The rabbis considered 'shame' (busha) as one of the three components of the Jewish ethico-genetical makeup. Together with the practice of benevolence (gemilut hasadim) and compassion (rahmanut). The Rabbis went as far as to say that presumably, whoever does not posses the trait of shame "his ancestors did not stand at Mt. Sinai" (an euphemism to say that he might not be ethnically Jewish).
Besides seeing "shame" as an innate condition of the Jewish character--in complete contradiction with the alleged Jewish 'chuptza'-- the Rabbis explained that "shame" is a prerequisite for a perfect Teshuba (repentance).
Maimonides writes that when a man or a woman commits a sin... "they shall confess [or articulate] the sin they have done... by saying, `O Lord, I have sinned, I have transgressed and rebelledin front of You. I have done such and-such. And I am ashamed of my actions, and I regret them and I will never do them again'."
Besides the confession, the regret and the resolutions, etc., the feeling of shame is a critical step for a sincere process of Teshuba.
Because unlike guilt, which is a private feeling, shame consists in the uncomfortable sensation of knowing that our flaws and misdeeds are known to others. Feeling 'shame' while articulating our sins in front of God means therefore that we really realize God's Presence!
Allow me to explain: God is invisible. It is extremely challenging to be aware of His constant presence. Therefore, we are not easily ashamed of doing something wrong in front of God (=privately) as we are naturally ashamed of doing something wrong in front of other people. Now, feeling embarrassed of our transgressions in front of God means that we have achieved an elevated level of closeness to God. It means that we are certain of His existence and that His presence is so real to us as the presence of other people (Remember what Rabbi Yohanan said on his deathbed? יהי רצון שתהא מורא שמים עליכם כמורא בשר ודם ) . The higher the state of our awareness of God's presence, the higher the feeling of shame we feel when we confess in front of God. And vice-versa.
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