We learned on yesterday’s daf (=page) that when something non-kosher falls into a pot with kosher food, the mixture will be permitted if the kosher food is at least 60 times greater than the non-kosher food.
The Gemara on today’s daf tells stories that appear to raise doubts about that ruling. The Gemara relates:
A certain man once came before Rabban Gamliel the son of Rabbi with his case. Said Rabban Gamliel: Did not my father permit such a case by the standard of forty-seven-fold? Then I might just as well be satisfied with forty-five-fold.
A certain man once came before Rabbi Shimon the son of Rabbi with his case. Said Rabbi Shimon: Did not my father permit such a case by the standard of forty-five-fold? Then I might just as well be satisfied with forty-three-fold.
Rashi offers two different explanations for these stories.
According to his first approach, these Sages permitted the mixture even though there was less than the 60 times that was required, since the amount of prohibited material in the mixture was only half the size of an olive. As we have learned (see above, daf 96), ordinarily only eating a full ka-zayit will be considered significant enough for someone to be held liable. Here, too, given the miniscule amount of prohibited material in the mixture, a smaller ratio could be accepted to nullify it (even though half of a ka-zayit remains forbidden on its own on a Biblical level).
Rashi’s second approach suggests that the ruling offered was said in an ironic tone. Upon being asked the question whether a ratio of 45:1 would suffice to nullify the prohibited food in the mixture Rabban Gamliel responded “My father did not accept 47:1, how could I accept a smaller ratio!?” According to this explanation, these stories reinforce the requirement that we need a minimum amount of 60 times kosher food to permit a mixture.