The Talmud Bavli begins its exploration today with a discussion from the Mishnah, which opens with several halachic principles. The first principle states that a mixture of produce that has become forbidden due to contact with heave-offering, known as mixed produce, does not forbid other produce except according to a specific calculation. This means that if heave-offering mixes with ordinary produce, making the mixture forbidden, this initial forbidden mixture will only forbid a subsequent batch of ordinary produce if the heave-offering within the mixture reaches a certain proportion relative to the second batch. This prevents an unlimited chain of items becoming forbidden, ensuring the prohibition is tied to the actual measure of heave-offering present.
For example, if leaven of heave-offering is introduced into a batch of dough, it will forbid that dough. However, if a piece of this forbidden dough then falls into another batch of ordinary dough, the second dough is only forbidden if the original heave-offering leaven within the first piece reaches a specific proportion relative to the second dough. This highlights that the prohibition is not simply transferred by contact with the forbidden mixture, but rather requires a calculated measure of the original forbidden substance to be present. As Rashi explains, the calculation is crucial; it's not an automatic chain reaction of prohibition.
The Mishnah then presents a similar case concerning drawn water in a ritual bath. Drawn water invalidates a ritual bath, but only according to a specific calculation of its volume. This implies that not every quantity of drawn water will invalidate the bath, but rather a certain measure is required. We will later delve into the precise measures involved.
Next, the Mishnah discusses the purification water prepared with the ashes of the Parah Adumah (Red Heifer). It states that the purification water does not become effective unless the ashes are placed into water, not the other way around. The water must be present first, and then the ashes are added to transform the water into purification water. This order is critical for the mixture to achieve its ritual efficacy.
A further case involves a field where a grave was buried, and the field was subsequently plowed. This plowing scattered the remains of the deceased throughout the field, rendering it a field of graves, which causes ritual impurity. The Mishnah clarifies that if this field of graves is then plowed again alongside other adjacent fields, the re-plowing will not cause the adjacent fields to become fields of graves. The initial plowing creates the first field of graves, but the subsequent plowing does not extend this status to other fields. The term "field of graves" refers to pieces of bones scattered by the plow, not an unlimited spread.
The Mishnah then moves to the laws of heave-offering and exchange. It states that one cannot designate heave-offering from produce that has already had heave-offering designated from it. There is no "double-dipping" in heave-offering; once designated, it's complete. Similarly, one cannot make an exchange of an animal that is already an exchange. An animal designated as an exchange is sacred, but it cannot then be used to create another exchange. The power of exchange is a one-time event.
Furthermore, the offspring of a consecrated animal cannot become an exchange. If an animal is consecrated, its offspring is also sacred, but this offspring itself cannot then be used in the process of exchange to consecrate another animal. Only the original consecrated animal can initiate an exchange.
The Gemara then delves into the first case of the Mishnah regarding mixed produce. It asks who is the author of this Mishnah. Rabbi Hiyya Bar Abba, in the name of Rabbi Yohanan, attributes it to Rabbi Eliezer. This refers to a scenario where one measure of heave-offering falls into less than one hundred measures of non-sacred produce, causing the entire mixture to become forbidden. If this forbidden mixture then falls into another batch of non-sacred produce, the second batch also becomes forbidden, provided the same ratio of one to one hundred is not met. The principle is that once the first mixture is deemed forbidden, it carries the status of heave-offering for subsequent mixtures, even if the actual proportion of heave-offering within it is less than a full measure. However, another opinion holds that only the actual measure of heave-offering from the first batch, not the entire forbidden mixture, is considered when it falls into a second batch, thus requiring a much smaller amount to invalidate the second batch.
Regarding the leavening of dough, the Gemara discusses different scenarios. If leaven of heave-offering falls into dough and causes it to leaven, and then a piece of that leavened dough falls into another dough, the second dough is forbidden if there is enough leaven from the original heave-offering to cause it to leaven. Rabbi Hiyya Bar Abba, in the name of Rabbi Yohanan, again attributes this to Rabbi Eliezer. A dispute arises concerning cases where both heave-offering leaven and non-sacred leaven contribute to the leavening process. One view states that the crucial factor is which ingredient was the last to be added, as that is considered the primary cause of the leavening. If the heave-offering leaven was the last to be added and caused the leavening, then the dough is forbidden. Another view, however, maintains that it doesn't matter which was added first or last; if both contribute to the leavening, and the heave-offering leaven remains in the mixture, the dough is forbidden. The Mishnah's ruling, which requires a specific measure of heave-offering leaven to forbid, aligns with the view that does not consider a mere combination of factors sufficient to forbid.
