The Top Idea in Your Mind

In an ideal world, you could sell the service of helping professors to prepare their research proposals. You could also keep an eye out for grants which the professors might be interested in, and generally handle the money side of things for professors who would rather be worrying about something else.

However, I don't think this would work, because the professors have no way to pay you. As far as I know, no funding agency will fund you for the cost of contracting someone to prepare your grants for you. And they probably won't want to do it out of their own pocket, because; heck, this kind of service will be really expensive (and professors hate funding their research out of their salaries anyway).

But if you've got another business model, I'm all ears.

It could be simply a matter of training your brain to have a strong stack for traversing the two or maybe three key areas or contexts that you're thinking about.

I.e., one solution is: make sure your top idea or ground state really is what you want. Another solution may be: train a better graph visitation algorithm.

However, trying to train one's unconscious may be sort of like quantum physics -- i.e., for lack of a better word: difficult. Perhaps you can just throw two or three main things you'd like to see happen into a collider, go to sleep or take a shower, and see what happens. But it may be possible to train yourself to think with very clear visitation between different contexts consciously, and actually have this process bubble down into the unconscious and take hold there too. I.e., hack your unconscious. Arguably it's the same sort of thing we do when we try to offload parallel processing onto a GPU or cloud (though in those cases the hardware is much more specific).

Your definition of "productive" has the same bias.

Turning the other cheek is by origin an alternative to an eye-for-an-eye. For a mind that can only be freed with an eye-for-an-eye settlement, turning the other cheek won't do it. But an eye-for-an-eye approach can be productive:

And Samson said, "Let me die with the Philistines!" And he bent with all his might so that the house fell on the lords and all the people who were in it. So the dead whom he killed at his death were more than those whom he killed in his life.

Those with ADD/ADHD among other "disorders" tend to be more prone for an outside-the-box thought process.

Some things you can do to stimulate your Alpha brain waves, which give you adequate conditions for what Paul Graham calls "drifting" include walking barefoot on grass, and staring into the darkness while laying in bed before falling asleep.

I tend to have a lot of abstract thoughts, some brilliant and many more ridiculous, and I have benefited greatly from writing them all down in my phone. Translating them into english is extremely beneficial, and it's surprising how easy abstract thoughts are to forget. I would suggest this for anyone who is in any field requiring an ounce of creativity.