If something is outside your grasp, it’s hard to know just how far outside it is.
Many times I’ve intended to sit down and understand something thoroughly, and I’ve put it off for years. Maybe it’s a programming language that I just use a few features of, or a book I keep seeing references to. Maybe it’s a theorem that keeps coming up in applications. It’s something I understand enough to get by, but I feel like I’m missing something.
I’ll eventually block off some time to dive into whatever it is, to get to the bottom of things. Then in a fraction of the time I’ve allocated, I do get to the bottom and find out that I wasn’t that far away. It feels like swimming in a water that’s just over your head. Your feet don’t touch bottom, and you don’t try to touch bottom because you don’t know how far away bottom is, but it was only inches away.
A few years ago I wrote about John Conway’s experience along these lines. He made a schedule for the time he’d spend each week working on an open problem in group theory, and then he solved it the first day. More on his story here. I suspect that having allocated a large amount of time to the problem put him in a mindset where he didn’t need a large amount of time.
I’ve written about this before in the context of simplicity and stress reduction: a little simplicity goes a long way. Making something just a little bit simpler can make an enormous difference. Maybe you only reduce the objective complexity by 10%, but you feel like you’ve reduced it by 50%. Just as you can’t tell how far away you are from understanding something when you’re almost there, you also can’t tell how complicated something really is when you’re overwhelmed. If you can simplify things enough to go from being overwhelmed to not being overwhelmed, that makes all the difference.