Signal and Noise: Part I

[Note: Sorry for taking so long. Elli wrote the following post. We were going to post this earlier, but several long and fruitful arguments about signal and noise delayed it, and brought it to the point where it was best split up for size. We have more material ready on this, and we should be able to get back to posting more frequently. Enjoy. –Moshe]

We have given a lot of attention to the “shape” of rabbinic careers over time. Specifically, we have looked at R. Yaakov Ettlinger and R. Moshe Feinstein and tried to consider what may have affected the shape. Factors like R. Ettlinger’s editorship of Der Treue Zionswächter and R. Feinstein’s presence in the Soviet Union during the years of Stalin’s religious purges, as well as his writing and publishing spike in the late 1950s and early 1960s, we argued, can help explain and understand how their careers developed and how they related to their own writings.

More broadly speaking, however, the goal of HaMapah is not to explain these phenomena as much as it is to show that they exist. Let us illustrate this with a table that shows the number of published responsa written by Hatam Sofer by year.

[Note: the data here is based on Hebrew year – 3760, not the actual Gregorian year. Our date parsing tools are accurate to the day where possible, however, choosing where to assign dates with year only and no further data to the Gregorian year is a bit of a question and a possible noise source].
Another map shows where the responsa were written to (for those with both dates and addresses) during those years. (ideally, open it in a new tab)

What we see here is very uneven. There is a general upward trend from the turn of the nineteenth century until the end of his life, but there is lots of variance from year to year. Before we ask how to account for that, we must ask what exactly needs to be accounted for. We should expect a certain degree of variance from year to year simply because that’s how life works. But what should we expect?

Let us discuss baseball for a moment. Unlike most other sports, much of baseball can be broken down into isolated events: pitcher versus batter. The outcome of any individual event is wildly uncertain, but over time patterns emerge. Certain features of a batter’s performance–the rate at which he strikes out, the rate at which he walks, the rate at which balls put in play result in hits–stabilize over time. There are also local environmental factors that come into play. Smaller parks tend to inflate offense and depress defense, while roomier parks have the opposite effect. Factors like wind, humidity, temperature, and altitude also affect performance. Strength of opponent is, of course, a significant factor. And, of course, there are factors in the personal lives of the players that can have an effect (usually detrimental): injury, illness, exhaustion, and grief, to name a few.

And then there is also simple, blind luck. There is only so much control that a batter can have over a ball hurtling toward him at speeds approaching (or exceeding) 100 miles per hour. Sometimes a well-struck ball finds the glove of a well-positioned fielder. Sometimes the weakest contact results in a base hit. That’s the way the ball bounces.

A basic idea of advanced statistical analysis is to try and isolate the relevant factors, the “underlying” performance of a player, that will give a better picture of who the player really is. It allows us to quantify who has been lucky and who unlucky, and it allows us to determine the specific skill at which a given player excels (or fails). We are able to separate the signal from the noise.

Because of all of the factors mentioned–the “noise”–there is a great deal of year-to-year variance in the actual results of a player’s performance. The overall trend is toward a late-20s peak followed by decline, but the number and rate of hits, home runs, doubles, etc. varies greatly from year to year. Advanced analytics develop different kinds of tools that “smooth” the jagged edges of the year-to-year variance by eliminating or accounting for more and more noise.

It is important to recognize that the “noise” itself has meaning. Poor performance is poor performance, even if it is not indicative of a player’s true talent level. A lucky win still goes in the W column. A player whose home run totals are inflated by Coors Field in Denver still has those home runs to his credit. When a batter faces a pitcher, he either will or won’t get on base. He either will or won’t strike out. This is what gives the game its drama: after all the analysis, the players must still go and play the game, whose outcome is far from certain. All advanced statistics can do is give a good idea of what to expect from a player–a better idea, in fact, than “traditional” statistics that count (noisy) results. They do not tell us what happened or predict with certainty what will happen, though they can predict what will happen with substantially better accuracy than traditional statistics. For instance, FIP predicts next year ERA better than ERA.

Can some of these insights be applied to the study of responsa? Certainly, although there is a certain tension here between the historian and the statistician. For the historian, each responsum is a discrete historical event to be studied on its own. To the extent that the “noise” is part of the event and can be determined, the historian wishes to do so. They are interested in what actually happened.

