It seems that your questions are addressed by the Vilna Ga'on in Bi'ur ha'Gra, Orach Chaim 12, DH ul'R"T.

1) The Vilna Ga'on cites Tosfos (41b, DH Beis, second paragraph) who writes in the name of the Sifri: "Since it says, 'They shall make for themselves Tztizis,' I would have thought that this means one." This is also written in the previous Tosfos there (that from the verse I would have thought it meant only one). The Vilna Ga'on writes that Tosfos gave a forced explanation concerning the number of Chutei Techeles, and he also writes that Tosfos' explanation about eight strings is forced.

2) However, the Vilna Ga'on does proceed to explain what the source of Tosfos' explanation is. He writes that indeed the word "Pesil" suggests one, and the word "Tzitzis" (which refers to the white strings) also suggests one. There is another factor at play here, namely that there is a Sevara that the number of white strings should be identical to the number of Techeles strings. (This is actually written by Tosfos to 38a, DH ha'Techeles, ten lines from the end of Tosfos, and Tosfos to 41b, DH Beis (first), that it is logical that the number of Techeles strings and white strings should be equal).

3) The Vilna Ga'on then proceeds to explain how Beis Hillel and Beis Shamai derived their respective opinions concerning how many strings there should be. Beis Hillel learns it from the word "Gedil." They learn that this word teaches that there are 3 white strings (as in fact is stated in the Sifri to Devarim 22:12, "Gedilim means that there must not be less than 3 strings") and it therefore follows that according to Beis Hillel there are also 3 Techeles strings.

Beis Shamai disagrees and maintains that from the word "Gedilim" we learn that there are 4 white strings. Their source is the Gemara on 39b which states that "Gedil" tells us 2, and "Gedilim" tells us 4. This Gemara follows Beis Shamai. Once we know that there are 4 white strings, it follows that there are also 4 Techeles strings, since we said that it is logical that the number of white and Techeles strings should be equal. The Vilna Ga'on notes that when it says in the Gemara the number of strings, this is always referring to the number of strings of one kind, not of both kinds.

4) To summarize, according to the Vilna Ga'on's understanding of Tosfos, there is a rule that the number of white and Techeles strings must be equal. In addition, the Gemara on 39b tells us that there are 4 Gedilim. Gedilim means only white strings. From here we know also that there must be 4 Techeles strings, so we have a total of 8 half-strings, and this means that according to Beis Shamai, whom the Halachah follows in this Sugya, there are two whole Techeles strings and two whole white strings.

Kol Tuv,

Dovid Bloom

I would just like to summarize very briefly what I wrote earlier about the source of Rashi and Tosfos' opinion, and then to relate to the question of why Tosfos is the more accepted explanation.

1) To recap, a major source is the Gemara (39b) that says that there are 4 Gedilim. This source alone is not sufficient, because the Rambam and Ra'avad learn that this means 4 whole strings, which are 8 half-strings; this Gemara does not relate to how many of these 8 strings are white and how many are Techeles. Therefore, Tosfos must go a bit further. Tosfos points out that whenever the Gemara states the number of strings (at the beginning of 39b or on 41b, where the dispute between Beis Hillel and Beis Shamai is cited), the Gemara never says whether these strings are white or Techeles. Therefore, the Vilna Ga'on writes that according to Tosfos these numbers in the Gemara always refer only to one kind, not to both. In addition, we know that "Pesil" means "Techeles" because they are stated next to each other in the Torah. It therefore follows that the other word mentioned in the Torah -- "Gedil" -- is not Techeles but rather white. So when the Gemara on 39b says that there are 4 Gedilim, it means that there are 4 white strings. Tosfos then writes the Sevara that things should be symmetrical and the number of white strings should always be equal to the number of Techeles strings. This is how Tosfos gets to his Shitah that there are 4 white strings and 4 Techeles strings. Of course, this has already been written by Rashi in the Mishnah on 38a, but Rashi did not tell us his sources, so we needed Tosfos and the Vilna Ga'on to elucidate the sources further.

2) After I wrote all of the above, I found that the Mesivta edition of the Gemara cites (in Yalkut Bi'urim, p. 199, #25) the Chemdas Daniel who asks, why did Tosfos go against the Sifri, when it does not say anything in the Gemara against the Sifri that there is only one Techeles string? The Chemdas Daniel remains with a "Tzarich Iyun Gadol" on Tosfos. The Mesivta also cites the Netziv of Volozhin who asks where Tosfos learned his Shitah. However, I think that on the basis of what we have seen above in the name of the Vilna Ga'on, we can now understand the approach of Tosfos.

