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Grapes of Math

In this week’s ‘Daf Yomi,’ the Talmudic calculations that make forbidden wine and food into permitted meals for religious Jews

Adam Kirsch
March 27, 2018
Inset images: Internet Archive Book Images; Digital Commonwealth; Library of Congress.
Inset images: Internet Archive Book Images; Digital Commonwealth; Library of Congress.
Inset images: Internet Archive Book Images; Digital Commonwealth; Library of Congress.
Inset images: Internet Archive Book Images; Digital Commonwealth; Library of Congress.

Literary critic Adam Kirsch is reading a page of Talmud a day, along with Jews around the world.

Of all the subjects treated in Tractate Avoda Zara, the one that takes up the most space is wine. The rabbis state as a general principle that Jews are not allowed to have anything to do with wine belonging to gentiles. Not only may Jews not drink such wine, they are not allowed to buy or sell it; nor can Jews have anything to do with wine that has been in the custody of a gentile, even briefly, or that a non-Jew has stirred or handled. The ostensible reason for this wide-ranging ban has to do with idol-worship: the rabbis are concerned that a pagan will use wine to pour out a libation to his god, thus rendering it abhorrent to Jews. The ban is also, of course, an effective way of discouraging business and personal relationships between Jews and non-Jews, which is also a goal of the rabbis in this tractate.

In Chapter Five of Avoda Zara, the subject of wine leads the rabbis to take up the issue of mixtures. When the prohibited wine of a gentile is mixed with permitted wine or other foods, is the resulting compound also prohibited? The answer turns out to depend on flavor, as the Mishna in Avoda Zara 65b explains: “This is the principle: Anything that benefits from imparting flavor is forbidden, and anything that does not benefit from imparting flavor is permitted.”

The Gemara goes on to discuss a type of question that the Talmud loves to pursue at length—a question involving the nature of a substance. Today, modern science teaches us to think of substances as compounds of atoms and molecules. But the rabbis inhabited a world governed by Aristotelian science, which saw substances as metaphysically distinct kinds. For them, wine and water are not just different arrangements of matter, but two absolutely distinct entities. This way of thinking about the material world makes it difficult to understand how one substance can turn into another, which is why the rabbis often ask about such liminal cases.

When permitted wine is mixed with forbidden wine, the resulting mixture is forbidden, because this is a case of “a substance in contact with the same type of substance,” and with such a mixture “any amount of the forbidden substance renders the mixture forbidden.” This makes intuitive sense: mixing wine and wine does not create a new substance, it only changes the quality of the existing substance. But in Avoda Zara 66a, Rava and Abaye, one of the famous pairs of antagonists in the Talmud, disagree about how to apply this principle in the case of prohibited unfermented wine—that is, grape juice—that falls onto grapes.

Abaye holds that, in this case, the grapes are forbidden, because he believes that substance is defined by flavor. Since grapes and grape juice have the same taste, mixing them is a case of mixing like and like. But Rava disagrees, holding that substance is defined not by flavor but by name. Since grapes and juice have different names, this is not a mixture of like and like, but of two different substances. In such a case, the law follows the principle stated in the Mishna, that a mixture is forbidden only if it represents an improvement in taste.

Rava and Abaye go on to debate the related question of smell. A Jew is forbidden from deriving any benefit from the wine of a gentile; but does this include smelling it? Is a pleasant smell substantial enough to constitute a benefit? Abaye says yes: “a smell is a substantial matter,” and so a Jew may not smell forbidden wine. Rava takes the opposite view, saying that “a smell is nothing.” Here, again, the rabbis are bumping up against the limits of the concept of a substance. Because a smell is invisible, it is hard to determine whether it constitutes a substance in the same way as a tree or a table. Modern science, which sees smell as the product of the interaction of human sensory organs with molecules, offers a clearer way of thinking about this phenomenon.

Now the discussion in the Gemara moves to a new level of complication. The rule, as we have seen, is that a mixture of forbidden and permitted foods is forbidden when it represents an improvement in flavor, but permitted if it represents an injury to flavor. The purpose of the distinction seems clear: It is meant to stop Jews from deliberately using forbidden ingredients to enhance the taste of food. When a mixture does not enhance but detracts from the flavor—as with “vinegar that fell onto beans,” to use the Mishna’s example—there is no need to be concerned that Jews will do it on purpose, so the ban is relaxed.

But what happens, the Gemara asks in Avoda Zara 67a, if the mixture “first enhanced its flavor and ultimately detracted from it”? Vinegar with beans, for instance, is considered to be a bad combination if the ingredients are hot, but a delicacy if they are cold. (Rav Dimi reports that, in the city of Tzippori, cold beans with vinegar was a special dish prepared on Shabbat eve.) So what if vinegar belonging to a gentile—which is forbidden, because vinegar is a derivative of wine—falls onto cold beans, and the dish is subsequently heated up? When the cold mixture was made, it was an improvement, and so forbidden; but when it was heated and consumed, it was a detraction, and so permitted. The rabbis decide that such a mixture is forbidden, because the initial enhancement in flavor renders it prohibited, even if it is subsequently reheated.

A little further on, the Gemara takes up a new variation on the problem. What happens if a mouse falls into a barrel of beer? Here the question no longer has to do with the wine of gentiles, but with a different kind of prohibition: Mice are one of the “creeping things” that the Torah forbids Jews from eating. It seems to follow that a barrel of beer with a mouse in it would be forbidden, and that is Rav’s ruling. However, if you invoke the principle that a detrimental mixture is permitted, it might seem that the beer should be permitted; after all, mouse-flavored beer is surely less appealing than regular beer.

But Rav Sheshet quickly closes this loophole. If the Torah forbids consuming mice, it is not because mice taste good. On the contrary, a mouse “is repulsive and people distance themselves from consuming it.” This suggests that the ban on consuming mice is “a novelty,” since God goes out of his way to forbid eating it, even though no one would want to eat it in the first place. It follows that, in this case, even a detrimental mixture involving a mouse is forbidden. A disgusting twist is offered by Rav Shimi of Nehardea, who maintains that, in fact, mouse “is served at the table of kings”: evidently, there were some people who considered it a delicacy! But “this is not difficult,” he explains, using a standard Talmudic formula: field mice are edible and delicious, while city mice are revolting.

Finally, the rabbis settle on a concrete formula, one that converts the subjective question of flavor into the objective, measurable terms of mathematics. In any mixture of forbidden and permitted foods, the mixture is permitted provided that the proportion of forbidden matter is less than one in 60. This holds “for all prohibitions in the Torah,” the Gemara concludes. It would have been possible to skip the whole debate over flavor and substance, simply by stating this formula at the outset. But as we have seen before, the Talmud values the process of discussion more than the actual legal conclusion.


Adam Kirsch embarked on the Daf Yomi cycle of daily Talmud study in August 2012. To catch up on the complete archive, click here.

Adam Kirsch is a poet and literary critic, whose books include The People and the Books: 18 Classics of Jewish Literature.