Somewhere just north of a decade ago -- so when I was 10 or so -- I was helping strangers in online forums troubleshoot games they were making. It was crazy fun. I still remember this one guy: He had a 3D FPS he was building in Game Maker, a tool that (for this use case) gives you a graphics engine and not much else. He had mouselook set up (no trivial feat) and had a bare-bones firing system, but it only worked when the camera was leveled out flat. You couldn't shoot up or down. That's a big problem, but the game was still pretty fun in spite of it, so in the spirit of trying to make a good thing better I offered to help.
With the right background knowledge, the solution is pretty clear. The mouselook system gives us an angle for how far up or down we're looking. What we want is for bullets to rise or fall at a steady rate determined by this angle. So we need a value to determine that rate, and that value will end up being a slope. You can turn angles into slopes using trig: slope = rise/run = sin(θ)/cos(θ) = tan(θ). So you take this slope, scale it based on horizontal speed, and periodically add that to the Z coordinate.
This is easy to figure this out if you know the concepts involved, but take it from me: it's a lot trickier when you've never heard of a slope and all you know about trig is what Wikipedia tells you. But with a few days' work I figured it out, sent the guy a patched version of his game, and went back to playing it. All this work, and yet for the life of me I can't remember his reaction.
About a year or two later, I joined a game making group. They already had programmers, so I told them I made music. They couldn't let me in fast enough when they heard that. I did make some music, but I also pitched in whenever anyone asked for troubleshooting help. Pretty soon I was the go-to guy for figuring out the really pathological stuff.
After a while I started working on my own project, a turn-based strategy game (tragically never completed, but surprisingly close to completion, and sporting a totally bonkers implementation of A*). I got hung up on the AI, lost steam, and turned to other projects. I wrote my own FPS, which (to my astonishment) people actually played. I wrote a couple RPGs from the ground up. I wrote a 2D, team-based multiplayer game inspired by laser tag. In fact, writing the login system for that game sparked my interest in security.
In my free time, I was pushing my limits by working with a fantastic math tutor (Naomi, whose debt I am deeply and eternally in). She taught me everything up to calculus, past which point I taught myself. By the time I started high school, I'd built up a working knowledge of multivariable calculus.
And now, here I am: 22 going on 23, and not feeling too different now than I did then. What happened?
The answer, it feels like, is "not much." People learn at different rates, and I happened to luck out by being someone who learns certain abstract subjects really quickly. That doesn't make me inherently better at them. It just means I got a sort of head start. And I'm coming to suspect that the same is true of many if not most talented young people (including many who were/are way above my level).
I've had the great pleasure in my life of knowing some real capital-G Geniuses -- people who, when you see them at work, it's hard to believe they aren't in touch with something beyond our understanding of the world. It's sublime. But these people are rare. They're literally one-in-a-million. And so, inspiring as they are, they don't change the fact that most talented young people seem to be exceptional not so much in the degree of their abilities as in how quickly those abilities develop.
It's a little bizarre that so many of us hold precocity in such high regard. Think about it: when you compliment a young person by calling them precocious, you're giving them praise that comes with an expiration date.
Say you have a ten-year-old who's reading at the level of someone twice their age. You might call that person talented, exceptional, precocious. If you have a twenty-year-old reading at the level of someone twice their age... well, that's just called being literate. Past a certain age, being pretty good at something ceases, by itself, to be exceptional. You have to find something more.
I was tempted to end here, because that "something more" is different for every person, so it's hard to imagine how to follow up on it. I'd actually left this post as a draft for about a week, dissatisfied but lacking any better idea for how to end, until a remark from my old, excellent friend Henry sparked my interest again. He observed, casually and offhand, that 'you're always making progress, just maybe not in the direction you thought.' To me, this really cuts to the core of what I'm trying to get at. Since I've put so many words into explaining my background, let me carry that a little further to try and show what I mean.
