I've been working with linear regression, both as a tool for understanding psychology and as a primary professional skill, for more than eight years now. At last, my conceptual understanding of statistics has advanced to the point where I've stopped understanding it. In a few years, I'll probably have to take some time off to think hard about what a "sample" is.
I only mean this to be mildly self-denigrating. I think it's similar to the way that anybody here could tell me what a "number" is without thinking -- unless they've studied mathematics in real depth, in which case they're going to get a glazed look in their eyes for a few minutes, and then launch into a two-hour lecture. Or maybe it's more like the way you drop acid and achieve a crystal-clear understanding of all reality, and then you look down and you're like, whoa, I've got this hand, and it's just sort of there. It's like there's a region of space with this propagating wave of handness.
Why do I make these posts? I guess because I spend a lot of time wandering around inside my head, and so for people who care about me it's kind of like telling you what's going on in my life. And in that spirit...
Special bonus entry: Boolean facepalm
The other day I was standing in the shower and I just sort of spaced out, thinking about logic. So there's AND and OR, and NAND and NOR, but are there other Ns? First I had to prove to myself that AND, OR, and XOR cover all possible combinations of two truth values, if you don't care which variable is which or which state you call True and which state you call False. And then I thought okay, so why do you never hear about NXOR? I drew some pictures in my mind, and eventually realized that you do -- it's called EQUALS!
Then I got out of the shower.
Then later on I found out that there is a NXOR, except that it's usually called XNOR.* I would have gotten out of the shower again, but I wasn't in it at the time.
* Demonstrating that NXOR is a more systematically appropriate name than XNOR is left as an exercise for the reader. Demonstrating that XNOR is inevitably going to be more popular anyway is left as an exercise for the other reader.