> You prove your understanding by the type of questions you ask. I can't find where I paraphrased this from. Maybe it was Better Explained [0] while explaining

> You prove your understanding by the type of questions you ask. I can't find where I paraphrased this from. Maybe it was Better Explained [0] while explaining the intuition behind complex numbers? As I remember, the context was "Now you understand that complex numbers are rotations through 2 dimensions, I bet a lot of you are asking 'can we extend math to rotations through 3 dimensions?'" (aka quaternions) The vibe I get from this article is "the meaning isn't important, so plug and chug away". No no no no no! Grokking the meaning is important because it allows us to extend our understanding from a strong foundation. E.g. HN a few days ago submitted a paper on "Half Coins"[1] which extends our conventional notion of probability to negative numbers. And after I read the paper, I realized it's not as weird as it sounds. [0] http://betterexplained.com/cheatsheet/ http://betterexplained.com/cheatsheet/ [1] https://news.ycombinator.com/item?id=8187457 https://news.ycombinator.com/item?id=8187457 disclaimer: I don't know anything about statistics.