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Answer: The gemara (Menachot 39a) posits that the "upper knot" of tzitzit is a Torah-level requirement, as we learn from the Torah’s connection between tzitzit and sha’atnez. Most Rishonim (see Beit Yosef, Orach Chayim 11; see China D’chayei 8, who cites dissenters) posit that a double knot is needed to connect the tzitzit to the garment, as we find that making a simple single knot is not a violation of Shabbat (Shabbat 74b).
There is also a machloket what the upper knot is – the part closer to the garment or further away from it (see Mishna Berura 11:66). A relatively strong consensus holds that it is the one further away from the garment, where it also secures the gedilim (section containing all of the string wrappings).
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Rava deduces from a halacha regarding a ripped string that one is supposed to make a knot between the chulyot (Menachot 38b). The gemara (ibid. 39a) deflects the proof by suggesting that knots were sometimes made but were not required. Many claim that while Chazal expected/preferred for there to be multiple chulyot and knots, basic Halacha only requires chulya with a minimum of three revolutions of a tzitzit string around the others (Mishna Berura 11:65).
The preference of more chulyot and/or knots is due to their being reminiscent of a variety of themes and numerical values. We will mention a few (the Mishna Berura 11:65 cites some): There should be seven knots in each tzitzit corresponding to the seven firmaments, but we leave out two knots when we do not have techeilet (Shut Radbaz 2333) because it is the techeilet that reminds of the sky. The gematria of tzitzit is 600, and when one adds eight strings and our present-day five knots, it comes to 613. 8+5 is also the gematria of echad. The five knots also remind us of the five books of the Torah. Since the five knots are doubled, it is also reminiscent of the ten sefirot (a Kabbalistic concept). None of these numerical significances are absolute requirements, as is true of the number of wrappings (Mishna Berura ibid.), but they are religious/spiritual preferences.
It is also possible that some of the gains of knots in between the chulyot do not depend on there being halachic knots. Single knots also are able to hold each chulya in place, take up some space, which is important (see Shulchan Aruch and Rama, OC 11:14), and make the different chulyot, with their significant number of revolutions, noticeable. The fact that a single knot is more secure than usual when it is in the midst of a g’dil that is surrounded by double knots might also give it prominence (see Maaseh Betzalel to Rikanati, Tzitzit 3). Again, despite this, the Shulchan Aruch at least recommends double knots each time.
There is another reason to want at least one of the middle knots to be a full halachic one. Sometimes the top knot starts getting looser, even to the point that it is no longer a halachic knot (see Living the Halachic Process IV, F-3). We are not usually overly concerned about this because the minimum requirements of the tzitzit are met when a minimal gedil is followed by a double knot. However, in your case, were the top knot to reach that point, there are no fallback knots after the beginning of the gedil.
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Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
Rabbis in Midrash
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Kuzari -Rabbi Ari Shvat Kuzari class 9 - "Seeing is Believing" (parag. 21-30)
These paragraphs elaborate on the theme that seeing and knowing is better than any attempt to prove logically, and begins explaining the difference between Israel and gentiles.
Ein Aya Various Universal Stages of the Geula Process
Rav Kook examines the various stages of redemption, explaining how (in addition to the obvious oft-mentioned stages of ingathering the exiles, reviving the Hebrew language, army, state etc.) the messianic dream of world prosperity, the State of Israel and world unity can and are realistically and logically gradually coming true.
Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
How do we know that the "claim" of mass revelation to 2,000,000 witnesses at Mt. Sinai is really true? This important class answers all of the questions skeptics ask about this claim of the Kuzari.
Ein Aya Armies Still Necessary for Balance & the War Against Wars
Rav Kook explains why the world was originally divided into the various seemingly contradicting ideologies and cultures, in order to develop each one respectively. Swords or armies symbolize how each respective ideology defends themselves, as well as deters their opposing ideologies and cultures. On the other hand, the messianic era will be one of peace, and Rav Kook explains the transition to that stage, which mankind is already undergoing.
The Land of Israel LGBT'S IN ISRAEL
The question was asked, how can one make Aliyah with the LGBT parades?
Kuzari -Rabbi Ari Shvat Kuzari class 7 - Five Accumulative Proofs of G-d
As a preparation for the Kuzari's classic proof of G-d from the mass-revelation at Sinai, we start here with 5 other directions to strengthen our belief which also contribute to what the Kuzari will present as well.
Ein Aya Muscle & Meaning: The Dual Nature of Gevurah (Physical Strength)
Is physical strength and fitness a necessity or an ideal? Although it if often totally overlooked among topics of Judaism, Rav Kook writes that it clearly is also a necessity to deter the many enemies of Israel, but even in Y'mot HaMashiach, in the Messianic era, to a certain extent, it's ideal continues even after our enemies will have been finished off.
