Link to Ptil Techelet website.

The Gemara brings two different versions of the incident involving Mar bar Rav Ashi, whose tzitzit were torn on Shabbat while he was walking home. This raises the subject of "kevod haberiyot" (human dignity), which overrides a "lo ta'aseh" (negative commandment) in the Torah. Both versions bring the explanation of Rav bar Shaba, who explained that this law refers specifically to the negative commandment of "lo tasur" (do not stray from the words of the Sages), meaning that it only overrides Rabbinic prohibitions.

For tzitzit, one must place two strings of techelet and two white strings. The Mishna rules, however, that this is not essential – one can have only white or only techelet. Also regarding the tefillin of the hand and the tefillin of the head - they are two independent mitzvot and do not hinder one another; someone who has only one of them puts it on and recites the blessing over it.

The Gemara suggests that the Mishna does not follow the view of Rebbi, who holds that the techelet and the white do hinder one another. He learns this from the verse "And you shall see him" (u're-item oto), which teaches that both must be together, while the rabbis learn that it is possible to see each kind separately. However, two other suggestion were brought to explain the Mishna according to the view of Rebbi:

• Rav Yehuda in the name of Rav: The law in the Mishna (that they do not hinder) was stated regarding the order of precedence. It is a mitzva to first place the white (since the white is the color of the "corner" of the garment, which appears in the verse first), but if one placed techelet before white, one has fulfilled the obligation, though the mitzva has not been performed in the most ideal way.
• Rava: The Mishna is speaking about gerdumin (remnants) of one of the colors - strings that were torn after they were already placed in the garment - the tzitzit remains valid. His words rely on the words of the sons of Rabbi Chiya, who said that remnants of techelet are valid. The minimum measure that must remain in a string to maintain its validity is "enough to tie them" (kedei le'anvan), meaning a length sufficient to make a slipknot.

From the statement of the sons of Rabbi Chiya, Rava concludes that one must tie a knot on each and every "chulya" (group of windings) in the tzitzit. The reason for this is that if one does not tie a knot at every chulya, if just a short strand is permitted, the moment the string is severed above the first knot, all the windings will unravel and disappear. The knots between the chulyot ensure that even if part of the string is cut off, the structure of the rest of the tzitzit will be preserved and it will remain valid under the law of gerdumin. However, Rava's assumption is rejected as the sons of Rabbi Chiya may only permit gardumim when there are knots at every chulya.