In the Talmud’s Most Difficult Tractate, the Rabbis Tackle Mathematical Probability

The talmudic tractate of Kinnim (“nests”) takes up only three pages in standard editions, and includes only Mishnah (the Talmud’s earlier stratum), without Gemara (the later stratum). As the title implies, it is concerned with bird sacrifices, which were mandated—during the time the Temple stood—for a handful of occasions. Traditionally, Kinnim is considered one of the most challenging parts of the Talmud, as Adam Kirsch explains:

[A] woman who has given birth but can’t afford to sacrifice an animal can bring a pair of birds, known collectively as a “nest,” instead. . . . The two birds are sacrificed in different ways: one is a burnt offering, which means that its blood is sprinkled on the lower half of the altar, and the other is a sin offering, whose blood is sprinkled on the upper half. The woman bringing the sacrifice can either designate which bird is for which purpose or she can leave them undesignated, so that it’s up to the priest [performing the sacrifice] to decide.

The problem . . . is that unlike sheep, which generally stay in a pen or a stall when you put them there, birds can fly. This means that it is easy for different groups of birds to get mixed up with each other: a bird from one woman’s pair could fly over and join another woman’s pair. In that case, the priest who has to sacrifice them is faced with a problem: how does he know which bird is intended for which sacrifice? What if he accidentally sacrifices a burnt offering as a sin offering or vice-versa, rendering them invalid?

This sounds like a practical problem, and no doubt it sometimes happened in the Temple that groups of birds got mixed up. But in tractate Kinnim, this simple premise seems to have been seized upon by some mathematically inclined rabbis as an excuse for inventing math and logic puzzles. . . . The basic rule, . . . is that the priest must avoid even the smallest risk of performing an invalid sacrifice by offering a bird that has been designated for a sin offering as a burnt offering, or vice-versa. . . . How can you maximize the number of acceptable sacrifices while ensuring that no bird is sacrificed for the wrong purpose? . . . The rabbis go on to make their hypotheticals more and more complex.

It’s obvious that [the thorniest of these hypotheticals] could never arise in real life—even before you take into account the fact that, in talmudic times, sacrifice was no longer practiced at all. It is a pure logic problem, a way of thinking about probabilities that delighted rabbis centuries before the invention of modern probability theory. But for the rabbis themselves, there was no clear separation between such mathematical challenges and the other matters discussed in the Talmud, from Shabbat observance to marriage and divorce law.

Read more at Tablet

More about: Halakhah, Judaism, Sacrifice, Talmud

When It Comes to Iran, Israel Risks Repeating the Mistakes of 1973 and 2023

If Iran succeeds in obtaining nuclear weapons, the war in Gaza, let alone the protests on college campuses, will seem like a minor complication. Jonathan Schachter fears that this danger could be much more imminent than decisionmakers in Jerusalem and Washington believe. In his view, Israel seems to be repeating the mistake that allowed it to be taken by surprise on Simchat Torah of 2023 and Yom Kippur of 1973: putting too much faith in an intelligence concept that could be wrong.

Israel and the United States apparently believe that despite Iran’s well-documented progress in developing capabilities necessary for producing and delivering nuclear weapons, as well as its extensive and ongoing record of violating its international nuclear obligations, there is no acute crisis because building a bomb would take time, would be observable, and could be stopped by force. Taken together, these assumptions and their moderating impact on Israeli and American policy form a new Iran concept reminiscent of its 1973 namesake and of the systemic failures that preceded the October 7 massacre.

Meanwhile, most of the restrictions put in place by the 2015 nuclear deal will expire by the end of next year, rendering the question of Iran’s adherence moot. And the forces that could be taking action aren’t:

The European Union regularly issues boilerplate press releases asserting its members’ “grave concern.” American decisionmakers and spokespeople have created the unmistakable impression that their reservations about the use of force are stronger than their commitment to use force to prevent an Iranian atomic bomb. At the same time, the U.S. refuses to enforce its own sanctions comprehensively: Iranian oil exports (especially to China) and foreign-currency reserves have ballooned since January 2021, when the Biden administration took office.

Israel’s response has also been sluggish and ambiguous. Despite its oft-stated policy of never allowing a nuclear Iran, Israel’s words and deeds have sent mixed messages to allies and adversaries—perhaps inadvertently reinforcing the prevailing sense in Washington and elsewhere that Iran’s nuclear efforts do not present an exigent crisis.

Read more at Hudson Institute

More about: Gaza War 2023, Iran nuclear program, Israeli Security, Yom Kippur War