This mishnah attracts little enthusiasm or excitement when compared with its immediate predecessors and slow readers are lucky to get to it when the third chapter of Avot is recited at breakneck speed in synagogue on Shabbat afternoon. But what is it about?
Rabbi Elazar mentions four fields of study that were pursued by rabbinical scholars in Mishnaic times. The feature they have in common is that they each require arithmetical skills. That, however, is where the similarity between the first and second pair of subjects ends
The first two, as explained below, deal with matters of halachah (Jewish law), while the second two—astronomy and mathematics—may be classified as useful sciences that can help train the mind and may even have some bearing on the performance of commandments, but which are not in themselves the subject of halachah. Let's look at this contrast a little further
The first two items mentioned in this mishnah—the laws relating to bird sacrifices offered after a woman had given birth and to the calculation of days before a woman was regarded as ritually pure—required computations that had great potential relevance to the performance of mitzvot in Temple times. In the case of bird sacrifices, these computations relate, for example, to the number of birds that had to be offered when two or more women who had given birth brought their pair of birds as Temple offerings at the same time, but where one bird had become lost or their birds had intermingled and it was not known to which woman each bird belonged. In the case of ritual impurity, what was at stake was, for example, a woman’s ability to eat or prepare food that was derived from Temple offerings and had the special and elevated status of kadashim: here the Talmud makes provision for calculations that arise from the various situations that can arise if a woman experiences an unexpected flow of blood which may or may not be menstrual.
By the time the tractate of Avot was compiled, neither bird sacrifices nor the eating of kadashim were areas of active Jewish practice. Nonetheless the laws relating to them remain to this day as part of the living corpus of legislation that is the Torah, an expression of the will of God: they lie at the very heart of halachah.
In contrast with the wisdom of the Torah that lies at the heart of halachah, as our Mishnah teaches here, we find the disciplines of astronomy and mathematics. These fields of intellectual pursuit—no matter how vital or exciting they may be in our lives today—do not of themselves constitute an expression of the will of God. That is not to say that there is anything wrong with the pursuit of astronomy and mathematics; rather, they are a sort of “supporting act” in the ongoing personal drama of man’s efforts to reach out to God. They sharpen a person’s mind just as a piquant hors d’oeuvres might sharpen a person’s appetite, but they never graduate to the status of the main course.
Knowledge of astronomy actually played an important part in establishing one of the most distinctive features of Judaism today—the perpetual self-correcting lunar calendar which, inserting an additional month into seven years within each 19-year cycle, skilfully avoids the problems that might occur if certain festivals fall on the wrong day of the week or, worse, the wrong time of the year. However, despite its importance, astronomy was never more than a sideline. Like most other natural sciences, and unlike mathematics, astronomy does not appear to be widely pursued by serious Torah scholars today.
