I've just finished reading a series of three Amish novels by Barbara Cameron. In them, Phoebe, a wise and feisty grandmother, always says that she never worries; worry is arrogant, suggesting that God doesn't know what He's doing, and God always has a plan. I believe this. I've come to believe it more and more, over the past 10 to 15 years. But trust (the antithesis of worry) is still a very intentional act of the will, for me; otherwise, I wander into fear and, yes, worry. (Or is that redundant?)
Some people would accuse me of practicing "positive thinking," a la Norman Vincent Peale, or simple affirmation, when I get nervous or fearful. The difference between either of those and intentional trust is in remembering that God does always have a plan (read Jeremiah 29:11-13, for starters), and in choosing to trust in Him. The key element is a Person.
My all-time favorite, relevant passage of scripture on this topic is Proverbs 3:5,6:
"Trust in the Lord with all your heart, and don't rely on your own understanding. In all that you do, acknowledge Him, and He will direct your way.
