The Stupid Stuff

by rrusczyk, Sep 13, 2008, 4:04 AM

Next week, I'll teach the opening WOOT class, which will focus on general problem solving strategies. Along with this class and the next class, which nsato will teach, we at AoPS will each be writing a WOOT article about a particular general strategy we like. My article was "The Stupid Stuff Works", in which I discuss the importance of going after problems with simple, i.e. "stupid", tools, rather than reaching for the fancy stuff first. Since writing the article, I've thought a lot more about the stupid stuff, and I think it's probably one of the most empowering observations in any pursuit -- the stupid stuff really does work.

I was working with my sister today on learning Asymptote to do some diagram building for us at AoPS. The first diagram she did was very well done. She found elegant solutions for everything. But she was stuck on the rest. As we discussed doing these diagrams, she got to see how I went about trying to figure out how to build them, and she saw that I very consistently did stupid stuff that would eventually work. And very quickly she got over the fear that she just didn't know the right command or the right math to do something. I think she realized that she's plenty smart enough to figure out how to get each diagram done -- there isn't some magic trick she doesn't know or can't comprehend, some special insight that only the illuminated mind can comprehend. There's the stupid stuff, and it usually works. And when she sets aside the conviction that there's something out there that's unknowable and insurmountable, she becomes powerful. I think a lot of life is like that.

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On the other hand, in higher math machinery really does enhance your understanding of a subject. But even in that case, you should generally try to be stupid before you try to be smart.

by JSteinhardt, Sep 13, 2008, 5:48 AM

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I think this is a very useful observation, rrusczyk!

by Singularitarian, Sep 13, 2008, 8:45 AM

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Jst -> very true. You need to master the stupid stuff before you can really use the smart stuff. Ideally, you get to a point where the smart stuff looks like stupid stuff, too. But you can't (well, I can't) just step right up to that point. Geometry is a good example of this. I've seen very, very few students who can employ very advanced tools the way I can use similar triangles and cyclic quadrilaterals. Those few are the few real master geometers I've encountered (and they're a clear step beyond me, I confess). But all of them can use the dumb stuff at least as well as I can, and could do so before they moved on to the fancy stuff. And then their mastery of the fancy stuff helped lend what seem like magical insights to their solutions. (Though I suspect even then that they often solved the problems first with the dumb stuff, and then found a nicer approach using the relationships they know between the dumb stuff and the smart stuff. I do this surprisingly often with hard counting problems.)

by rrusczyk, Sep 13, 2008, 1:48 PM

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