3) Now to the question of why Tosfos is more accepted than the Ra'avad and Rambam. Firstly, I am not convinced necessarily that it is more accepted. If we look at the Bartenura on the first Mishnah in this chapter, we notice that he cites both the Shitah of 2+2 as well as the Shitah of 1 + 3. The Tosfos Yom Tov writes that the Bartenura copied this from the Sefer Mitzvos Gedolos (SMaG). Then, Tosfos Yom Tov cites the Beis Yosef who also cites the SMaG and writes that the reason why the SMaG cited both Shitos and did not decide who the Halachah follows is because anyway nowadays it makes no Halachic difference since we do not possess Techeles. We see clearly that the Beis Yosef did not decide between the Rambam and Tosfos.

4) I also suggest that it is possible that since the Vilna Ga'on writes that the explanation of Tosfos is forced, this implies that the Vilna Ga'on prefers the Peshat of the Rambam and Ra'avad. However, this is not so clear, because afterwards the Vilna Ga'on does explain Tosfos thoroughly, so possibly this means that he agrees with Tosfos.

It is true that the Taz (11:13) writes that when they possessed Techeles they used to make 2 strings from Techeles and 2 from white. However, I suggest that possibly the Taz mentions this opinion because it is more symmetrical, but it does not necessary mean that he is ruling like Tosfos, since it is not necesary for him to rule on the matter since nowadays we do not possess Techeles. The Mishneh Berurah (11:58) copies the words of the Taz.

5) However, I did see there in Mesivta #23 that he cites the Piskei Ri'az, Hilchos Tzitis #8, who says that the majority of Poskim hold like Tosfos. I hope I have managed to show how this Shitah fits well with the Gemara.

Kol Tuv,

Dovid Bloom

I am now going to approach the matter of why the Shitah of Tosfos is more accepted by trying to show some challenges which have been made to the Rambam's approach. I should note, however, that in fact several Acharonim actually show how well the Rambam's explanation fits in with the Gemara; see especially Teshuvos Mishkenos Yakov OC #13 and #18, and Or Same'ach Hilchos Tzitis ch. 1, and Emek Berachah (Pomerantz) Inyanei Tzitzis #1. However, there are certain difficulties that have been raised on the Rambam's opinion and possibly it is because of this that so many Rishonim side with Tosfos.

1) First, one should realize that what is special about the Rambam's Shitah is not only that there is only one half of a string that is Techeles, but in addition this half-Techeles string has a special role. It is the string used for "Kerichah" -- for winding around the white strings. The Rambam (Hilchos Tztizis 1:7) explains that it is only the first and the last windings which are done with white strings (and each time it is only 1 winding which is done) while all the other windings (which seem to be performed by doing 2 windings each time) are done with the one Techeles string.

2) If so, there is now a question that can be asked on the Rambam from the very first Mishnah in our chapter. The Mishnah states that if there is no Techeles available, this does not prevent the white strings from being valid. This does not present a difficulty according to the Rambam, but the problem is from the next part of the Mishnah which states that if no white is available, this does not prevent the Techeles from being valid. This means that it is possible to have all 8 strings from Techeles. How can this possibly reconcile with the Rambam's opinion that there is only 1 Techeles string and that this string is wound around the white strings? The Rambam learned the latter Halachah from the verse (Bamidbar 15:38), "And they shall place on the Tzitzis of the corner the Techeles string." From here the Rambam derived that the Techeles string must be wound around the white strings, so how is it possible that all 8 strings could be Techeles, which would mean that there are no white strings around which the Techeles string could be wound? This part of the Mishnah appears to present a significant difficulty to the Rambam's position. (This difficulty is raised by the aforementioned Teshuvos Mishkenos Yakov #18.)

3) This question is in fact answered by the Rambam himself in Hilchos Tzitzis 1:4 where he codifies the first Mishnah. He writes that it means that if someone possesses no Techeles he may use white only. This works well witht he Mishnah. However, the Rambam continues and writes that if somebody used both white and Techeles strings, but later on the white strings were all cut and only the Techeles remained, it is still kosher. We see from this that the 2 parts of the Mishnah are not similar. Indeed, one cannot make Tzitzis solely from Techeles strings according to the Rambam for the reasons that we saw above. This is why the Rambam had to say a new Peshat in the Mishnah, "ha'Lavan Eino Me'akev ha'Techeles," which is specifically connected with the Sugya of "Gardumim" -- that if the strings were in order to start off with, sometimes it does not matter that they were broken afterwards.

