Here's an interesting passage from Anne Lamott, found in Bird by Bird: Some Instructions on Writing and Life, that requires some consideration.
You get your intuition back when you make space for it, when you stop the chattering of the rational mind. The rational mind doesn't nourish you. You assume that it gives you the truth, because the rational mind is the golden calf that this culture worships, but this is not true. Rationality squeezes out much that is rich and juicy and fascinating.
The great French mathematician Henri Poincaré said something adding to our understanding of the roles that both rationality and intuition play in discovery: “It is through science that we prove, but through intuition that we discover.”
Furthering our understanding, I ran across a quote by Steve Jobs on the same topic: “Intuition is a very powerful thing, more powerful than intellect, in my opinion.” The source of that quote is Walter Isaacson's biography of Jobs:
The people in the Indian countryside don’t use their intellect like we do, they use their intuition instead, and the intuition is far more developed than in the rest of the world… Intuition is a very powerful thing, more powerful than intellect, in my opinion. That’s had a big impact on my work.
Western rational thought is not an innate human characteristic, it is learned and it is the great achievement of Western civilization. In the villages of India, they never learned it. They learned something else, which is in some ways just as valuable but in other ways is not. That’s the power of intuition and experiential wisdom.
It's not really acceptable to admit but most of the time we make our decisions on intuition, rationalizing them after the fact by cherry picking. (If you want to see what it looks like to make rational decisions and catalouge your data, try using our decision journal for a month.) Intuition can be thought of as subconscious pattern matching, honed over weeks, years, and decades. The more we are within our circle of competence the more likely our intuition proves correct.
The point isn't choosing between cold rationality and intuition but rather understanding that each serves a purpose. If we let it, intuition can be an able guide but we must check it when the consequences of being wrong are high.