The discussion shifts to the drawn water in a ritual bath. The Mishnah states that drawn water invalidates a ritual bath only according to a specific calculation. For instance, if a ritual bath contains 21 measures of valid water, and one needs 40 measures to be valid, 19 measures are missing. If these 19 measures are drawn water, they can be made valid by channeling them into the ritual bath through a furrow in the ground, as long as the majority of the bath's water is valid. This method of drawing water is acceptable when the majority of the ritual bath's water is already valid. However, if the drawn water constitutes half or more of the total water, this method would not be permissible. The Gemara identifies the author of this view as Rabbi Yehuda ben Yaakov, while the Rabbanan (Sages) would disagree, asserting that even with a majority of valid water, drawn water cannot be made fit in this manner.
The Gemara then presents a teaching from Yosef Ben-Honi regarding drawn water. He states that if water is transferred from two or three vessels into a ritual bath, it is invalid, but if from four or five vessels, it is valid. Rashi explains that the Rabbanan are lenient regarding the channeling of water, allowing it as long as each vessel contains less than a specific measure. The Mishnah's lenient approach, allowing four or five vessels, aligns with this view, suggesting that the individual quantities from multiple vessels are too small to invalidate the ritual bath.
Returning to the purification water, the Mishnah states that the ashes must be added to the water, not the water to the ashes. The Gemara asks who authored this Mishnah, concluding it is not Rabbi Shimon. A teaching is cited where Rabbi Shimon permits placing the ashes first, then the water, citing an analogy to the ritual of the accused wife, where ashes may be placed over water. However, the Gemara clarifies that while Rabbi Shimon allows placing ashes first, we still need proof that this is valid. Two verses are presented: one implies placing the ashes first, and another implies placing water first. The verbal analogy between these verses teaches that either order is acceptable for the Parah Adumah and, by extension, for the accused wife. The opposing view argues that the primary meaning of the verse indicates water first, and the other verse refers to mixing, not order. The principle is that the ingredient that makes the mixture valid should be placed on top, and in the case of purification water, the ashes are the ingredient that makes the water valid.
Regarding the field of graves, the Mishnah states that plowing a field containing a grave creates a field of graves, scattering the bones. However, re-plowing this field will not extend this ritual impurity to adjacent fields. The initial plowing scatters the remains within that specific field, but a subsequent plowing does not cause them to spread further into neighboring fields. The maximum distance a plow blade might scatter remains is considered to be 100 cubits, thus limiting the impurity to the field itself and potentially two adjacent fields on either side, each extending up to 100 cubits.
Finally, concerning heave-offering, the Mishnah states that one cannot designate heave-offering from produce that has already had heave-offering designated from it. The Gemara asks who authored this principle. It cites a teaching where Rabbi Akiva rules that if partners in produce each designate heave-offering from the same batch without the other's knowledge, neither designation is valid. This is because each partner is particular about the other's unauthorized action, effectively invalidating both designations. This aligns with the Mishnah's principle that there is no double designation of heave-offering.
Regarding exchange, the Mishnah states that an animal that is already an exchange cannot itself become an exchange again. This is derived from a verse that emphasizes the singular nature of an exchange: "it shall be its exchange," implying it cannot be the exchange of an exchange. Similarly, the offspring of a consecrated animal cannot become an exchange. While the offspring is sacred, it does not possess the power to effect an exchange. Rabbi Yehuda disagrees, arguing that a specific word in the verse implies that the offspring can indeed become an exchange. The Rabbanan, however, interpret that word to include unintentional acts of exchange, meaning that even if one mistakenly designates an animal for exchange, the exchange is valid, rather than extending the law of exchange to offspring.