ברוך אתה ה´ אלוקינו מלך העולם מתיר אסורים
The expression matir asurim, "HaShem sets free those who are imprisoned" appears in the book of Psalms (Tehilim, 146) and it is part of the pesuqe dezimra, the Psalms that we read every day in the morning prayer. In Tehilim its author King David praises HaShem for His compassion with the needy. God defends the cause of those who are oppressed, He gives bread to those who are starving, and He sets free those who are imprisoned.
In the 'Amida the idea of setting free the prisoners appears in the second berakha (blessing). This blessing, Geburot (God's powers), describes God's infinite might asserting that He employs His power to nurture, to support, to cure and to deliver (matir asurim).
In Birkot haShachar the Rabbis used the idea of matir asurim, applying it to a different context. Almost as a poetic motif. They instructed to say this berakha in the morning, at the time of waking up, when a person stretches his body and sits in his bed. The question is: what is the connection between the idea of setting free the prisoners and the movements of our body?
The simplest explanation is that when we are sleeping we have no control over our body. It moves involuntarily. Our conscious mind, i.e., the seat of our willpower, is asleep. And we are, in a sense, imprisoned inside our bodies. Not only our bodies but our minds as well are beyond our control. While asleep we have no voluntary thoughts, but involuntary dreams. When we wake up and we start moving our limbs we realize that we have recovered control over our mind and body. Now, our body moves if we just will so. We are in control. We are free.
When saying this blessing we recognize the power and wisdom of HaShem behind the recovery of our ability to move our body.
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