the baraita means that ritual fringes do not have a maximum measure, i.e., the strings can be as long as one wants; however, they do have a minimum measure, and if the strings are shorter than this measure they are not fit. As, if you do not say so, in a case similar to it, where it is taught that a lulav has no measure, is it possible that it also has no measure whatsoever?

But didn’t we learn in a mishna (Sukka 29b): A lulav that has three handbreadths in length, sufficient to enable one to wave with it, is fit for use in fulfilling the mitzva? This indicates that if the lulav is less than the measure, it is not fit. Rather, it must be that a lulav has no maximum measure, but it does have a minimum measure. So too, ritual fringes have no maximum measure, but they have a minimum measure.

§ The Sages taught in a baraita: The verse states: “That they prepare for themselves strings” (Numbers 15:38). The term strings [tzitzit] means nothing other than strings that hang down [anaf], and so it states in the verse: “I was taken by a lock [betzitzit] of my head” (Ezekiel 8:3). And Abaye says: And one is required to separate the ritual fringes like a gentile’s lock of hair, part of which is braided and the rest of which is allowed to hang loose.

The Sages taught in a baraita: If one affixed the ritual fringes to the tip of the corner or to the border [gadil], they are fit. Rabbi Eliezer ben Ya’akov disqualifies them in both cases.

The Gemara asks: In accordance with whose opinion is that which Rav Giddel says that Rav says: Ritual fringes must be inserted into a hole above the corner and hang down onto the corner of the garment, as it is stated: “On the corners of their garments” (Numbers 15:38)? In accordance with whose opinion is this? The Gemara answers: It is in accordance with the opinion of Rabbi Eliezer ben Ya’akov.

Rabbi Ya’akov says that Rabbi Yoḥanan says: And one must distance the hole through which the ritual fringes are inserted into the garment the length of a full thumb joint from the edge of the garment.

The Gemara notes: And it was necessary to state the ruling of Rav Pappa (41b) that the ritual fringes must be inserted into a hole within three fingerbreadths of the edge of the garment, and it was also necessary to state the ruling of Rabbi Ya’akov. This is because if the location of the hole was taught only from the statement of Rav Pappa, I would say that his ruling that the hole must be within three fingerbreadths of the edge of the garment was to teach that one may not distance the hole from the edge of the garment by more than this amount, but the closer the hole is to the edge of the garment, the better. Consequently, it was necessary to include the statement of Rabbi Ya’akov.

And if the location of the hole was taught only from the statement of Rabbi Ya’akov, I would say that his ruling that it must be a full thumb joint away from the edge of the garment was to teach that one may not situate the hole closer than that to the edge of the garment, but the further he places it, the better. Therefore, both statements were necessary.

The Gemara relates that Ravina and Rav Samma were sitting before Rav Ashi. Rav Samma saw that the corner of Ravina’s cloak was torn and therefore the hole through which the ritual fringes were inserted was less than the full length of a thumb joint from the edge of the garment. Rav Samma said to Ravina: Doesn’t the Master hold in accordance with that statement of Rabbi Ya’akov that the hole must be at least the length of a thumb joint from the edge of the garment? Ravina said to Rav Samma: It was stated that this distance is required at the time when the ritual fringes are made. If the corner tears later, causing the hole to be closer to the edge of the garment, the ritual fringes remain fit.

Rav Samma became embarrassed because he had asked his question based on a mistaken assumption. Rav Ashi said to Rav Samma: Do not be upset that Ravina is a greater scholar than you are; one of them, i.e., the Sages of Eretz Yisrael, is like two of us, i.e., the Sages of Babylonia.

§ With regard to attaching ritual fringes to a garment, the Gemara relates that Rav Aḥa bar Ya’akov would affix four strings to the garment, and he would first fold them in half and then insert them at the point of the folds into the hole of the garment, so that on one side there were eight strings and on the other side there were four loops. He would then take the eight strings and loop them through the four loops and pull them tight, thereby attaching them to the garment. The Gemara explains that he held that we require eight strings when they are initially placed in the garment, in order that there be twisted cord and “twisted cords” (Deuteronomy 22:12), i.e., four doubled strings, at the place, i.e., the time, when he creates the loose hanging string.

Rav Yirmeya of Difti would affix eight strings that are sixteen strings after they are placed in the hole of the garment and half of each string hangs down on each side, and he would not loop them as Rav Aha bar Ya’akov did. Mar, son of Ravina, would prepare ritual fringes like ours, placing four strings through the hole and allowing both ends of each string to hang down, thereby forming eight.

