Avodah Zarah, chapter five, mishnah nine. In the previous mishnah we learned that there is no nullification in a mixture of yayin nesech with kosher wine - yayin nesech that falls in and mixes into a liquid of kosher wine. Our mishnah comes to list additional items that have no nullification, whose status does not lapse, and a mixture that includes them is forbidden. But we must be careful not to confuse the two: this mishnah deals with an entirely different type of mixture.
The two types of mixtures:
Liquid into liquid - liquids that merge with one another, so that their taste spreads and blends. That is what the previous mishnah dealt with.
Dry into dry - the items remain separate and do not merge into one another. Here we have a set of items, one of them forbidden, and the identity of the forbidden item within the set has been lost. This is not wine that fell into wine, but barrels of wine, one of which is yayin nesech and the rest kosher wine. That is what our mishnah deals with.
On the Torah level, in a dry into dry mixture the rule is that there is nullification by a majority - a simple majority, what is called 'chad bitrei', one against two, is enough to nullify the minority. Therefore, three barrels, one of which is yayin nesech - all three are permitted, since the one loses its identity among the other two. This rule was stated regarding a substance mixed with its own kind, where everything is of the same type, and it holds true both on the Torah level and on the rabbinic level.
The two criteria that prevent nullification:
There are certain items, and these are the items listed in this mishnah, in which two separate criteria combine, causing them, on the rabbinic level, not to be nullified in any ratio at all, even one against a thousand:
Forbidden to derive benefit from - these are not items forbidden only for eating, such as a piece of pork, but items from which any benefit whatsoever is forbidden and off limits.
Significant items - most of them are a 'davar shebeminyan', items that are counted as discrete units and sold as individual units. They are whole, large items, and therefore too significant to lose their identity.
So, for example, in the first case in the mishnah - yayin nesech that is not nullified - the reference is to a whole barrel of yayin nesech, since a whole barrel is a significant item. But three cups of wine, one of which is yayin nesech and the other two kosher, which got mixed up so that it is not known which is the forbidden cup - all three are permitted. How to handle this in practice, given that one person drank all three and the like, is beyond the scope of our discussion here; in short, three people may drink the three cups, and for each one of them it is permitted.
But the items that the mishnah will list, because they are entirely forbidden to derive benefit from - no benefit and no economic use is permitted from them - and because they have reached the status of significant items, a 'davar shebeminyan' and the like, are not nullified at all. Even one against a thousand - the entire mixture of a thousand is forbidden.
The language of the mishnah: "Elu asurin ve'osrin bechol shehen" - the following list enumerates items that are forbidden when they become mixed into others in a dry into dry mixture, and that render the mixture forbidden in any ratio at all. There is a dispute among the Rishonim as to whether this applies even to a substance mixed with a different kind, with different types, but we will speak about a substance mixed with its own kind, which is the plain reading of the mishnah: kosher wine and non-kosher wine, or kosher meat and non-kosher meat - two items of the same type. In these there is no nullification at all.
And these are the items that are not nullified:
"Yayin nesech" - the wine of idolaters, when we are dealing with a significant item, that is, a whole barrel that became mixed in among the barrels. One in a thousand - all thousand are forbidden.
"Avodah zarah" - an actual idol, which is a significant item sold by the unit. Therefore, if there were a thousand garden gnomes and one of them was an idol that is worshipped as a deity, while the rest of the figurines are merely decorative, and they all got mixed together - the entire mixture is forbidden, since avodah zarah is forbidden to derive benefit from, and the single idol is a 'davar shebeminyan', a significant item that is not nullified.
"Ve'oros levuvin" - we already saw this at the beginning of the tractate, in chapter two, mishnah three: a whole hide of an animal that has an incision near the place of the heart ('levuvin' - the place of the heart), which indicates that the heart was removed through the animal's chest, and this is a sign that the animal was offered to avodah zarah. The rule is that anything offered to avodah zarah is forbidden to derive benefit from, as we have seen throughout the tractate. Here we are dealing with a whole hide, like a complete fur, which is a significant item and not merely a piece of leather. Therefore, one hide with such an incision that became mixed among a thousand hides that look just like it, which are clearly known not to have been used for avodah zarah - all one thousand and one are forbidden.
"Veshor hanniskal" - the ox that is stoned. One of the halachos is that an animal that killed a Jew stands trial, and if it is convicted it is put to death. An ox sentenced to death is forbidden to derive benefit from, and this prohibition takes effect even before it is stoned: even if it was slaughtered with a knife and its meat cooked, the meat is forbidden. Here we are dealing with a whole animal that escaped and became mixed among other permitted animals - all one thousand and one are forbidden, for a whole ox, and whole animals in general, are considered a significant item.