4) We now may note that this Peshat of the Rambam seems to be quite forced, while according to Rashi and Tosfos the Mishnah can be explained much more simply. According to Rashi and Tosfos, l'Chatchilah there should be 2 white strings and 2 Techeles strings which play an equal role. However, if either white or Techeles were missing entirely, it is still possible to make the Tzitzis with the other kind only. This appears to be a more straightforward approach to the Mishnah. In fact, we notice that this is included in what we wrote in a previous reply in the name of Tosfos, that it is a Sevara that the white strings and the Techeles strings should be equal, but we have now strengthened this Sevara with a source from a Mishnah which can be explained more simply once we say that they are equal.

5) Now let us address a different question on the Rambam. This is from the Gemara in Eruvin 96b, where we learn that if one finds tongues of Techeles in the market place they are invalid to be used for Tzitzis, while if one finds strings of Techeles they are kosher. The Gemara asks why are the strings kosher and answers that the scenario is that the strings that were found had been broken and then re-tied. One would only bother to re-tie them if he needed them for use on a Tzitzis garment and not merely if one needed the strings for a mundane item of clothing. The question is that, according to the Rambam's opinion that the Techeles string used for Tzitzis is half- white and half-Techeles, there should be no problem recognizing such a string if one found it in the street! This is an unusual double-colored string which no one would dye in such a way for an everyday item of clothing, and the fact that one found such a string should be a clear proof that the strings were prepared for the purpose of being used for doing a Mitzvah. The Gemara in Eruvin 96b should not need to take resort to different reasons to explain why the strings are kosher! The fact that the Gemara did not give this answer appears to present a difficulty to the Rambam's explanation that the Techeles string was half-white and half-Techeles.

6) I hope I have managed to show some examples which seem to be more consistent with the Shitah of Tosfos, and possibly this may help us understand a little why Tosfos' opinion appears to be the more accepted one.

Kol Tuv,

Dovid Bloom

Now I will try, b'Siyata d'Shemaya, to look into the sources and the advantages of the Rambam's Shitah.

1) First, I would point out that in fact there are two places in the Sifri where there is a text which supports for the Rambam. The first is in Parshas Shelach (15:63) as you write, Yehoshua, and there it states, "Beis Shamai says 'three of wool and the fourth of Techeles' and the Halacha follows Beis Shamai".

The second passage is in the Sifri to Parshas Ki Tetzei (22:84) which cites a text as follows, "'You shall make fringes' (Devarim 22:12... Another explanation: 'You shall make fringes' refers to white strings. How do we know to include one string of Techeles? -This is learnt from Bamidbar 15:38, 'And you shall place on the Tzitzis of the corner the Techeles string,' and the Halachah follows Beis Shamai." We learn from both of these passages in the Sifri that there is one string of Techeles, so if this is the text which the Rambam and the Ra'avad had, it is an excellent source from Chazal for their opinion that there is only one Techeles string, and in addition it is consistent with the simple explanation of the verse "the *string* of Techeles."

2) Tosfos (41a, end of DH Beis #1) also writes that the Sifri states that there are two white strings and one Techeles string (there is a difference between Tosfos' text and the text of the Sifri in Parshas Shelach which I cited above concerning the number of white strings, but both texts agree that there is only one Techeles string). However, Tosfos learns that there is a dispute between the Sifri and between the Talmud Bavli, and therefore Tosfos rules like the Bavli. In contrast, the Rambam learns that there is no such dispute, which leaves him free to rule like the Sifri.

3) Now I am going to try to show some passages in the Bavli itself which appear to fit well with the Rambam's opinion. These are cited by Teshuvos Mishkenos Yakov, Orach Chaim #13. The Mishkenos Yakov was written by a Talmid of Rav Chaim of Volozhin, which means that he was a Talmid of a Talmid of the Vilna Gaon. I once heard from a Talmid Chacham that the Derech of the Mishkenos Yakov is to go through Sugyos and show how the Gemara fits well with the explanation of a particular Rishon and he thereby justifies in Halachah the opinion of that Rishon. This is in fact exactly what the Mishkenos Yakov appears to be doing with the Rambam's opinion concerning the number of Techeles strings.

4) First, I will return to an idea that I mentioned briefly in my third reply (see above) -- that according to the Rambam the Techeles string has a special role of being the string wound around the white strings. The Mishkenos Yakov claims that this is apparent from the Gemara (end of 39a) which states that when one starts to wind the strings he starts with white, and when he concludes he concludes with a white string. The Mishkenos Yakov asserts that the implication of the Gemara is that it is only the beginning and the end of the winding which is done with the white string, while the chief job of winding is done in the middle using the Techeles string.

