Learning to Learn

The Aug. 29, 2011 episode of 60-Second Science talks about a finding that drawing helps scientists develop their ideas.

I can’t say I’m terribly surprised at this. Drawing seems to me to be more concrete than speech (or raw thought). Just as a simple example, I can say “two circles”, or I can draw two circles. If I draw two circles, rather than just talking about them, I must necessarily place them next to each other, or one above the other; close together or far apart; of equal or different sizes; and so on. Depending what the circles represent, these small choices might matter, and force me to think about some aspect of the problem.

Chabris and Simon’s The Invisible Gorilla describes something similar: pick some object that you know well — the example they use is that of a bicycle — and draw a diagram of it. No need for artistic verisimilitude, just try to get all the important parts and how they relate to each other. Now, compare your drawing to the real thing. Are the pedals attached to the frame? Do the pedals go through the chain? Is the chain attached to both wheels, by any chance? According to the authors, a lot of people make glaring mistakes. I think it’s because, while people know how to use a bicycle (or a stove, or a TV set), we rarely if ever need to think about the way the parts have to fit together to actually work.

Which brings me to my own field:

It has often been said that a person does not really understand something until after teaching it to someone else. Actually a person does not really understand something until after teaching it to a computer, i.e., expressing it as an algorithm.

— Donald E. Knuth, in American Scientist:61(6), 1973, quoted here

What I mean is that if you really want to understand something, the best way is to try and explain it to someone else. That forces you to sort it out in your mind. And the more slow and dim-witted your pupil, the more you have to break things down into more and more simple ideas. And that’s really the essence of programming. By the time you’ve sorted out a complicated idea into little steps that even a stupid machine can deal with, you’ve learned something about it yourself.

— Douglas Adams, Dirk Gently’s Holistic Detective Agency

Computers have a nasty habit of doing exactly what you tell them, and only what you tell them (or at least they did back when I learned programming; since then, they’ve occasionally attempted to be helpful, which usually means they’re not even doing what you tell them). This means that to write any kind of program, you have to think about absolutely every step, and make decisions about everything. And the machine isn’t at all shy about letting you know that YOU GOT IT WRONG HAHAHAHA LOSER!, although it usually lets you know through a cryptic error message like segmentation fault (core dumped) or dropping your Venus probe into the Atlantic.

But in most disciplines, we are not so lucky to have such stupid students, or to receive the kind of feedback that programmers do, so we need to resort to other methods.

Explaining things to someone else helps, probably because it forces you to explicitly state a lot of the things that you can just gloss over when you’re thinking about it. John Cleese has talked about the importance of test audiences in improving movies: they’ll tell you about all sorts of problems with the film that you never would have noticed otherwise. One of the cornerstones of science is peer-review, which basically means that you throw your ideas out there and let your colleagues and rivals take pot-shots at them. And the study I mentioned at the the top of this post says that it helps to draw pictures of what you’re thinking about.

It seems to me that the common element is looking at every aspect of a design, the better to try and make its flaws evident. The human brain is a remarkable organ, but it’s also very good at rationalizing, at overlooking details, at making connections that aren’t there, and the like.

But the good news is that we do have techniques like doodling, explaining, soliciting feedback, and so on. And that suggests that we can learn to think better. Genius may not be something innate, something bestowed by whichever Fates decided your genetic makeup, but rather something that you can learn over time and improve through practice, like playing piano or baking a soufflé.

I hope this is the case. It would mean that our children can be better than we are, and there’s something we can do about it. Heck, it would mean that we can improve ourselves.

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