As I ventured out on my long run today, I tuned my iPod to the world music genre with the intention of finding the next song I would choreograph for my dance classes. Although I was not very inspired by the task at hand, I did seem to be solving other problems without conscious attention to them. 
This weekend, I was helping a friend brainstorm a new business venture, including concept details, logistics, name, and branding. Although we tossed around a lot of ideas and developed a pretty solid plan of what he wants to achieve, we were never quite satisfied with the naming/branding aspect. When I got back from my run, I was able to email him three new name ideas and a picture on which he could base a logo. He may reject them entirely, but I think it is a great illustration of how our brains work.
If we push too hard in any area (physically or mentally for example), we will burn out and cease to be able to function; however, if we allow ourselves time to recover we can continue to function at a normal level. Further more, if we push ourselves beyond what we are used to and allow ourselves to recover, we build our capacity in that area (physical, mental, etc). That is exactly what I was doing with my long run today, which I ended with a sprint. I am now sitting quietly writing while my body recovers. In the same way, I am now able to engage my brain more because I allowed it to rest while I was pushing myself physically.
Have you ever noticed that your best ideas come when you are at rest or distracted, like when you are in bed, in the shower, or exercising. In addition, I find I have new ideas and come to new understandings while drying my hair. When you get stuck on a problem or find you’re not being as productive as you would like, oscillate to a new activity and allow that part of your brain to rest. Engaging yourself physically will help you grow physically and mentally.