Tags: math

Growing up, people told me I was good at math. People told me I was good at a lot of things, and math was one of them. That was fine as long as math kept coming easily to me. I internalized this idea that being good at something meant that it should come easily or naturally to you, and I hit some point in high school where it didn’t anymore.

Suddenly math was hard. And it made me hate myself. I’d tell myself, I’m smart, I’m good at math, this shouldn’t be so hard.

So I started saying I’m bad at math, and I meant I can’t do math so I won’t even try, and I stopped trying.

Oddly enough I moved into philosophy where, it turns out, I discovered a love of symbolic logic, and then into linguistics, where generative syntax and drawing X-bar trees were my thing, and then eventually, by hearing about type theory, into Haskell.

And now Haskell has brought me back to math. Those other things – symbolic logic, abstract syntax, and Haskell – are all sort of like math. Haskell has led me back to the hard drugs, though, and by drugs I mean category arrows.

I don’t understand it much, but it interests me. Over and over I keep going down Haskell rabbitholes until I hit some kind of mathy bedrock and it’s quite delightful.

Earlier today, I was proofreading and indexing the chapter of my book on applicatives. Applicatives are neat; I just gave a workshop on them a couple of weeks ago, and now I’m turning that into a series of blog posts. I remember writing that chapter, though, and at the time it made me hurt so bad I could barely stand it. It was so hard.

Sometimes people, impressed by how fast I seemed to be making progress at learning Haskell, would tell me I was good at Haskell, I was so smart, and that would make it hurt so much worse.

If I’m good at this, why is it so hard?

### Trivialities

I’ve got this friend, a real mathy sort of dude, who keeps quoting this to me:

It’s a succession of trivialities. The problem with mathematics is the accumulation of trivialities. - Jean Bellissard

For a long time, this enraged me. If they are trivialities, then why can’t I understand them?

Ah, well, you see, that was bad thinking. Trivial doesn’t mean easy, and that part about the accumulation complicates matters.

Still, in my fluffy head, it makes it sound like it should be easy, like i should expect it to be relatively easy and painless and it’s not. So then I get a lot of anxiety about how it’s so hard for me when it’s just a matter of training, of accumulating trivialities. Even if they are not all easy, they are trivial so why am I torturing myself this way?

But then I noticed today how much of the Applicative chapter keeps harping on the monoids and the functors and how it combines those two basic ideas. A lot of the repetition of that came from me, because I understood monoids by then, and I understood functors, so I was reassuring myself that this thing that seemed alien was … an accumulation of things I already understood. Of trivialities, in a sense.

Anyway, so Haskell is making me want to learn some math. A little set theory, a little graph theory, a little category theory. Someday those things are going to make sense to me.

But for right now I keep reminding myself I am bad at Haskell and bad at math because it reminds me that they are not easy things, they are hard things, and if I am going to get them, it will not come easy.

Linguistics, even really abstract syntax, comes somewhat easy to me because I am interested in exploring the (somewhat mathy) bedrock of human language. That’s it. Language is what I got in the lottery of fascinations. That and an abiding love of being able to synthesize areas of knowledge, which is what I end up doing with logic, syntax, Haskell, and now math. The generalizations and ignoring of petty implementation details that this leads to frustrates some of my more precision-loving friends, the ones who are good at Haskell and good at math.

Now that I’m interested in math again – but, god help me, so late in life – it’s not going to be easy because I’ve missed accumulating a nontrivial number of trivialities, but the interest (and my good, mathy friends) will keep me going.

### Even More Trivial Trivialities

This is not true of video games. I am terrible at video games, and I do not have the interest to get better at them.

Except I swore I would beat my kids at Mario Kart this year. Hmm. I guess I should practice.

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