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.

Ockham’s Razor and Hatam Sofer

Let’s start with a trivia question: Hatam Sofer (1762-1839) sent responsa to every single Jewish community (in existence at the time) in one modern-day country. What country is it?

Not long ago, I (Moshe) was in the backseat of my grandfather’s car, and we were schmoozing about HaMapah. I mentioned we were mapping the responsa of Hatam Sofer and his first question was: “and was he sent questions from all of Europe?”

We’ll get to that in a minute.

One of our central goals is to try to understand the halakhic world as it was perceived by people at the particular time, not as we presently interpret it. Today one might hear in the oylem that “Hatam Sofer sent teshuvot to all of Europe”. But is this assertion in fact, true?

Let’s try to refine the question a bit. Europe is a big place and Jews were only in some parts of it. Poskim only sent responsa to places with Jews, so “all of Europe” really means “every Jewish area in Europe.” So to answer the trivia question we opened with, Hatam Sofer sent teshuvot to the only two towns in Switzerland where Jews were allowed to live at the time.[1] Thus, trivial as it may sound, in Jewish terms, Hatam Sofer sent teshuvot to all of Switzerland.

But even on this relatively lenient standard, the prevailing assumptions are all wrong. Out of 675 responsa of Hatam Sofer for which we have place data, a grand total of three were sent anywhere within the vast Russian Empire. While it is possible that he in fact wrote several hundred teshuvot to Russia, and they were all chucked into a fire by some angry Hungarian muttering obscenities about Litvaks, this strikes me as incredibly improbable.[2] Ockham’s Razor tells us that we should dismiss the common belief. I also want to preempt an objection–“but look at how widely he’s quoted”–by noting that all of Hatam Sofer’s works were published posthumously.

Let us compare Hatam Sofer to the person with whom we would most intuitively associate him: his father-in-law and near exact contemporary–they were born within a year of each other and died within two–Rabbi Akiva Eger. Both established themselves far from where they were born but in German-speaking areas: Hatam Sofer was born in Frankfurt but established himself in Central Europe: first in Dresnitz (Strasnice, Czechia), then Mattersdorf (Mattersburg, Austria), and finally, for the last 30+ years of his life, in Pressburg (Bratislava, Slovakia). R. Akiva Eger, on the other hand, was born in Eisenstadt (Austria–very close to Mattersdorf; both are part of the Siebengemeinden, the “Sheva Kehilot” in Burgenland, or, in Elli’s preferred parlance, “the Seven Dorfs”). His rabbinic career took him north into Silesia and then to the territories that Prussia had recently sliced off of Poland. The last two decades of his life he was the rabbi of Posen (Poznan, Poland).

Today, they are considered transcendent figures. However, in their lifetimes, they were not transcendent. Consider this map of the two of them, and see for yourself what they did not transcend. (In a new tab)

(Hatam Sofer is blue, R. Akiva Eger is red)

The sorting effect is really dramatic–the choice between R. Akiva Eger and Hatam Sofer falls cleanly on Austrian vs. Prussian lines. The main outliers for both R. Akiva Eger and Hatam Sofer are one another. An inordinate number of responsa written by Hatam Sofer to Prussia were to R. Akiva Eger, and an inordinate number of responsa written by R. Akiva Eger to the Austrian Empire were to Hatam Sofer and his son, R. Avraham Shmuel Binyamin Sofer (Ktav Sofer).

Why does psak tend to stay within the same country? There’s no per se halakhic reason; the halakhic system and methodology, as generally laid out, should not assign any value to the Austria/Prussia border. However, how the system “should” work is ultimately not the point.

