Regarding the tekhelet, what did you mean by “Raavad 2 threads”? Tying 2 according to Raavad’s method and the other 2 according to the Vilna Gaon’s method?
And what about a tallit gadol? Do you have tekhelet there too?

According to the Raavad, two of the eight threads are tekhelet. That’s not a tying method but a proportion.
I also put tekhelet on the tallit gadol.

Hello Rabbi,
Why specifically Raavad and the Vilna Gaon?

I made a mistake. It’s Sefer HaChinukh. It’s also the common practice among most people, and I didn’t get into the details. It doesn’t matter that much, because the matter is not indispensable.

Hello Rabbi,
Let me sharpen the question.
The Talmud in Menachot (with parallels in Hullin, Sotah, and Sifrei) speaks about tekhelet being similar to the sea, etc. First—how do you read that saying?
And second, in your view, alongside the Talmud in Menachot 39a about the windings and segments, is there a connection between that saying and the various tying methods? The relationship between tekhelet and white in tzitzit, and so on? In general, where did all these different methods come from—Maimonides, Raavad, the Vilna Gaon, Sefer HaChinukh, and so on?

I didn’t understand the question. What does that saying have to do with it?
As for the tying methods, you can find material online, for example: https://www.etzion.org.il/he/%D7%9C%D7%97-%D7%A7%D7%A9%D7%99%D7%A8%D7%AA-%D7%94%D7%AA%D7%9B%D7%9C%D7%AA

Just a reminder that according to the Torah, the tzitzit should be on the garment itself, not as is practiced today with a special garment for tzitzit.
“On the corners of their garments throughout their generations.”
And tzitzit is not a collection of strings, but rather a kind of ornament like a flower, and on the ornament one is to place a thread of tekhelet: “And they shall place on the tzitzit of the corner a thread of tekhelet.”

The saying I brought speaks about the role of tekhelet. It’s an aggadic saying. I assume the medieval authorities took it into account and didn’t invent a tying method based on a revelation or a dream.
So I’ll ask again—the Talmudic passage that describes the segments and windings can be understood in various ways; is every tying method built on that and nothing beyond it?
To “The Last Decisor” — what do you mean that tzitzit is an ornament like a flower? How do you know from the verses at all what tzitzit is?

You can’t learn from the verses what tzitzit is. For that you need tradition. I don’t know where the halakhic decisors derived their tying methods from (I didn’t look into it). In any case, I don’t see any connection to the midrash you cited.

Most of the medieval authorities hold that one needs to put four tekhelet threads, so it’s a bit strange that suddenly the Rabbi remembered to rely on the common practice.
It’s very interesting where the assertion comes from that this is not indispensable.

The tying is not indispensable.

In my humble opinion, the number of tekhelet threads is part of the essence of the commandment and is presumed indispensable unless it has been clarified otherwise.
Likewise, it is explained from the view of Rabbenu Tam (in Beit Yosef and Mishnah Berurah, siman 12) that he took it as obvious that this is indispensable (otherwise, even when 3 threads were snapped, they would still all be from the white threads

But it seems that the Rabbi is emphasizing that he only said this about the tying, that it is not indispensable, and indeed ex post facto that is the case, since even if one tied only one segment it is valid, and there is no tying method that does not tie at least one segment.

https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%A4%D7%AA%D7%99%D7%9C-%D7%AA%D7%9B%D7%9C%D7%AA-3

And see here, where from the wording it seems that this is indeed what the Rabbi meant here as well.

Yosef Yuda,
It seems to me that you didn’t read the Rabbi’s second comment in this thread here.