Complex Numbers

Learning

Check out this One Weird Trick.

How I Rewired My Brain to Become Fluent in Math  
The building blocks of understanding are memorization and repetition.

You might have noticed that I have a wide range of interests. I could never choose between math things and language things. As a result, I never got really good at any of them.

But here I am spending my time attempting to improve my writing and learn new languages. For me, learning won't stop until I'm brain-dead.

I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague.

This article is from 2016. It turns out most of us don't actually avoid the plague.

So it’s a little strange how I’ve ended up now—someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering.

And already the author is beyond my paltry knowledge of mathematics.

But these hard-won, adult-age changes in my brain have also given me an insider’s perspective on the neuroplasticity that underlies adult learning.

The point being that if a person wants to learn something, is motivated to do it, they usually can.

If you can explain what you’ve learned to others, perhaps drawing them a picture, the thinking goes, you must understand it.

Pretty sure Richard Feynman, the late physicist, was an advocate of that technique.

The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition.

I'd say this is the case for anything. Since my memory isn't great, I have to repeatedly review earlier language lessons, doing exercises over and over. I still don't always get it right, but I get better.

There is an interesting connection between learning math and science, and learning a sport. When you learn how to swing a golf club, you perfect that swing from lots of repetition over a period of years. Your body knows what to do from a single thought—one chunk—instead of having to recall all the complex steps involved in hitting a ball.

Again, that's probably the case everywhere. A while back, I came to the conclusion that learning is largely about consolidation. Simple concepts build up to more complex ones. You see this a lot in math, where they often consolidate complex equations into one symbol for ease of manipulation, and then unpack it later. It's kind of like a compressed file on a computer.

But in my case, from my experience becoming fluent in Russian as an adult, I suspected—or maybe I just hoped—that there might be aspects to language learning that I might apply to learning in math and science.

This, too. Math is really just another language, or at least that's one way to look at it.

I think this is the money quote, though:

Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.

Her path is opposite mine - she learned languages first and then mathematics, whereas my journey is reversed from that - but I think her insights are helpful in either direction. If I have one quibble with what she says here, and there's a whole lot that I'm leaving out so definitely check out the article, it's a focus on learning for a purpose rather than learning for the sake of learning. However, if having a purpose for what you're learning keeps you motivated, I can't fault that.

But in my view, the biggest obstacle to learning anything is when you tell yourself you can't. Sometimes this comes from outside, as when a parent or a teacher might have discouraged you from pursuing a particular field. But sometimes it comes from having tried, and failed. If you think you can't, then it becomes a self-fulfilling prophecy. But once you open your mind to the idea that you can learn something, then you will, at least to some extent.

And I say this as someone who has been convinced, from time to time, that he can't. But I want to change that. And I think I can.