Statisticians, on the other hand, want to isolate performance from all but the most directly relevant factors. As long as the number of responsa that a given posek wrote in a year is somewhat consistent with expected year-to-year variance, it does not trouble them too much. Whatever may have inflated or depressed the number of responsa that year, even if it was not sheer luck, should be ignored when trying to determine the longer arc of the posek’s career, if the spike or dip is within the typical noise pattern. They want to see transition periods, when the posek breaks out (or in stages), if he declines at the end of his life due to health,  and other larger trends, not blips and aberrations. They’ll want this:

Hatam Sofer & EMAs
Hatam Sofer & EMAs

We’ll get in to more details soon. Stay tuned.

What We Can and Can’t Learn from our Data on Rav Moshe Feinstein

Several readers have pointed out, in Facebook threads and private messages and via email (keep commenting!), that whatever data we have on Rav Moshe Feinstein is incomplete; not all of Rav Moshe’s responsa have been published, and Rav Moshe answered untold numbers of questions orally—in person or by phone. Both of these points are true and important. We alluded to this a bit in “Zoom In”, but, in light of these comments, we will flesh out what we think can and can’t be learned from the table that shows the shape of Rav Moshe’s career, especially since this addresses some of the underlying assumptions of our project.

Rav Moshe’s responsa were not the first to undergo a process of editing and curation; that distinction may belong to Terumat Ha-deshen (possibly resulting in the claim that its author, Rav Yisrael Isserlein, “made up” the responsa therein). The idea that a volume of responsa can be something other than a dropbox for a rabbi’s halakhic correspondence is a crucial one—and one that is just now being studied (in, for example, Dr. Tamara Morsel Eisenberg’s recently completed dissertation; several insights in this discussion are based on her work). Our hope is that HaMapah becomes a tool to further that study.

To take a specific example, after one of our earlier posts a reader asked about responsa written by Rav Moshe to R. Meir Kahane. It turned out that there are two such responsa—Oraḥ Ḥayim vol. 2 no. 32, and Oraḥ Ḥayim vol. 4 no. 36. The first was published in 1963, and the second in 1979. The most interesting thing is that both are dated to 2 Sivan, 5719 (May/June 1959). Clearly, Rav Moshe answered both of these questions at the same time, probably in the same letter. However, the editorial decision was made to publish one part of the letter and hold on to the other part.

The part of the letter published in 1979 is the most lenient of all of Rav Moshe’s responsa on the celebration of a bat mitzvah. Though he retains his generally negative attitude toward such celebrations even in this responsum, he allows the girl to speak before the congregation at a kiddush, and even, if the family had already been so promised, from the pulpit.

It seems clear, and has been subsequently confirmed in discussions with members of the Feinstein family, that Rav Moshe indeed waited until later in his career to publish some of his more surprising and controversial positions. This is one sense of the famous Talmudic dictum, “ko’aḥ de-heteira adif”: the authority needed to issue a lenient ruling and have it be accepted is much greater than what is required for an audience to accept a stringent ruling. In 1979, Rav Moshe spoke from a different place of authority than in 1963. Looking at the various editorial phases of the work can yield a great deal of insight about phenomena like these.

We will circle back to this, but first we have to answer the phone.

Israel L. Shenker’s 1975 New York Times article on responsa includes the above picture of Rav Moshe on the phone. It begins:

Tradition has it that young rabbis completing their training are given an ordination certificate and the telephone number of Rabbi Moshe Feinstein. He is the closest that Orthodox Jewry comes to a court of last resort.

During much of the day he sits plumped atop a fat cushion in a chair in his study on the Lower East Side, great volumes of religious law and opinion stacked from floor to ceiling behind him, his telephone in hand.

Shenker’s article places Rav Moshe’s answers by telephone within the tradition of responsa-writing, but in truth it is something new and different. Every posek, and every rabbi, probably answers more questions orally than in writing. However, until relatively recently, the questioner was limited by distance and modes of communication. Rav Moshe was one of the first great poskim who was instantly accessible to people anywhere on earth. The work Masoret Moshe consists of Rav Moshe’s laconic oral rulings, faithfully recorded by his grandson. We were told that there is enough material to fill twenty volumes.

