When something doesn’t make sense, it’s easy to look at it and think that it is just a collection of random rules. Unfamiliar topics look incomprehensible, so naturally we miss the structure behind them. This doesn’t mean that the structure isn’t there. It’s simply that you can’t see it because you don’t understand the topic well enough. This happens all the time in mathematics. On the one hand, this is very odd. Mathematics is the…

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I am keenly aware that we live in a culture that likes things to be optimized. We are bombarded with messages of the finiteness of our time, which makes us seek activities that will give us the greatest return on our time. (Just that phrasing should set off alarm bells.) We aren’t supposed to “just” have hobbies. Our hobbies should boost the rest of our life in some way. Furthermore, we should engage in hobbies…

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If you’re like me, chances are you have felt like you aren’t doing enough. Maybe that means not studying enough in school, or perhaps it means not doing enough extra-curricular activities. Maybe you do have hobbies, but you feel like you need to do more. I’ve been there. If this is something you identify with, I would like to pose a simple question. Where did the idea of not doing enough comes from? Sure, you…

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There are points in our lives where we can feel that we are at a junction. Sometimes, we can only notice this after the fact, but there are instances in which it is clear. At those points, we are faced with a choice. Do we continue on, or do we retreat? In the abstract, we all know the answer. “Continue!” But that’s much easier said than done. Even if it is clear to everyone (particularly…

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Are you slow at what you do? This is a bit of a trick question. After all, what does “slow” even mean? The reality is that speed is relative. If you don’t have something to compare yourself too, it’s difficult to talk about speed. However, it’s equally easy to forget that speed is a relative quantity. In other words, we often declare things like, “I’m so slow!”, forgetting that this doesn’t mean anything in the…

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