Equations as Constraints

Can you construct a right cone that has a height of 4, a radius of 3, and a slant height of 6? This question has an easy answer, but only if you know what to look for. The reason is that the question is posed in a way that requires a “yes” or “no” answer. If your answer is “yes”, then you have to prove it by giving me a cone that has the desired…

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Going After The Average

When making work that’s important to you, it’s tempting to focus on improving your best work. After all, when you think of your work, that’s what first comes to mind. (You don’t think about the mediocre work.) Therefore, it makes sense to focus on that. By definition, this should be scarce. It’s not that you decide to sometimes do great work. Rather, it’s a simple consequence of looking at many pieces. Some will jump out…

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The Right Touch Of Novelty

We all like new things. It’s exciting to try a new activity, to do something we’ve never done before. It breaks us out from the usual rhythm of our lives. A novel activity ends up looking much more enticing than the regular activities you usually do. We are wired to respond to novelty. This is a double-edged sword. On the one hand, it means we don’t get trapped doing the same things all the time.…

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Safe Questions

The process of learning with another person is a tricky thing. When you’re on your own, it’s fine to ask as many dumb questions as you can come up with. After all, nobody is going to judge you, since you can simply look up the answer in a book or online. As such, learning by yourself is safe (though it can be slow). On the other hand, I’ve come to realize how vulnerable you can…

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