Therefore, when trying to understand, measure, and describe Rav Moshe’s halakhic authority and how he accumulated it (his own answer in that NYT article: “If people see that one answer is good, and, another answer is good, gradually you will be accepted”), we must acknowledge that we are operating under limitations that do not exist with respect to other halakhists. In any given period, Rav Moshe received a certain number of questions. Of those, he answered a certain number. Of the answers he gave, only some were written. Of the written answers, only some were published. We are therefore looking only at the tip of a 4-tiered pyramid. What can we hope to learn from this? After all, it is possible that Rav Moshe received and even answered the same number of questions in 1947 and 1967 as he did in 1957.

It turns out that we can learn a great deal once we accept the basic assumption that Rav Moshe, like all great halakhists, was very deliberate in crafting his public persona.

It is clear that between 1957 and 1963 Rav Moshe made a huge effort to both write and publish his answers. Of the 101 responsa in the second Oraḥ Ḥayim volume of Igrot Moshe, all but four were written before 1958. The same pattern holds for Even Ha-ezer. In all, during the seven years between 1957 and 1963, he published the first four volumes of Igrot Moshe and also penned close to 400 (c. 21%) of his published responsa.

We may now return to the question of why there is such a marked spike in these years, and we believe that Rabbi Berman’s hypothesis is a good one. Rav Moshe recognized that Rav Yosef Eliyahu Henkin was aging, had too many other commitments, and in general could no longer shoulder the burden of being America’s leading halakhist. Rav Moshe, stepped into that breach by beginning a seven-year frenzy of responsa-writing and publishing. By the time the dust settled in 1963, Rav Moshe had cemented his status as America’s leading halakhist.

It is true that we still do not know how many questions Rav Moshe answered in a given year, though we suspect that his peak was in the late-60s and 70s, the period described in the NYT. Since he had a telephone, his published responsa cannot tell us as much about all the ways he communicated.

However, for that very reason, the responsa that he took the time to write and publish can tell us even more about how he shaped his public image and how he became Rav Henkin’s successor. In short, how he “became” Rav Moshe.

This, in turn, opens up new ways to hypothesize about Rav Moshe’s career and to test our hypotheses. This, ultimately, is our vision for HaMapah.

Zoom In

Last week we used the Maharsham to take a look at some large scale phenomena, especially cultural boundaries. Now we’re going to zoom in on some of the things we noticed that are going on within those boundaries.

One of the major questions we are trying to help answer with this project is whether rabbinic authority can be quantified. Can we use metrics to give a sense of how important Maharsham is? And if so, how?

We have already looked at number of responsa and geographical spread. Those are important data. But are all responsa created equal? If a gabbai asks a rav whether the congregation should skip tachanun on Erev Tu BiShvat, and the rav sits down and writes a lengthy treatise in response, does it really tell us anything about his authority? There are certain types of questions that demonstrate real influence. If people carry on Shabbat based on an eruv approved by a particular rabbi, over and against competitors, it indicates authority. The higher the stakes, and the more lives the question affects, the more important the responsum, and the more authority demonstrated by the responding rabbi.

Let’s take a more concrete example. Through volume 8 of Igrot Moshe, there are 1805 published responsa of Rabbi Moshe Feinstein (RMF). Of those, 48 are written to Rabbi Yaakov Kantrowitz (h/t Michael Pitkowsky). R. Kantrowitz was hardly submitting to RMF’s authority, as he was at least 20 years older than him. Moreover, almost all of these responsa are what we might call “recreational”. These are not responses to halakhic questions, but long letters written by a severely underemployed rabbi in the early years of the Soviet Union (there is not much for a rabbi to do when religion is effectively banned). These 48 responsa to not evince much rabbinic authority.

As for spread, RMF’s responsa are very clustered. He runs up his score in particular cities and with particular people–about 90 are to Memphis (mainly to Rabbi Ephraim Greenblatt), for instance, or 5% of the total (we’re still working on quantifying how many to NYC, and whether to count different boroughs as different cities, but we will get there).

