Customs: Why are three steps taken backward and forward before the silent Amida prayer?

We take three steps backward to make sure that the four cubits around us are unoccupied. We take three steps forward for numerous reasons, among them: when a servant approaches a king, he does so with short, hesitant steps to display respect; when the priest was ready to mount the altar with the sacrifice it was necessary for him to take three steps to do so.