Well, our old guy is now up in dog heaven. I really wish we hadn’t let him go on so long. Not that we could have predicted the rapidity of his decline in any case. I know this sounds weird, but the extent to which I got attached to him without meaning to makes me want to get a dog when I can afford it. It’s so weird to see his spot in front of the fireplace empty all day. It’s going to be weird for a while.
I’m sure nails serve a purpose, but I rarely notice mine except when they’ve been involved in a horrible accident.
Perhaps… they were really basic proofs though. I think the first one in calc III was prove the dot product of two vectors is commutative or somesuch. I couldn’t get it done because it didn’t “seem right” to me that you could just expand arbitrary vectors on both sides, do the operations, and show that RHS = LHS. It struck me as “too obvious” and I thought the instructor was looking for something way more profound. I didn’t think I was allowed to prove by demonstration in that way. I think I tried to prove commutativity from associativity, which is of course impossible. All my math professors seem to have commented to me that I tend to use too much “technology” or work too hard to relate disparate concepts.