There's an incredible gap between being good at something and being good at explaining that thing. To find evidence of this, one need look no further than the average research university lecture hall. In fact, it's often the case that the better you get in your area of specialty, the harder it gets to explain it. As you learn more, you end up with more and more levels of abstraction separating you from your audience, and so the gap gets ever harder to bridge.
This was something I experienced trying to implement a secure login system -- I'd be going on to one of my game-making buddies about, say, secure key exchange, and after describing how this lets us lock down the login protocol, I'd get back a reply like "ok, but wait, wouldn't it be easier to just send everything in plaintext?" I was so far down the security rabbit hole that it was almost inconceivable to me that anyone would even suggest such a thing. When you focus on a problem for long enough, it's easy to lose touch with outside perspectives.
Now, it's easy to blame awkward exchanges like that one on ignorance. 'Oh, man, how could this guy not even know about sniffing passwords?' There's a certain selfish satisfaction in knowing stuff, especially stuff that other people don't know. But if you know something that the person you're talking to doesn't, and their ignorance is impacting the conversation, whose fault is that? You could fault them for their ignorance, or yourself for failing to be a better communicator. The latter option tends to be more productive.
It can be really difficult, though, to communicate well about difficult topics. Maybe that's obvious, but it's something a lot of people seem to underestimate, to their own detriment. I certainly see that underestimation in myself as I was around the time I outlined earlier. I may have been good at math, but how good was I at explaining it? I may have been interested in security and committed to personally getting it right, but how good was I at showing other people why security is important? Not very, and I think this is somewhere I've grown, practically without meaning to or even being aware of it.
I think this experience generalizes. Suppose for example that you're someone early on in their college career who's always been really good with literature -- reading well above your level, laughing at reading comp questions, writing insightful analyses -- and you come to feel, in college, like somehow you've plateaued. The best is behind you, it feels like. In high school you were hot shit, but now you're just another 20-something with a notebook and some colored pens. You might feel like you're stuck in a rut, like you're not going anywhere, maybe even like being in college is a mistake.
But what if, while you aren't learning anything new about (say) literary theory, you are learning about how to communicate what you know? After all, odds are that if you were hot shit in high school, there was a pretty short list of people with whom you could have a really good back-and-forth about this stuff. Not so with college (though this is not unique to college). Learning how to have a productive discussion without arguing or talking down, learning how to explain something without patronizing, learning how to ask good questions -- all these are valuable skills, and also skills that it's hard to realize you're even working on. That is, until you've made enough progress that you can look back and see how far you've come. When it comes to math, I don't feel like I know a whole lot more now than I did then, but I do feel much more qualified to share what I know.
There's an absolutely beautiful moment in this 1950 movie, Harvey. The movie (adapted from a play) is about this super sweet, middle-aged, heavy-drinking dude, Elwood, whose best friend is a giant rabbit that no one else can see. The whole film is magnificent, but especially one moment near the end, after Elwood's family tries to have him committed to an asylum. The plan backfires when Elwood's simple charm wins over the asylum staff.
The chief analyst tries to explain to Elwood just how awful his sister's plans for him are -- "She's trying to persuade me to lock you up!" -- and can't understand why Elwood isn't more upset. By way of explanation for his good-naturedness in the face of all this, Elwood replies that he's come to understand that in life, "you must be oh so smart, or oh so pleasant. Well, for years I was smart. I recommend pleasant."
There's also this great story about Richard Feynman -- who was, above almost all else, famously good at talking clearly about complex subjects. About a year before his death, when it was clear that cancer would kill him but unclear just how long it would take, he was out on a walk with a good friend. This hardly made for cheerful conversation, it seems, and so his friend was kind of down. Feynman asked him what was wrong, and his friend said, "I'm sad because you're going to die."
Feynman replied that he was sad about that too. It wasn't so bad, though -- he'd come to a realization, you see. "When you get as old as I am, you start to realize that you've told most of the good stuff you know to other people anyway."
May we all be so fortunate.