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The Eastern peoples in that day took few important steps without consulting the stars and the omens. When King Nebuchadnezzar and his generals couldn’t agree on a campaign strategy, they paused to consult their gods.
“Shaking the arrows” was something like our modern “drawing straws,” with the arrows marked with the possible choices of action. “Consulting images” had to do with seeking help from the images of the gods they carried with them. “Looking at the liver” involved offering and animal sacrifice and getting directions from the shape and marks on the liver.
The Babylonians were without divine guidance in the form of true prophets and the Urim and Thummim, so they had to make do with other counterfeit methods of receiving direction. As weird as their methods sound to us, it shows that throughout time, people have always been searching for a source of wisdom above their own.
How happy we should feel when we contemplate the blessings of inspired prophetic counsel and the direction of the Holy Ghost!