Commentary for Avodah Zarah 137:7

Hillel seems to think that the vinegar with the mouse in it is prohibited because you can taste the mouse and even though the taste is a bad taste, it is still prohibited.
Ashi responds that in that case the mouse was, or at least might have been, broken up into pieces. One who drinks the vinegar may actually eat a piece of moust. But if the mouse was whole and could be fished out (moused out?) the vinegar would be permitted because the taste is bad.

Ravina thought that if there was 100 times more vinegar than mouse parts that the mouse would be “neutralized.” Meaning that the mixture would be permitted, as long as the volume of the mouse was removed. This is the rule with regard to terumah that falls into non-holy produce. If there is 100 times more non-holy produce, the mixture is permitted, although he does have to remove the volume of terumah that fell in.

The mishnah about terumah being neutralized at a ratio of 100 to 1 referred to cases where one cannot taste the terumah. For instance terumah oil falls into ordinary oil. But if terumah spices fall into food and they can be tasted, the ratio does not matter. The same should be true for the case of a mouse—it should be subject to the test of taste.

We can see here how the concept of “imparts taste” is transformed into a concept of set ratios. The early amoraim operate through a system of imparting taste. This is a sensible system but hard to follow—who wants to taste the mouse beer or vinegar. Therefore, to solve the problem, they come up with set ratios. The latest voice in the Talmud gives the same ratio to everything—60 to 1. In Hebrew this is called “batel beshishim” and is a very important concept in halakhah.

If, while transporting the wine with the non-Jew the non-Jew assumes that the Jew was always watching the wine, the wine is permitted. As long as the non-Jew suspects that the Jew might catch him opening up the wine and drinking from it, the non-Jew will not do so. The Jew might even leave the wine with the non-Jew for a while, as long as the Jew does not tell him that he is doing so.
If the Jew leaves the non-Jew and tells him that he is doing so, then the non-Jew knows that he has a certain period of time in which he might be able to drink the wine without being caught. There are two opinions in the mishnah about how long this period of time must be. According to the first opinion, the non-Jew must have enough time to make a hole in the stopper of the jug (the stopper was made and sealed with clay), and then fill the hole back in, and the new seal to dry, so that the Jew will not be able to tell that it was opened when he returns. If the Jew did not tell the non-Jew that he would be away for this period of time, the wine is permitted. The second opinion is that of Rabban Shimon ben Gamaliel. He assumes that if the non-Jew merely makes a hole in the stopper and then reseals it, the Jew will see the damage. The only way the non-Jew will avoid getting caught is if he removes the whole stopper, and then closes the jug with a new stopper and then the sealing on this new stopper dries. If the Jew does not stay away for the period of time it takes to do all of this, the wine is permitted.

In this situation the Jew again leaves the non-Jew with his wine, this time to make a quick excursion into the city. Note that he uses a short cut into the city. The fact that he is going and returning quickly will make the non-Jew fear getting caught should he open the cask. Therefore the wine is permitted.

In this scenario the Jew leaves the non-Jew in the store. Although the Jew is constantly going in and out of the store, and frequently leaving the non-Jew alone with the wine, the wine is permitted. Again, as long as he doesn’t tell him that he is leaving and when he is returning, the wine is permitted.

When the Jew leaves the non-Jew alone at the table with an open flask of wine, it is of course assumed that the non-Jew will drink from the wine, thereby making it forbidden. However, since it is not customary for guests to drink from the “side-table”, the wine there is not forbidden. This side-table is evidently somewhat like the shelf behind the bar in our time. If you leave your guest with a bottle on a table it is acceptable for him to drink from the bottle. It is much less acceptable for him to go behind the bar and take out his own drink.
If, however, the Jew told the non-Jew that he could mix some wine with water (this is how wine was always drunk during the time of the mishnah), then of course we must assume that the non-Jew will take also what is on the side-table. Although he did not specifically tell him to take from the wine on the side-table, it is as if he had done so. It is like someone today saying, “help yourself” to his friend sitting at his bar. Therefore all of the wine is forbidden.
If the Jew leaves the non-Jew with open casks of wine in the house, they are forbidden. The closed casks are permitted, as long as the Jew was not absent long enough for the non-Jew to open the cask, make a new stopper and then let the stopper dry.

To understand our mishnah, the Talmud cites a parallel from the rules of purity. The situation describes a Jew who wants to preserve the ritual purity of his food, but hires workers who are not ritually pure. If he just leaves them alone with his food, the food remains pure. But if he tells them he is going, then as soon as they are out of his site he must be concerned that they have touched the food and thereby defiled it.

The Talmud asks why in the first case the food is assumed to be pure and the second it is assumed to be impure. R. Yitzchak explains that in the first case the Jew made sure that his workers were pure. We should not that this is clearly not the simple reading of the baraita.
Clearly the difference is between telling them that he was going away and simply going away. The Talmud will get to such an explanation below.

The Talmud struggles with R. Yitzchak’s interpretation. First of all, if the Jew had his workers’ purify themselves, then the same would seem to be true in the second clause? If we answer that the am haaretz, while himself pure, will not make sure that others, who are not pure, do not touch the pure things, then the same should be true of the first clause. When the Jew leaves, there is no way of ensuring that someone impure did not touch the pure food.

Rava says that in the first clause the pure things remain pure because the owner could come back in some roundabout path and they would not see him coming. Since they cannot see him coming, they will be afraid to touch the food.