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Texts on the Krekhtz
Abraham Joshua Heschel, The Earth is the Lord’s (Chapter One, “The Sigh,” p. 16):
“There were many who did not trust words, and their deepest thoughts would find expression in a sigh. Sorrow was their second soul, and the vocabulary of their heart consisted of one sound: “Oy!” And when there was more than the heart could say, their eyes would silently bear witness.”
Rabbi Nachman of Bratslav, Likkutei Moharan 8:1:
(https://www.sefaria.org/Likutei_Moharan.8.1.3)
See how precious is the sigh and groan (the krekhtz) of a Jewish person. It provides wholeness [in place] of the lack. For through the breath, which is the ruakh-of-life, the world was created. As is written (Psalms 33:6), “… and by the ruakh of God’s mouth, their entire hosts [were created].” The renewal of the world will also come about by means of the ruakh, as in (Psalms 104:30), “You will send Your ruakh —they will be created; You renew the face of the earth.”
This [ruakh] is also the vital force of human life. This is because a person’s breath is their life-force. As is written (Genesis 2:7), “God breathed into the human’s nostrils nishmat (the breath of) life,” and (ibid. 7:22), “All in whose nostrils was a nishmat (breath of) ruakh-of-life.” Regarding this, the sages said: To the extent breath is lacking, so is life (Maaseh Tuviah, Bayit Chadash 2; cf. Zohar II, 24b).
We find then that the quintessential life-force of everything is its ruakh. Whenever a lack exists, it is essentially in the life-force, which corresponds to the ruakh-of-life of that thing. This is because it is the ruakh which gives that thing its existence.
And sighing is the extension of the breath. It corresponds to erekh apayim (patience)—i.e., extended ruakh. Therefore, when a person sighs over the lack and extends his ruakh, that person draws ruakh-of-life to that which they are lacking. For the lack is in essence a departure of the ruakh-of-life. Therefore, through the sigh, the lack is made whole.