A point I've been making repeatedly to my maths tutees is that there's at least two categories (really a spectrum) of solution to problems: * A slow, plodding, way that will reliably work. * A clever, elegant, fast, way that may or may not work. You need to be able to do both.
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Replying to @DRMacIver
Something I enjoyed about the Polymath Project (online collaborative mathematics) was that it showed over & over that the way the world's best mathematicians get to the second type of solution is to do an awful lot of the first. I wish I could show every grad student this...
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Replying to @michael_nielsen
Yeah, that makes a lot of sense to me. It's the same in programming - there's the occasional point where you need some clever insight to crack the problem open, but even then you're usually better off doing the work the gross ugly way and then rewriting it when insight strikes.
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Replying to @DRMacIver
A favourite memory is of three very well known theoretical physicists arguing at the blackboard over how to find an elegant way of writing down the product of two particular 2 x 2 (maybe 3 x 3?) matrices, without actually explicitly doing the multiplication. I walked away...
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Replying to @michael_nielsen @DRMacIver
... came back an hour later, and they were still arguing.
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Replying to @Meaningness @DRMacIver
You've seen this movie before, I'm sure, albeit with a different cast! Hell, you've probably starred in it. I know I have.
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Yes, “three CS PhDs flailing together for half an hour on a basic computer task because there somehow ought to be a less painful way of doing it than the obvious one which would take all of three minutes” is the analog
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Replying to @Meaningness @michael_nielsen
I feel like this is definitely a group failure mode more than an individual one. When you've got people to talk about the problem you can talk about it indefinitely, but when it's just you you might as well roll up your sleeves and dig into it.
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