Note just how many questions the top few generate – there are 318 by the top ten alone.
Top questioners in Igros Moshe. [Click to enlarge.] Note just how many questions the top few generate – there are 318 by the top ten alone.
Now let’s go back to Maharsham. Of more than 1600 responsa, very few are “recreational.” They are all based on real, practical questions. Moreover, the top destination is Krakow, which received 29. In total, he wrote to 437 different places (out of the 1427 addresses we’ve identified). That is simply a mind-boggling number. And no more than 2% of his responsa come from any one place or person, except perhaps for his hometown of Berezhany. Nothing like RMF’s 5% to Memphis.

The point of this exercise is not to minimize the greatness of RMF. Rather, it is to show what a big deal Maharsham was, and he was a Big Deal. This has largely been forgotten over the course of a century of Lithuanian supremacism. Hundreds of community rabbis from hundreds of communities asked him their questions. His influence in his time and place was massive. There’s even a book called Maharsham: The Last Posek.

Yet for all his influence, there are certain places that his authority simply did not penetrate.

Drohobych was a huge Galician community in Maharsham’s later years. In 1910 it had over 15,000 Jews. Yet Maharsham addressed not a single responsum there. It’s not due to a regional lack of influence–he has 19 responsa to Stryi, which is less than 20 miles away and two-thirds the size. Another glaring hole is Przemyśl (Pshemyshl in Yiddish; vowels are overrated). Przemyśl’s Jewish population was slightly larger than Drohobych’s. Again, there’s no broader regional absence, as many nearby villages and towns have responsa addressed there, yet the big city is missing.

A final example: On the eve of WWI, the community of Sighet numbered c. 8,000 Jews–a sizable community–while nearby Bychkiv had just over 1,000. Yet only 5 responsa were addressed to Sighet, while seventeen were addressed to Bychkiv. In contrast to the other examples, Bychkiv is punching well above its weight.

We can posit explanations for the three cities with low (or nonexistent) numbers. Przemyśl was the seat of Rabbi Yitzchak Schmelkes, author of Beit Yitzhak and probably Maharsham’s main rival in Galicia in the generation after R. Yosef Shaul Natansohn. He was rabbi of Przemyśl for a long time, whereupon he was succeeded by his nephew and disciple. So Przemyśl remained under his “jurisdiction”, so to speak, even after his departure to Lviv.

As for Drohobych, we note that Rabbi Yitzhak Leib Sofer (1848-1907) was the city’s rabbi, and he had other influences: he was the son of Rabbi Avraham Shmuel Binyamin Sofer (Ktav Sofer) and thus a scion of the greatest rabbinic family in Western Hungary. If anything, his presence in Drohobych indicates that the Sofer family’s sphere of influence was expanding into Galicia.

As for Sighet, by this time its rabbinate was firmly controlled by the Teitelbaum family.

To understand what’s going on here, we borrow a concept from astronomy. The International Astronomical Union (IAU) defines a planet as: “a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.”[1]

A major posek like Maharsham exerts a massive gravitational pull on the entire region. He vacuumed up the questions from hundreds of towns and villages in Galicia. However, there were a few cities whose rabbis “cleared the neighborhood”. They remained the dominant gravitational force in those cities. It seems that there were cultural institutions–like a family rabbinate, for example–that were able to resist outside influence, or individuals with enough authority. In turn, Galicia’s cultural identity and rabbinic tradition is powerful enough to clear its neighborhood and monopolize questions from within its territory, in contrast to regions like Volhynia and Podolia, which send a large chunk of their questions to Galicia. Another example of a city that cleared its neighborhood might be Prague, which seems to have sent very few questions elsewhere over an extended period of time.[2]

These observations are tentative. We need a lot more research before we have anything conclusive, but we would not have even known to ask the question without the data. And we think it holds promise.

For now, think of this post as a study aid and as a way to quantify (and appreciate) rabbinic authority. We will tweak the methodology as we have more data to work with and as we are able to use more advanced metrics and software. This is really just the beginning.

That, in turn, brings us back to a feisty little Carpathian town that punches above its weight: Bychkiv, to which we will return in the next post.

[1] For those wondering at home, Pluto lost planethood over (c).

[2] Expect more on this later, but, in short, we’ve come near completion on a few more poskim, starting from 1800 or so, and we’ve seen virtually nothing to Prague and fairly little to Czechia as a whole.