had suggested that an agudah is the five fingers of the hand, which can be joined into one unit; Maharal does not. Finally, since the Mishnah uses the same prooftext for two here as earlier, why does it change prooftexts when it comes to one?

MY OWN IDEA

Although I recognize that our main goal in this shiur is to study Maharal’s construction of these texts, I have an interpretation of the last part of this Mishnah that I am perhaps inordinately proud of; regardless, I would like to share it with you.

Note that in the previous Mishnah, the Mishnah did not start with ten. More importantly, the Mishnah did not start with the positive qualities of Torah study. Rather, that Mishnah started by saying that two who sit together without words of Torah create a moshav letsim, a gathering of idlers. It occurred to me that that Mishnah and this one are concerned with different aspects of the social gathering problem. In the earlier Mishnah, the concern was largely defensive, avoiding an instance where a gathering could be considered a negative event. To avoid that label, the people at that gathering had to involve themselves with Torah. The Mishnah mentions that when they do involve themselves in Torah, they will merit a visitation of the Divine Presence. In that context, the single person who sits and learns is also simply avoiding the negative consequences of sitting and idling—for which he gets reward, a situation perfectly summarized by the verse "yeshev badad ve-yidom, ki natal alav, he shall sit alone silently, for he shall garner reward for so doing."

In our Mishnah, however, the focus seems to be on producing a visitation of the Divine. The Mishnah starts with ten—the quorum for a minyan, as we’ll discuss in a moment—and goes down to one. In that context, the single person is not only sitting silently, but is attempting to create a presence of God. The verse "yeshev badad ve-yidom" is not relevant, then, because a silent person does not create the presence of God, he(she) just avoids sitting idly. The verse "be-khol hamaqom asher azkir et shemi, in all the place I cause My Name to be mentioned" is therefore more appropriate.

BACK TO MAHARAL

When Maharal confronts these questions, he takes a different approach than I have. First, he asserts that each of the levels here indicates a different level of Divine involvement with the group (as others did as well). What makes his approach so interesting is the way he defends those different levels. First, though, let’s pause to mention that it’s not clear, in any of the sources that I know, what we mean by different levels of the Divine Presence. In one sense, the notion seems obvious that there would be greater and lesser closeness or presence of God, but it’s an ill-defined concept that is worthy of more thought.

Maharal starts with ten, noting that it is the highest number that has significance in Jewish communal terms—once there are ten Jews present, that is a grouping that represents the entire Jewish people, and the Presence that joins such a group is the essential Divine Presence, the hashra’at haShekhinah. Maharal doesn’t mention this, but I think it’s worth pointing out that that characterization of ten ignores indications that higher groups might also have meaning. In the discussion of zimmun in Berakhot, for example, R. Yose haGelili was of the opinion that at several levels of groups, one would adjust the reference to God accordingly (we only say eloqenu, regardless of whether there are ten or 10,000). This Mishnah, according to Maharal, must follow the opinion of R. Aqiva, who does not differentiate.

More importantly, we have a general principle of be-rov `am hadrat melekh, that the larger the grouping giving praise to God, the greater the honor to Him created. This means that if there are two shuls of equal quality (an impossibility, but it helps make the point), it is preferable to daven with the larger shul. In our case, apparently, the Mishnah does not see that principle as affecting the level of Divine Presence that joins the group. That means that the Divine Presence does not come as a function of the honor to Him created (since a group of a million Jews that learns and praises to God creates a greater presence than one of ten), but simply as a response to their status as a representative group of the Jewish people.

LESS THAN TEN?

Below ten is five, three, two, and one. Maharal deals with these numbers by claiming that each represents a significant level of unity over those that came before. The numbers between one and ten that were left out did not add to the unity created (a group of six is in no meaningful way different from a group of five), and the numbers over ten are just add-ons to ten.

FIVE AS THE HIGHEST UNIFIER

In what sense does five create a unity that four (or three) does not? Maharal here mentions two aspects of the number five. First, he points out that two is the first group (because one is just a single person, not a group) and that three is the first odd number (he calls it a number that’s nifrzd; I believe he means that you can’t match all the numbers to each other). Five is the first number that combines an even and an odd (3+2=5), so that it embodies both aspects of numbers. In this part of his discussion, then, Maharal is suggesting that the number five as a grouping has an importance because of a quality of the number. Since that number (or a group with that number of people) incorporates the two kinds of numbers, it has a significantly different quality than the earlier numbers and therefore deserves a qualitatively different visitation of the Divine.

The second explanation adds a little bit to why the nature of the number should affect the nature of the Presence merited. In the second explanation, Maharal notes that two is the first group, apparently giving it an advantage over one. Three has a unity that two does not have—two can be at opposite ends, but with three there has to be a middle created (in two dimensions, three points can’t all be at opposite ends from each other). Five, he says, has an added unity over three, in that five brings together the four points of a square, whereas three only brought together the two points of a line. Thus, while four points can all be at their own space, the fifth one will unify them. It's not clear why Maharal configures three as two points unified by a third, rather than as a triangle. Even if we grant that a triangle has a unity that a line does not, he still seems to envision five as four with a point in the middle, rather than a pentagon, where there is seemingly equal lack of unity as a square. Further, in his reasoning, it’s not clear why seven isn’t even more of a unifier in bringing together the separate points of a hexagon.

Regardless of all that, Maharal’s assumptions are clear: the Mishnah’s criterion for Divine Presence is the level of unity in the group. At each significantly new level of unity, there is a corresponding jump in the level of Divine Presence. The point of the Mishnah, then, is to make us aware of our need to join in a group to become closer to the Divine. In fact, while the Mishnah seems to equate one person with the rest of the groups, Maharal assumes it only means what the earlier Mishnah said, that one person gets reward for his personal study. Joining a group in Torah study, in Maharal’s world, is the way to get to enjoy hashra’at ha Shekhina, an idea that fits well with the upcoming Pesah holiday.