§ The Gemara relates that Rav Naḥman found Rav Adda bar Ahava affixing strings to a garment and reciting the blessing that concludes: To prepare ritual fringes [tzitzit]. Rav Naḥman said to Rav Adda bar Ahava: What is this tzitzi sound that I hear? This is what Rav says: Ritual fringes do not require a blessing when one attaches them to the garment.

With regard to this statement of Rav, the Gemara relates that when Rav Huna died, Rav Ḥisda went into the study hall to raise a contradiction from one statement of Rav to another statement of Rav, as follows: Did Rav actually say that ritual fringes do not require a blessing when one attaches them to the garment? But doesn’t Rav Yehuda say that Rav says: From where is it derived that ritual fringes attached by a gentile are unfit? It is derived from a verse, as it is stated: “Speak unto the children of Israel and command them that they prepare for themselves strings” (Numbers 15:38). The Sages derive from here that the children of Israel shall prepare ritual fringes, but the gentiles shall not prepare ritual fringes.

The Gemara asks: But what is the contradiction between these two statements of Rav? Rav Yosef said: Rav Ḥisda held that in the case of any mitzva for which the necessary item is fit when produced by a gentile, if it is produced by a Jew, he does not need to recite a blessing. Conversely, any mitzva for which the necessary item is unfit when produced by a gentile, if it is produced by a Jew, he needs to recite a blessing when he produces the item.

The Gemara asks: And is this an established principle? But what about circumcision, which is valid if performed by a gentile, as it is taught in a baraita: In a city in which there is no Jewish physician, and in which there is an Aramean, i.e., a gentile, physician and a Samaritan physician, it is preferable that the Aramean circumcise the Jewish boys of the city and the Samaritan not circumcise them; this is the statement of Rabbi Meir. Rabbi Yehuda says: It is preferable that the Samaritan circumcise the boys and the Aramean not circumcise them. Nevertheless, all agree that a circumcision performed by a gentile is valid.

And despite the fact that circumcision performed by a gentile is valid, when it is performed by a Jew, he must recite a blessing, as the Master said: The one who circumcises a child says: Blessed are You, Lord our God, King of the universe, Who has sanctified us through His mitzvot and has commanded us concerning circumcision.

The Gemara answers: Is there reason to resolve the contradiction according to anyone but Rav? Rav himself invalidates circumcision performed by a gentile, as it was stated: From where is it derived that circumcision performed by a gentile is not valid? Daru bar Pappa says in the name of Rav: This is derived from the verse: “And God said unto Abraham: And as for you, you shall keep My covenant, you, and your seed after you throughout their generations” (Genesis 17:9). The verse indicates that only the descendants of Abraham may perform circumcision.

Rabbi Yoḥanan says that this halakha is derived from the doubled verb in the verse: “Must be circumcised [himmol yimmol]” (Genesis 17:13), which he interprets to mean: Only one who is circumcised [hammal] may circumcise [yamul] others.

The Gemara notes that the halakha with regard to a sukka supports the opinion of Rav Ḥisda, who holds that when an item used for a mitzva can be created by a gentile, a Jew who creates it does not recite a blessing. And the halakha with regard to phylacteries is a conclusive refutation of his opinion.

The Gemara explains: A sukka is fit even if it was built by a gentile, as it is taught in a baraita: With regard to a booth built by gentiles, a booth built by women, a booth for domesticated animals, a booth built by Samaritans, a booth of any sort, each is fit for use as a sukka, provided that it is roofed in accordance with the halakha.

And if a sukka was built by a Jew, he is not required to recite a blessing upon its construction, as it is taught in a baraita: One who constructs a sukka for himself recites: Blessed are You, Lord our God, King of the universe, Who has given us life, sustained us, and brought us to this time. When he comes to sit in the sukka, he recites: Blessed are You, Lord our God, King of the universe, Who has sanctified us through His mitzvot and commanded us to reside in the sukka. The Gemara notes that the baraita indicates that he recites a blessing at the time of construction, whereas he does not recite a blessing including the words: To construct a sukka, which confirms the opinion of Rav Ḥisda.

By contrast, the halakha with regard to phylacteries is a conclusive refutation of Rav Ḥisda’s opinion. Phylacteries are unfit when written by a gentile, as it is taught by Rav Ḥinnana, son of Rava,