How does intuition work exactly?
Well, obviously, no one really knows...
Still, as I see it, intuition works from a database of notions that the brain has previously integrated. The database is essentially what you've learnt through your life since birth. However, it's not knowledge as such. Rather, it's what you've learnt, which may well be bullshit.
When you're interested in a problem, the key point to let your intuition come into play, is to give your brain the time to integrate the new data. So, a good idea is to work for example two hours a day on this problem, so that your brain takes in the stuff and has the time to "integrate" the new information.
Another key point, is to diversify the points of view, the kind of data relative to the problem, because brains are really champions to establish correlations between apparently unrelated sets of data.
A third key point, is to articulate whatever ideas you've got so far. Your brain will also work on that, given the time to do it.
Intuition is probably the only intelligence we have. When we think, we toy with bits and ends literally without knowing what we're doing. It's only our intuition that will come into play to tell us that this bit and that end have to do with each other.
Thus, our unconscious brain is probably more intelligent than our conscious mind. It's clear for example that when you're trying to solve a problem, your brain may find the solution perhaps several days before you. And it will give you the solution through intuition, i.e. you're thinking about a problem and there it is, you suddenly have the intuition something you're thinking is the answer. Sometimes the brain may have the solution, or part of the solution, years before you finally get round to it, if you ever do.
A last point perhaps... Intuition is not just some idea that pops up in your mind as most people seem to believe. Intuition is really your brain insisting on telling you that something is the case or is true or is the solution. It tells you you should really pay attention to this one. If you feel that both A and not A are both possibilities, then neither is an intuition.
Still, remember your intuition works on whatever you've learnt, and this may actually be complete bullshit. So, perhaps another key point is to keep an open mind and resist dogmatism. Whatever pet theory you're working on, remember it may well be trash. It's still best to stand your ground as most people do, but that shouldn't prevent you from considering the possible value of the arguments other people put forward. Let your brain sort out which is true. This is the only fountain of truth you can trust you will ever have. You just need to give it the time to work its magic and to consider and learn the possibly relevant facts.
EB