I have noticed that sometimes people will be wearing their tallit as in the below image, with one of the front tzitziot thrown back. Why is this?
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S.A. O.Ch. 8 (4) says,
מחזיר שתי ציציות לפניו ושתים לאחוריו כדי שיהא מסובב במצות:
One should return two of the fringes in front, and two behind, in order to be surrounded by the commandments.
M.B. (9) says that we make an “atoro” for the tallis so that the same two tzitzios are always at the front and the same two at the back.
So it seems that it is not correct to have three tzitzios at the back and the reason it is being done is unwitting ignorance of the halocho.
I didn't see you ask about the halachic permissibility of doing this. (I don't THINK it's a problem, but I need to research).
There are just plain practical reasons for the tallit "fold". It is long, and in some cases, esp. while seated, the tzitzit are on the floor. I read the Torah, and my shul has some huge tallitot that I nickname "tablecloths". When I put them on, the tztzit are trailing behind me on the floor. If I didn't fold the tallit, everyone else and I would be walking on them.
Also, folding the tallit seems to reduce the chance of the whole tallit slipping off of you. I can't quite explain why that makes a difference (I'm a Ba'al Kri'ah, not a physicist!)
BTW - Nice pic. (It seems like your neighbor's snooping?) But, the back of the tallit seems too long, also, and it looks like it will take one "Oseh Shalom" to become "ta listless" :-)