I laid myself down and slept. I awakened; for the LORD sustains me. Psalm 3:5
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What does it take to be able to get to sleep? Exercise, a clean conscience, medications? Depending on the reason that sleep eludes you, any one of those might be useful. Whatever the problem may be, sleep IS a valuable part of our lives. It isn't a waste of time - far from it. As a recent news report notes:
Doctors are beginning to stress that we need our sleep. New studies point to a number of health problems that can be caused by a lack of Zs. They indicate lack of sleep can not only effect moods, memory and weight, it can also put stress on your heart, because the body doesn't get enough oxygen. [http://www.wlns.com/Global/story.asp?S=4707538]
It shouldn't be a surprise that God wants us to rest - commands it in fact as part of a code as universal as the Ten Commandments. As Psalm 127 says:
It is vain for you to rise up early, to stay up late, eating the bread of toil; for he gives sleep to his loved ones.
yashen yaw-shane' is the Hebrew word David uses here, and appears in this form fewer than 20 times in the Bible - though there are related terms, notably shehnah which appears a couple of dozen times. Translated here in Klingon as Qong - you might hear it when an exasparated Klingon parent might shout "DaH yIQong" (sleep now!) to encourage their child to get needed rest. You hear it in the Klingon word for "bed": QonqDaq, literally sleep-place.
The Life Application Bible notes:
Sleep does not come easily during a crisis. David could have had sleepless nights when his son Absalom rebelled and gathered an army to kill him. But he slept peacefully, even during the rebellion. What made the difference? David cried out to the Lord, and the Lord heard him. The assurance of answered prayer brings peace. It is easier to sleep well when we have full assurance that God is in control of circumstances. If you are lying awake at night worrying about circumstances you can’t change, pour out your heart to God, and thank him that he is in control. ...
This was the heart of David's rest, and it can be the key for us, too. Not that our prayer to God will magically all our problems, but if we turn them over to God, we can find peace from the only one who can see us hrough. This can be our key to rest - not just rest for a night, but the rest that comes from being at peace with God, a peace that will at last bring us to him in a rest and peace that is eternal.