Daf Yomi at Beren: The Math in the Masekhta

By: Professor Lawrence Teitelman  |  November 18, 2021

By Professor Lawrence Teitelman

When invited by a student editor to contribute an article to the YU Observer’s “Daf Yomi at Beren” series, I became curious as to the nature of this column: Does one summarize a recent daf [page] or set of dapim [pages] in easily digestible form? Explore in greater detail one particular Halakhic [Jewish law] or Hashkafic [Jewish thought] topic arising in the Daf? Highlight actual Daf Yomi activity occurring on the Beren Campus?

An online search soon revealed that several past postings have focused on the retention of one’s Daf Yomi learning. Surely this challenge is not unique to Daf Yomi, but attempting to study an entire daf in the typically allocated 30-60 minutes (or the increasingly popular 10- or 8- or 5-minute editions), that in a regular Beit Midrash [designated place of Torah study] setting might otherwise take several days or even weeks, raises the likelihood of forgetfulness if not failed acquisition in the first place. One is reminded of the famed Brisker Rosh Yeshiva who began his keynote address at the Siyum [completion of Jewish text] of an especially ambitious program of Mishneh Torah study by musing, “I mean, how can anyone actually complete three perkakim a day of Rambam? I cannot finish even one halakha!”

One methodology referenced by previous authors in the articles “Memorizing all of Masechet Berachot” and “Daf Yomi at Wilf: Reviewing all of Shas in Your Head” is the Zichru program. In this approach, cleverly crafted simanim [mnemonics] link the actual daf number (bet, gimmel, etc.) with a few salient points from the daf. As a passive subscriber to (albeit not an active practitioner of) the Zichru emails, WhatsApp messages, and other resources, I can attest to their outstanding potential and successful implementation by others. This standalone system when “practiced religiously” — in both senses of both words — leads to remarkable results. 

Another approach is ostensibly inspired by a position posited by Tosafot (Berakhot 11b). R. Yitzchak was asked, why do we say a separate blessing each and every time we eat in the Sukkah, yet a single utterance of Birkhot Hatorah [the blessing on learning Torah] early in the morning suffices for learning interspersed and interrupted throughout the day? Tosafot famously answers that Torah is different in that even as one engages in other activities, one retains some degree of attention to Torah (shani Torah she-eino meya’esh da’ato de-khol sha’ah adam mechyuv lilmod…).

Tosafot, however, does not directly define how that ongoing engagement with Talmud Torah [learning Torah] is preserved. Does the obligation itself that continually devolves upon the individual become metaphysically equivalent to involvement? Is it a more conscious and conscientious attempt to integrate broad-based Torah values into one’s conduct? The application of Halakha to one’s decisions even in seemingly secular contexts? Perhaps one way to implement this imperative, particularly in the context of a university, is to associate one’s Torah learning — Daf Yomi and otherwise — with one’s other academic studies. 

To quickly illustrate with just a few examples from Masekhet Rosh Hashana and two courses, Discrete Structures and Networking & Communications: On page 6b (and again on page 20a), the Gemara presents the opinion of Acherim: “There are four days between one Atzeret (Shavuot) and the next, and one Rosh Hashana and the next; and if it was a leap year, then five days.” A typical twelve-month Hebrew year, with alternating months of 29 and 30 days respectively, yields a total of 354 days. In the “modular arithmetic” of number theory (also known as “clock arithmetic” because its measurement of time resets at 12- or 24-hour intervals), 354 mod 7 = 4, i.e. the remainder after dividing by seven, the number of days in a week, is four. Thus, the number of weekdays by which a holiday will shift from one Hebrew year to the next will be four. Similarly, in a leap year in which one more 29-day month is added, there are now 383 days, and 383 mod 7 = 5, translating into a shift of five days by the same holiday from one year to the next. 

Another instance of mathematical reasoning in Rosh Hashana is the “predicate logic” that appears on Daf 22a. After enumerating various individuals disqualified as witnesses, the Mishna asserts that “Any testimony which a woman is ineligible to offer, they too [the aforementioned individuals] are ineligible to offer”. The Gemara then also stipulates that “where a woman is eligible, they [the aforementioned individuals] are also eligible.” According to the ordinary rules of logical reasoning, one cannot infer the “inverse” of a statement from the statement: just because “p implies q”, does not mean that “not p implies not q.” One must either conclude that the Rabbis already had a tradition to the latter ruling, and were just attaching it to the Mishnah because of its natural relevance, or the original statement should be reinterpreted as “bi-implication,” that is, the two types of testimony or woman and others were already bidirectionally linked.    

Aside from dealing with Rosh Hashana per se, the tractate also addresses the more general matter of Rosh Chodesh: the sighting of the new moon, the declaration of the new month, and the transmission of that information to cities well beyond the Beit Din [Jewish court] where the formalities take place. This is essentially a networking problem, only that the packets are encapsulated in fire signals (an early form of wireless technology) and the routers are mountaintops in the various legs (“hops”) of the end-to-end communication (see 22b). The contemporary cybersecurity issues known as man-in-the-middle and spoofing also come into play. The Gemara also entertains the challenges of “acknowledgement” and “negative acknowledgement” used in the Transport-Layer of networking: What can reasonably be inferred from the absence of such signals? Does it mean that Rosh Chodesh has been postponed, or other factors may be responsible? 

The Gemara (33b) discerns the type of sounds blown from the wailing of Sisera’s mother when her son did not return home from battle. Jewish tradition takes this source even further by saying that we blow 100 Shofar blasts on each day of Rosh Hashana because she cried 100 times. When did she begin to cry? In the language of networking, we might say after the RTT (“round trip time”), the reasonably expected duration of the journey to the destination and the return home.  

While the potential correlations and connections between Daf Yomi and other subjects will necessarily vary depending on both the pursuers and the pursuits, applying the “Associative Property” not only makes our Birkhot Hatorah more pertinent but also our Talmud Torah more permanent.      

Lawrence Teitelman is a faculty member in Stern College’s Department of Computer Science and Rabbi of Young Israel of New Hyde Park.