Mathematics, Logic, and Waiting

When I was in college and grad school, I did a lot of formal logic. I took logic classes both on their own and as part of linguistic semantics. Logic is basically mathematics, even though it uses letters instead of numbers. Two things were really hard about it: first, understanding principles of a logic and its manipulation enough to do exercises, to express things within the system, and to understand proofs about the system; second, to stop trying to understand in order to learn to do exercises and proofs. The latter version is like learning to type; you have to just keep doing it until it works right- then you can. Unlike typing, then you can perhaps start to understand what you’re doing. you do any logic or mathematics, you know that proof by induction feels like it makes no sense if you try to understand it before learning it. That’s a pretty hard thing for me, because I tend to learn by having a conceptual framework, knowing what we’re getting at in the general sense before I look at the details. To do anything else is generally just confusing, or in the case of logic classes, it was a leap of faith.

I was thinking about this today because I just heard about a mathematician in the news, Grigori Perelman, whose work on the Poincaré Conjecture has earned him some fame and awards, although he has opted to stay at home rather than accept them. I have gotten to know quite a few mathematicians (and logicians). What strikes me is that the career of the theoretical mathematician involves quite a bit of thinking- and then waiting until you come up with a way of proving something. Think, wait, think… I don’t know if I really liked doing logic, but I did benefit in some sense from its structure; it gave me some way of trying to squeeze and shape my thinking into something a bit more focused and a bit quieter. It’s not exactly meditation, but whatever works is just fine. I guess that’s not enough for me. Perhaps that’s because I get distracted by other interesting things, or perhaps it’s because I find other things more interesting or important. I do know that my doctoral research advisor’s stated motive for his work in very abstract logic did not hold for me; he told me that he did this because “it keeps me off the street.” What he did was describe logics that described other logics. An outlet for meta-meta thinking?

Funny thing is, while logic itself embodies structure, that doesn’t mean that the time spent working on a dissertation is structured. In hindsight, that’s why research didn’t end up being the thing that kept me off the street. Thinking about structure doesn’t provide one with structured days.

Where’d the world go?

When my hyperthinking is at its worst, I wake up in the morning thinking. I notice that I’m thinking, perhaps about some errands I need to run, and do them in my head. I drive to the grocery store, pick out some vegetables, get distracted by the cupcakes, and get tired. Oops! I’ve forgotten meanwhile that I’m sitting in bed thinking about my errands. I think about that for a moment and forget that I’m doing that because I’m mentally getting up and taking a run.

If I notice that my body is attached to my brain, and that the world is here, it breaks the thinking, at least for a moment. I’ll notice my body, feel my legs, etc, and then forget that I did that. One thing I’ve learned is to distinguish thinking from ruminating. This isn’t me worrying about everything I have to do- it’s just going through the mental motions without the body joining in. That’s important, because techniques for calming worry tend to involve some thinking- so they just add fun to the thinking frenzy.
Luckily, this doesn’t happen so much anymore.

Thinking in another language

I spent my twenties living in the Netherlands. My do people like to ask me why. Here’s why: I wanted to think in a foreign language.

Before I knew the name for my kerjillion-thoughts-per-nanosecond, I knew I was tired. I wanted some distance. Between that and studying linguistics, I thought perhaps thinking with an entirely structure would be a nice rest.

So, I went native, got headaches refusing to speak English, and practiced some of the most challenging diphthongs there are in while taking the showers. After a while, I could order “uiensoep” in a cafe without the waiter responding in English. The Dutch switch to English when they hear a trace of a foreign accent in your Dutch- so much so that a Dutch woman I know was spoken to in English upon returning from many years abroad. It’s been that way for a long time, as evidenced by the 1908 book An Irishman’s Difficulty With The Dutch Language.

Apparently I’m bloody persistent, because after a while people guessed I was from a particular part of the country that has an ‘r’ closest to English, and now… I think a lot in two languages.

Now I think a lot in two different languages. Gek is dat. Jeetje. If you want to do the same, I highly recommend a strict immersion approach to learning a foreign language. And I also highly recommend starting by reading children’s stories in that language. Pick some that have actual stories that make sense. I started with the amazing stories about a girl and a boy called Jip en Janneke, by Annie M.G. Schmidt.

Jip en Janneke from the Annie M.G. Schmidt site.

Predominantly Hamlet-like

The kindest doctor I’ve ever had didn’t know why I struggled so. He said my thinking was like Hamlet, but that wasn’t a name for it. Now not to wax Shakespearian here but a rose by any other name… is attention deficit disorder. Back then that label wasn’t known to apply to adults. But diagnostic labels leverage information, and this information helped me understand what it was that was so hard.

Medically, it’s called attention deficit disorder- predominantly inattentive; or “spacey add.” It may be inattention, but for me it means I think a lot. I call it cognitive hyperactivity. I’m not missing the “hyper” in adhd; I’m hyper in the mind.