Halakhah, and I thank Russ Roberts and EconTalk for inspiring this point (Elli touched on some of this in our first post, but I prefer a different angle, specifically, less top-down and more bottom-up or agent driven, perhaps more Hayekian?) is a case of emergent order. Nobody designed our modern halakhic apparatus. Nobody assigned you to a specific posek, and no “posek ha-dor” was ever voted on and elected (at least not in the last millenium). It is an organic, spontaneous, informal system that arises from the decisions of independent agents. These independent agents might think that their posek should be a good Prussian, and there is little that can be done about it. A few generations later, different independent agents might decide that Hatam Sofer was the posek ha-dor of a generation when none of those agents were alive.

Today, any respectable beit midrash needs a Hiddushei Rabbi Akiva Eger and a Responsa Hatam Sofer, yet the converse is not true: Responsa Rabbi Akiva Eger and Hiddushei Hatam Sofer are not mainstays in the same way. No grand theory of halakhah can easily account for why their works should be so bifurcated in terms of importance. How is it that R. Shabbetai Cohen wrote arguably the most important commentary on Shulhan Arukh Yoreh De’ah, and an utterly forgotten book on Tur Yoreh Deah? This is emergent order created by the independent actions of independent agents.[3]

One last note: Hatam Sofer is interesting. Unlike almost everyone else we’ve done so far, who were usually “just” poskim, he was an influential pedagogue. His students express tremendous love for him, not just as a posek or a scholarly role model, but in a personal way, too. Our operative theory here is that his influence really begins to expand as his students take up positions around Hungary. This can be seen on a map of Hatam Sofer’s responsa as function of time:

(In a new tab)

[1] These are Ettlingen and Lengnau, which are actually only a couple kilometers apart; they even shared their cemetery.

[2] Though as a dependent probability, if an angry Hungarian did chuck them into a fire, it seems pretty probable that he was muttering obscenities about Litvaks.

[3] F.A. Hayek writes (Law, Legislation and Liberty, pp. 118-119):

“The judge, in other words, serves, or tries to maintain and improve, a going order which nobody has designed, an order that has formed itself without the knowledge and often against the will of authority, that extends beyond the range of deliberate organization on the part of anybody, and that is not based on the individuals doing anybody’s will, but on their expectations becoming mutually adjusted. The reason why the judge will be asked to intervene will be that the rules which secure such a matching of expectations are not always observed, or clear enough, or adequate to prevent conflicts even if observed. Since new situations in which the established rules are not adequate will constantly arise, the task of preventing conflict and enhancing the compatibility of actions by appropriately delimiting the range of permitted actions is of necessity a never-ending one, requiring not only the application of already established rules but also the formulation of new rules necessary for the preservation of the order of actions. In their endeavour to cope with new problems by the application of ‘principles’ which they have to distil from the ratio decidendi of earlier decisions, and so to develop these inchoate rules (which is what ‘principles’ are) that they will produce the desired effect in new situations, neither the judges nor the parties involved need to know anything about the nature of the resulting overall order, or about any ‘interest of society’ which they serve, beyond the fact that the rules are meant to assist the individuals in successfully forming expectations in a wide range of circumstances.”

I think every word here applies to halakhah, even more so than the original, given how the selection of the judge/posek is a case of spontaneous order in and of itself.

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.

The Shape of a Rabbinic Career: Rav Moshe Feinstein and Rav Yaakov Ettlinger

Until now we have mainly been looking at the distribution of responsa through space. In this post we will begin looking at their distribution through time.

What would we expect a typical respondent’s career to look like? When I (Elli) started, I imagined a relatively steep incline in the number of responsa written per year as the rabbi’s reputation grows, then a plateau, then a decline, either gradual or abrupt, at the end of the rabbi’s life.

Of course, the shape would not be completely smooth. Any number of factors over which the respondent has no control could affect his output during any particular period. Nevertheless, over the long run, we would expect the chart to look something like this:

The above chart has nothing to do with responsa or rabbis. It represents what Joe Posnanski imagines the typical baseball player’s aging chart should look like. There’s a slow start, then a “breakout” to stardom, followed by a peak, followed by decline.

