Intuition

Intuition is a combination of heuristics, connections, old frameworks, mental maths and a bunch of other tools our mind employs when it sees the answer without fully solving the problem mathematically or rigorously, but as if it has done so.

I often wonder if intuition is what we are born with or comes with practice. Today I think I have a better idea.

Simply put, we can gain intuition both ways, but they give different intuitions. Intuition includes old framework. With practice, we get familiar with those old frameworks, and it is not surprising we gain intuition, and we can see the answer without doing the algebra when we see a similar problem. Of course, our crude intuition only helps us in problems really similar to problems we did. As we practice more, we see the problems' pattern more clearly, and we stripe down all those irrelevant factors and know which part of the algebra corresponds to which feature, and which part will be altered if something changes. That can come naturally. I have seen people who can just see right through problems in their fields the first time they run into them.  I guess that's the overlap between acquired and natural intuition. However, natural intuition can get far more creative. I'd like to think that gained intuition is for engineers, while natural intuition is for scientists, both are useful in different situations.

When I say natural intuition, I do not mean we have it right at our disposal. We often need to dig for it. Many times, I never thought of any intuition to a specific problem, until the professor pushes me. After thinking about them, they do come, but it is not something that when I see the problem, it jumps right out (seldom).

I am obsessed at identifying where my natural intuition lies. I often feel that if I enter a field where I do not have much intuition, I will be doomed---everyone can work hard, but at the frontier, intuition is what distinguishes one out. Unfortunately, it is hard to get a clear signal. We can feel we are gaining more and more intuition, but is it the natural intuition? and how do we compare to others? In the states, professors are so nice, and always so encouraging, but sometimes I wish they could be more blunt and just tell me: Oh Wei, you have no intuition in this field. Go and do something else.