I had a long talk with a PI yesterday about my academics and research in general. The question on my mind, was how do you pick up on conceptual errors? How do you know when you’re doing it wrong?
The obvious answer is practice tests. But when you don’t have examples or practice problems to do, what do you turn to? Reading things and understanding them works, but it’s hard to catch conceptual errors that way. To me it seems like the best way to overcome these short comings, is to build intuition. We often realize our conceptual errors in retrospect, after failing to properly apply a concept we thought we understood to a problem we have never seen before. How then, does one build intuition?
I’ve always thought that intuition is inherent. It’s something that we just have a “feel” for, which is even more frustrating because my goal has always been to improve my intuition. For a while, I figured intuition came from ability to problem solve, which is likely a result of my time in the Integrated Science Curriculum at Princeton.
I went through the Integrated Science Curriculum here at Princeton, which is a 2-3 year program, which emphasizes problem solving, by constantly introducing new material, so that as soon as you’re on the brink of familiarity, the subject changes completely and you’re forced back to square one. This has its benefits in that it forces you to always problem solve but at the same time, there’s just never enough time to get adequate familiarity and practice.
Yet, there are so many times when I get a test back, I look at it, and upon seeing my errors I wonder, why wasn’t my intuition enough? Why is it that my intuition was wrong to begin with? Did I learn the concept incorrectly to begin with, or was it something else?
“The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”
~ Albert Einstein
What talking with my PI made me realize was that intuition comes from practice and repetition. For the longest time, and having seen the way that various subjects were taught in both high school and college, I always looked down upon pure memorization. I believed, rather naively, that pure problem solving ability is all that was enough. I’d look towards the math majors and use them as a benchmark by which to compare myself. I needed to get to that level of problem solving.
What I failed to realize is that they memorize just as much as the rest of us do. Through repetition and practice, something I did often as a child, they build intuition so that they can free up mental capacity to actually do hard problems. I had forgotten after all those years, that one of the most important things that allowed me to succeed when I was younger was the fact that I had so many things memorized.
Practice, which builds connections, can only bring genius out.
And from there, we can work towards our real goal — intuition.