Introduction to Tractate Kinim


Kinim is the plural of the word “ken” and it refers here to a pair of birds brought as a sacrifice (in Biblical and modern Hebrew, ken is a nest). There are several cases in the Torah where a person has to bring a pair of birds, either turtledoves or pigeons, one as an olah and one as a hatat. For instance, concerning the zav (man with abnormal genital discharge), Leviticus 15:14-15 states, “On the eighth day he shall take two turtledoves or two pigeons….The priest shall offer them, the one as a sin offering and the other as a burnt offering.” The zavah brings the same offerings (ibid 29-30). A woman also brings these offerings after childbirth (Leviticus 12:6-8), if she is not wealthy enough to bring a ram. A nazirite who was made impure brings them on the eighth day of his purity ritual (Numbers 6:10-11). There are other such cases as well (see Leviticus 5:1-10). A person can also voluntarily bring bird sacrifices (see Leviticus 1:14-17). In this case the bird is a sacrificed as an olah (burnt offering) and not a hatat.


When a person brings a pair of birds as a sacrifice (a ken) the hatat must be sacrificed before the olah. Our mishnah deals with cases where birds get mixed up and it is not clear which was meant to be an olah and which was meant to be a hatat. There are several rules and definitions that will help with learning this mathematical masekhet.


1)      When a person brings a pair of birds as a ken, he can pre-determine which is an olah and which is a hatat. This is called a “determined ken” (sounds like a doll who wants his Barbie!)

2)      If he doesn’t determine which is which, the priest offering them can decide. This is called an “open ken.”

3)      If a person brings several open kinim together, the priest can mix them up and offer half as olot and half as hataot.

4)      If she brings them each as an individual pair the priest cannot mix them all up, and in each pair he must offer one as a hatat and one as an olah.


It seems that there is both a practical and a theoretical interest in our tractate. On the one hand, it is likely that in the Temple, with the many, many bird sacrifices that people must have brought, these sacrifices would have become mixed up one with the other. The mishnah uses the feminine throughout because women would have had to bring these kinim upon childbirth, which seems to be the most frequent occurrence.

The tractate also has great theoretical interest because rabbis seem to enjoy trying to figure out the status of mixtures, be they mixtures of milk and meat, terumah and hullin or hatat and olah birds.


In any case, the tractate is full of mathematical conundrums that have interested rabbis and mathematicians alike. It’s quite a change of pace from the descriptive tractates, Tamid and Middot. It’s also the last tractate in Seder Kodashim. So I hope you enjoy and good luck!