As one who reaches conclusions intuitively, I’ve taken a lot of grief from some of you who are more the mathematical-proof types.
So, I appreciated this piece in the WSJ over the weekend, headlined “Great Scientist ≠ Good at Math.” The thrust was that it’s a shame that so many people turn away from a career in the sciences because they aren’t good at math. An excerpt:
Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.
Everyone sometimes daydreams like a scientist. Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.
Yeah, baby! That’s what this INTP is talking about: Intuitive reasoning!
Not that I’m bad at math or lack skills in that regard. I was always in the 99th percentile on standardized tests of mathematical aptitude in school. I’ve just never been overly fond of it.
I lack the patience for the methodology. Here’s what I mean: In geometry class, I’d be asked to prove that triangle A was congruent to triangle B, or some such (I’ve forgotten most of the basic concepts now, which shows what you can accomplish when you really apply your mind to forgetting). I would say, well, it is congruent, and that’s obvious. I didn’t mean that it looked congruent. I meant that I knew all the theorems and such, and in glancing at the triangles, I could tell that all the tests were met. Because I perceived it holistically. Having to go through all the infant-school steps, one at a time, made me want to bang my head against a wall. I hated it. And as I went on, I didn’t like algebra II, or analytical geometry, or calculus, either. I just took all those courses because I thought that’s what you were supposed to do in school. (And yeah, I suppose that proofs have more relevance when you get beyond such simple stuff as congruent triangles, but I didn’t have the patience to pursue it that far.)
I had a calculus professor in college who was very enthusiastic about what the Brits are pleased to call “maths.” He drove me crazy. One day he came in all excited because someone had taken pi out to a million decimal places. I raised my hand and asked, “Why?” He said because it showed the numbers never repeat, even that far out. I asked what possible purpose knowing that could serve. He said it taught us things about the principles governing randomness. I said randomness had no principles governing it, because it was random. I basically was saying anything I could to damp his enthusiasm, because it irritated me. I was unsuccessful; he was a natural enthusiast.
I wasn’t the kind of kid you wanted in your class.
Of course, I would have run into the same problem in science as in math, since there’s all that mind-numbing step-by-step methodology. (The piece in the WSJ later says, “Eureka moments require hard work. And focus.” And not the fun kind of work, either.)
But I was pleased to see the plug for intuition.