Nonverbal thinking is extremely powerful, but it has a limit, which is lack of recursion. It can't build on itself. It can reach beyond what you think you know, but only a certain distance. Hence, use verbal thinking. Nail down what exactly the intuitive systems are telling you.
It's easy to think you've nailed it down when you haven't. It's important to go back and try to naively intuit again and see if it really matches. It's normal to take a few tries, regardless of how much experience you have with the process.
Once a new verbal foundation is built, the intuition can make new intuitive leaps. These leaps can in turn be verbalized, and the cycle repeats.
In theory you can also make purely verbal extensions. Mathematics often works this way. However, it's slow. There's no advantage to doing it that way, except among the mentally deformed freaks who want to signal loyalty to wordcel Science. That said, sometimes the intuition will direct verbal logic down particular alleyways, and it will be correct. Go ahead and do what it says to do.
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New failcomment system also fails to publish my comments, it's not limited to yours. Keep trying, it will usually work, eventually.
Blogger deliberately trying to kill itself, I expect.
Captchas should be off. If it gives you one anyway, it's against my explicit instructions.