"Ve'eglah arufah" - the calf whose neck is broken, which is brought down to a hard valley, that wadi to which the elders of the city nearest the body go down when a slain person is found and it is not known who the murderer is, and there the process of the eglah arufah is carried out. The eglah arufah is forbidden to derive benefit from, and the Amoraim disagreed as to when the prohibition takes effect: some say from the moment it is brought down to the hard valley, and some say after its neck has been broken. In any case, once the prohibition has taken effect, if it became mixed among other calves that look like it - the entire mixture, a thousand calves, is forbidden.
"Vetzipporei metzora" - the birds used for the purification of the metzora at the conclusion of the process, when he completes his obligations. For the metzora who has been healed of his affliction, part of his purification process involves two birds: one is slaughtered, and the second is dipped in its blood together with water. These birds are forbidden to derive benefit from, and there is a dispute as to when the prohibition takes effect: whether from the time the bird is slaughtered, or already from the time the birds are taken for the purpose of the process. If the prohibition takes effect from the time of the taking - both birds are forbidden to derive benefit from; and if from the time of the slaughter - only the slaughtered bird is forbidden, since the second one is sent away and flies off. In any case, a forbidden bird that became mixed among a thousand others - all of them are forbidden.
"Usa'ar nazir" - the nazir accepted upon himself not to drink wine and not to derive benefit from grape products, not to become tamei through contact with a corpse, and not to cut his hair. At the end of the days of his nezirus, whether he vowed for thirty days or for three years, part of the process is the shearing of his hair. We are dealing with an entire mane of hair that was shorn off, which was significant and served in the time of the Mishnah as raw material for making sacks. This is not a matter of individual hairs, which are insignificant, but of an entire mane of hair - just as people today donate whole heads of hair for making wigs for cancer patients. Therefore, if such a mane of hair became mixed among a hundred other manes - the entire mixture is forbidden.
"Ufeter chamor" - the firstborn male born to a donkey, which must be redeemed with a sheep, with a lamb or with a goat. As long as it has not been redeemed, the firstborn donkey is forbidden to derive benefit from, and if it became mixed among other donkeys - all one thousand are forbidden.
"Uvasar bechalav" - a mixture of meat and milk that were cooked together, which is a Torah prohibition not only regarding eating but even regarding deriving benefit. We are dealing with a portion that is a 'chatichah hare'uyah lehiskabed', a portion significant enough that it cannot be considered nullified, of the kind served as a single portion to a guest at a meal - a whole hamburger, a steak and the like. Therefore, such a portion that became mixed among a thousand other portions similar to it - the entire mixture is forbidden.
"Usa'ir hamishtale'ach" - the goat cast to Azazel from the cliff on Yom Kippur. Apparently it does not belong in this list, and in the versions of the Rishonim it is not counted among them, and it should be removed. For there is a dispute as to whether the goat is forbidden to derive benefit from, and even if it was not forbidden until it was cast down - the Gemara concludes that it is permitted and is not forbidden to derive benefit from once it has been cast off the cliff. Therefore it is not appropriate to include it here, and in the printed mishnayos before us it appears in parentheses.
"Vechullin shenishchetu ba'azarah" - non-sacred meat or animals that were slaughtered in the courtyard of the Beis HaMikdash. This is forbidden, and their meat becomes forbidden to derive benefit from. Therefore, a portion of meat that is a chatichah hare'uyah lehiskabed, a portion significant enough, that became mixed among other cuts of meat - since it is forbidden to derive benefit from and cannot be nullified because of its significance, it renders the mixture forbidden in any ratio at all.
Why does the Mishnah repeat the rule a second time:
The Mishnah concludes: "Harei eilu asurin ve'osrin b'chol shehen" - all of these items, if they became mixed in and the identity of the forbidden one was lost, render the entire group forbidden. At first glance this is a repetition, since the point was already stated at the opening of the Mishnah. The repetition comes to stress that both criteria are required together:
Something that is forbidden to derive benefit from but is not significant, such as a small crumb of chametz on Pesach, is nullified in a majority after all, since it lacks importance.
Something too significant to be nullified but which is not forbidden to derive benefit from, such as a whole cut of pork - even though it is not nullified on account of its importance, since cuts of pork are forbidden only for eating and not for benefit, if such a piece became mixed among other pieces of meat that look like it, nullification does apply.