Welcome to Math Mutation, the podcast where we discuss fun, interesting, or weird corners of mathematics that you would not have heard in school. Recording from our headquarters in the suburbs of Wichita, Kansas, this is Erik Seligman, your host. And now, on to the math.
To celebrate this month’s Jewish holidays, I thought it might be fun to talk about the legendary Jewish comedian Jackie Mason, who passed away recently at the age of 93. Now you might be wondering what this topic has to do with math. This episode was inspired by an intriguing quote that’s shown up in some of his online obituaries: “The Talmud is the study of logic… Every time I see a contradiction or hypocrisy in somebody’s behavior, I think of the Talmud and build the joke from there.” You may recall that before becoming a comedian, Mason studied to become a rabbi. The Talmud, in case you’re not familiar with it, is the ancient book of Jewish law. Could this book really be viewed as a study of logic?
To test this theory, I picked a joke I remembered from Mason’s show that I saw many years ago, and decided to see if I could relate it to formal logic in the Talmud. This joke was referencing the battles in Israeli courts at the time, over the legitimacy of conversion to Judaism by various types of rabbis. Here’s a paraphrase, as I remember it: “The Israeli Supreme court finally made up its mind on the Jewish conversion laws. If you were converted by an Orthodox rabbi, you’re a Jew. If you were converted by a Conservative rabbi, you’re a half Jew. If you were converted by a reform rabbi, you’re a Puerto Rican.” In case you didn’t get the joke, it references the tensions among the many ethnic groups in New York City, which in the 20th century often put Jews and Puerto Ricans at odds with each other. Trust me, it’s funny, though I can’t match Mason’s delivery!
Searching the Talmud for relevant quotes on this topic, I found an interesting one, discussing how to handle a candidate for conversion. “If he accepts, we circumcise him at once… Two learned men stand nearby, reminding him of some of the easy mitzvot and some of the hard ones. As soon as he emerges and dries himself, he is an Israelite in all respects. “ This would seem to indicate that being Jewish after conversion is a binary value, of 0 or 1— you are or you aren’t. Thus many proposals that came up in the conversion debate might be considered absurd, attempting to apply different degrees of Jewishness: as defined by this quote, you’re Jewish as soon as the ritual is done. So that joke might be said to be mocking the contradiction of attempting to assign fractions to a 0 or 1 value, and thus fall out of the logic of the Talmud.
Now, I’m not claiming to be a Talmudic scholar, so I could be way off here. I did a bit more Google searching, and found that Mason was not alone: there are many philosophers and logicians who do believe the Talmud makes extensive use of formal logic, though couched in confusing human-language phrases. One example is a book by someone named Avi Sion, called “Logic in the Talmud”. He points out that unlike many other religious books, rather than just pronouncing laws commanded from above, the Talmud often uses formal logical arguments to show why these laws must follow from earlier premises. One common example is a fortiori arguments, which mainly work as follows: Suppose we have two subjects, P and Q, which have some attribute R, and we want to find out if P also has a related attribute S. If we agree that P has more of R than Q, but Q has enough R to automatically possess S, then P must therefore also possess S. As my cousin Ben David puts it, “ The humdrum example people are given of the principle is that if person P is stronger than person Q, and if person Q can lift a certain weight, then certainly person P can lift it.”
Now let’s look at one of the examples Sion points out in the Talmud, a debate over how much a woman should be shamed for offending God. The Talmud says: “If her father had but spit in her face, should she not hide in shame seven days? Let her be shut up without the camp seven days, and after that she shall be brought in again. ” We should point out that this spitting in the face was meant to symbolize that the woman had offended her father somehow, though it probably would not be considered very appropriate on the father’s side these days. Looking at the elements of the logic, in this case, the subjects P and Q are God and one’s father, and R is the amount of offensiveness. If in a religious framework where you believe God is more important than any one human, certainly the idea of offending P contains more R, offensiveness, than offending Q. Since offending Q produces punishment S, seven days’ worth of shame, certainly offending P should result in at least that much punishment as well. So applying the formal logic does seem to produce the result here.
Anyway, as you can see, this does get a bit confusing. It requires understanding both the cultural norms of the time— like the face-spitting— and a lot of previous context, like the established rules about shame for offending one’s family. Thus we can see there may be some merit to observing that the Talmud actually does follow rules of logic to some degree, but with the need for a lot of human interpretation. I’m not really into all this complex religious law stuff, but I am happy that Mason was able to successfully convert it into a bunch of great jokes.
And this has been your math mutation for today.