At AllFaith.com I share numerous studies into the world's religions based on my personal quest for Truth. Over the years this research has led me to embrace Judaism. That is now the main focus of the domain.
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Orthodox Judaism teaches that one should pray not only with ones whole heart, mind and soul but with ones whole body as well. This is based on the Torah.
At Exodus 20:18, immediately following the giving of the Ten Commandments, the Torah says (JPS Version of 1917):
Exodus 20:18 (20:15) And all the people perceived the thunderings, and the lightnings, and the voice of the horn, and the mountain smoking; and when the people saw it, they trembled, and stood afar off.
The KJV has this as:
Exodus 20:18 And all the people saw the thunderings, and the lightnings, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off.
The word translated as trembled in the Jewish Publication Society version (JPS) and removed in the KJV is the Hebrew word noo'-ah. This word is:
A primitive root; meaning to waver, in a great variety of applications, literally and figuratively (as subjoined): - continually, fugitive, X make to [go] up and down, be gone away, (be) move (-able, -d), be promoted, reel, remove, scatter, set, shake, sift, stagger, to and fro, be vagabond, wag, (make) wander (up and down) -- Strongs H5128.
For this reason many Jews not only bob their heads but sway their whole bodies when davening (praying), demonstrating awe for He to Whom they pray.
Jews have traditionally swayed this way during prayer since the giving of the Torah at Mount Sinai whenever they turn their hearts towards HaShem.