5) The Mishkenos Yakov writes that the source for this is the verse "Pesil Techeles." The word "Pesil" has the same root as the word "Pesaltol" in Devarim 32:5, "Dor Ikesh u'Fesaltol" -- "A crooked and winding generation." "Pesaltol" or "Pesil" means something which is wound around.

6) The Mishkenos Yakov also writes that there is a proof for the Rambam's opinion from the Gemara on 39a in the name of Rav that the string which is wound around is counted as part of the number of eight strings. The Mishkenos Yakov writes that one can understand according to the Rambam why it was necessary to say that the winder string is part of the 8: Since the Torah says (Devarim 22:12), "You shall make Gedilim," we might have thought that this means that there are 8 white Gedilim and around them one must wind the separate Techeles string. This is why Rav tells us that we should not use such reasoning; rather, the winding Techeles string is counted as part of the number of 8. The Mishkenos Yakov writes that according to Rashi and Tosfos, it is difficult to understand why it was necessary for Rav to tell us that the string used for the winding is counted as part of the 8, because according to Rashi and Tosfos this is obvious since there is no essential difference between the white strings and the Techeles strings, and so the winding could be done by either.

7) To summarize, so far we have seen that there appear to be 2 proofs for the Rambam from 39a: (a) the Gemara that says that we start winding with white and we finish with white which implies that the chief winding is in the middle and is done with Techeles; (b) Rav's statement that the winding string is counted as part of the 8 which is necessary to state only according to the Rambam's explanation.

There are other supports that can be offered to the Rambam's Shitah but I will close here for the moment.

Kol Tuv,

Dovid Bloom

Here are more sources on the side of the Rambam:

1) The Mirkeves ha'Mishnah (on the Rambam, Hilchos Tzitzis 1:7) points out further support for the Rambam's Shitah that there is just the one string which is specially designated for the winding. The first support is from the same Gemara (39a) that I cited in my previous reply in the name of the Mishkenos Yakov, but from a slightly different angle. He points out that Rav said "Chut Shel Kerach" -- "the string of Kerach." "Kerach" means "winding," which suggests that there is only one string which is used for winding. The Mirkeves ha'Mishnah points out immediately that this is not quite true, as we saw in my previous reply from the Gemara (end of 39a) that one starts off and concludes the winding by using the white string. However, the Mirkeves ha'Mishnah writes that since only the minority of the windings are done with the white strings, it is only the chief winding string to which Rav refers as the "string of winding."

2) The Mirkeves ha'Mishnah now points out that there is another statement in the Gemara (39a) that appears to read better according to the Rambam than according to Rashi. Rava said in the name of Shmuel: "Techeles she'Karach Rubah, Kesherah." Rashi explains that the word "Techeles" here refers to the entire Tzitzis. Shmuel therefore means that if the majority of the area of the strings were composed of wounded strings ("Gedil"), not free-hanging strings ("Anaf"), it is still Kosher. Rashi writes that l'Chatchilah the Mitzvah is to have one third of the length of the strings as a wounded section and two thirds as a free-hanging section. However, this is required only l'Chatchilah; Shmuel is telling us that b'Di'eved if one did it the other way it is also Kosher.

3) Rashi's explanation that all of the Tzitzis together are called Techeles seems rather forced. In contrast, the Rambam (Hilchos Tzitizis 1:8) phrases this Gemara as follows: "If one wound the Techeles string around the majority of the Tzitzis, it is Kosher."

This means that if one took a very long winding string that was so long that it could be wound around the majority of the length of the other strings, this is also Kosher.

The advantage of the Rambam's Peshat is that one does not have to say that the entire system of Tzitzis is termed "Techeles" as Rashi must say. Rather, the word "Techeles" used by Shmuel is referring to the one, winding string which -- according to the Rambam -- is the one Techeles string. Shmuel tells us that if one wound this string around the majority of the other strings, it is in order, at least b'Di'eved.

4) In fact, if one thinks about it, this Peshat is very nice according to the Rambam because the whole idea of the Techeles string is to be the winding string. This idea goes so far that the Halachah is that even if one exagerated and used the winding string to cover most of the other strings and ended up with more windings than open strings from all the other strings put together, the Tzitzis is still Kosher. We see from here the great improtance of the Techeles winding string.

There are still other supports that can be given for the Rambam's position, but I will close here for the moment.

Kol Tuv,

Dovid Bloom