In math and engineering, there’s a thing called a forcing function, which is often used to describe the inputs to a system. When you take away the input, you get what’s called a transient state, before eventually, a steady state.
Imagine for a moment that you close your eyes, put in your ear plugs, and enter your sensory deprivation chamber (why do you have a sensory deprivation chamber?) What you’ve done, in mathematical terms, is taken away your forcing function; you’ve taken away your inputs. And the question is, what happens then? What’s your transient state? What’s your steady state?
I find this to be a fascinating question, not so much because of any particular answer, but because of the implications of every answer.
The very fact your thoughts change when you take away your inputs, implies that your inputs change your thoughts. Or thinking of the inputs as a forcing function to a differential equation, the environment forces your thoughts; it drives them. Your senses keep you moving in concert with the outside world.
Take away the stimulus from your senses though, and your thoughts enter a transient state; a state that depends only on your own inner world.
If you stayed in this state forever, you’d end up in a steady state, which… you probably don’t want. But if you re-apply the forcing function again at a later time, there’s — mathematically speaking — a chance that you’ll end up responding to the inputs in a different way than you did before.
If you want proof for all of this, you can go study up on differential equations.
But if that sounds like a lot of work to you, the thing is, all I’m really trying to say is, if you take a break, you’ll sometimes solve a problem faster than if you just keep at it for hours on end. And there just so happens to be math that proves it!