Inspiration often seems to pop up unpredictably—in the shower, on a long walk or even at the grocery store. But one place I never expect it is during sleep. I tend to think of myself as a computer: at bedtime I power myself down with teeth brushing and pillow fluffing, and soon enough my brain switches off.

That analogy, however, is dead wrong. Your sleeping brain has simply entered an alternative mode of thinking, as psychologist Deirdre Barrett writes in “Answers in Your Dreams.” With your eyes closed and limbs immobilized, your brain spins fanciful webs of ideas that your waking mind might have filtered out. In that rich environment, your creativity and problem-solving skills can blossom.

You can even sometimes steer the course of a dream. Along with the high entertainment value of, say, suddenly gaining the ability to fly, this control could prove useful for overcoming anxiety and other troubles, as psychologist Ursula Voss explains in “Unlocking the Lucid Dream.”

Dreaming is not the only state the brain inhabits outside the boundaries of our awareness. Even when you sit quietly doing nothing, your brain bustles with activity. Groups of neurons continue to fire unbidden, forming patterns of activity that neuroscientists are now using to produce stunning maps of the mind. Scientific American Mind’s Ann Chin and I collaborated to bring you “Head Shots.”

As you take in those colorful images, reflect for a moment on the marvel of your eyes—another example of how the brain works behind the scenes. When your eyes focus, they do not zero in on one spot: they actually dart around, using tiny subconscious movements called microsaccades. These motions keep your vision healthy, but they can also reveal your hidden desires, as Susana Martinez-Conde and Stephen L. Macknik write in “Shifting Focus.” Paradoxically enough, although we strive—and sometimes manage—to control our thoughts and actions, our brain often seems to have a mind of its own.