Note from Moshe: I expected to see roughly the opposite shape – basically this chart flipped on the X axis. I think this was based maybe on my first-hand experience with R. Aharon Lichtenstein – slow ascent, then rise, peak, and precipitous decline. In baseball terms: the steroid aging curve. A grafting of two equations – “chashuv” increases as a function of age, but infirmity takes its toll at some point. I think this may loosely approximate a couple poskim, but it’s also not accurate too broadly. Back to Elli.

At this point, we have very good bar charts chronicling the careers of five major halakhists. Not a single one fits the pattern outlined above. Nothing is even close. We will look at two of them now and think about what they can tell us about their careers. The other three we will save for another time.

The chart below (once again, based on Michael Pitkowsky’s data) gives us the tally of responsa written by R. Moshe Feinstein broken down by year (as well as volume, which can be toggled).

plot from API (1)


We see that Rav Moshe wrote a significant number of responsa in the 1920s, but then, at the beginning of the 1930s, there a dip that lasts until the late 1940s. A gradual rise spikes in the late 50s and early 60s, followed by a decline and plateau that lasts until the early 80s and a short period of decline before his death in the mid-1980s.

What does this mean?

A full answer will require a much deeper dive. A lot has been written on Rav Moshe, and this could provide a good place for the next generation of research to start. In broad brush strokes, this is what we think we are looking at —

Rav Moshe began to emerge as a significant halakhist in the 1920s in Russia. Many of the responsa he wrote then were “recreational,” but there were rabbis to correspond with and real halakhic questions to answer.

All that changed in the 1930s, the height of Stalin’s campaign against religion. Rabbinic communication by mail became a dangerous endeavor. This campaign played a significant role in Rav Moshe’s immigration to the United States, where did not yet have much of a reputation as a halakhist. That changed after World War II, with the influx of (mainly observant) Holocaust survivors from Eastern Europe, who both knew of Rav Moshe from Europe and were more likely to ask questions of rabbis.

By the late 1950s, the leading American halakhist before Rav Moshe, Rav Yosef Eliyahu Henkin, began to slow down the pace of his halakhic output as he aged and took on more communal leadership responsibility (this was suggested to us by Rabbi Saul Berman). It was at that point that the number of responsa written by Rav Moshe spiked dramatically, and it is also when he began to publish Igrot Moshe. If one were to ask, “When did Rav Moshe become the poseik of America,” the answer is quite clear: between 1957 and 1963.

The subsequent decline and plateau can be attributed to several factors. One is that he, like Rav Henkin before him, began to take on more communal leadership roles. Another is that the growing Hasidic communities in America began to turn to their own poskim, like Rav Menasheh Klein (this, again, was suggested by Rabbi Berman). It is also possible that once he had cemented his status, he did not see as much need to write and publish responsa at such a breakneck pace. Poskim are very conscious of the public personas they create, and there is no doubt that the writing and publication of responsa help to curate and project that persona.

Let us now turn to Rav Ettlinger. Here is a bar chart of his responsa output by year:

BZ - by year


This dataset is somewhat incomplete as many of Rav Ettlinger’s responsa are not dated, but we do have 310 out 362 – 86% of the his responsa – and also, we are confident about what we will find in the additional data, because most of the undated responsa were initially published in the same place as many of the dated responsa: in the rabbinic journal Der Treue Zionswächter, or Shomer Tziyon Ha-ne’eman, which Rav Ettlinger edited.

Consider: the majority of Rav Ettlinger’s responsa were written between 1847 and 1856, precisely when he was editor of the journal. The nature of the journal was that one rabbi would write in with a question or idea, which was then “peer reviewed.” Rav Ettlinger had control over whose answers and responses were printed, and, unsurprisingly, he often published his own answers, which were then collected in Binyan Tziyon. Once he stopped editing the journal, the number of answers he was writing (to questions that were not asked of him specifically) dropped off dramatically.

Stay tuned, Moshe will post about Chatam Sofer later this week (both dates and locations). You can follow us on Facebook or subscribe to email updates.