I'm sitting with the last bit of a large mug of coffee and my algebra book in front of me, getting ready for my exam tomorrow. I just had a lovely "aha-moment" - reading something that I know to be true but never quite grasped why, and all of a sudden, without thinking about it further, I knew exactly why it was true. I think math has really taught me what actual understanding feels like. I know how I feel when I'm only "getting" something enough to be able to use it in a proof, for example, but it's not tangible to me yet. I don't have a picture of it in my head, if that makes sense. When I really do understand a concept or a statement, though, it appears in my head whenever I read it. There's no question about whether that statement is true or what that abstract object is really like - I have the blueprint of it in my head and it so clearly couldn't be, couldn't exist any other way - it simply has to be true. And it feels great!
However, knowing what real understanding feels like, I also know when I don't understand something fully, and then I can't help but be impatient. That's the thing about math sometimes. Sometimes, you could read the definition fifty times in a hour and still not "get" it. Sometimes, you just have to wait. Then, in the shower, during your second cup of coffee, while you're walking the dog - there it is! It appears in your head, fully formed, just like the simplest thing in the world. And you think, "well, brain, if it was so damn simple, why didn't you just let me understand it before!?!" Humbling, I suppose. :)
I hope I have a few more of those moments during studying today. That would make me feel good about tomorrow.
In other news, it's still kind of rainy in Oakland and I can't find my raincoat. Unfortunate, but we persevere! :)
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It got sunny at the end of the day - thought I'd share a bit with you:
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