Black boxes
A claim I came up with recently: “There exists a person who can learn to juggle five balls in an hour.”
One can of course quibble over the operationalization, but let’s pick: the person achieves 100 catches during that hour, with the baseline being that they have never before managed 20 catches with three balls.
I’m fairly confident that the claim is false. My uncertainty comes from the operationalization and edge cases. Like: what if there are people who have done absolutely insane amounts of things very similar to juggling, and for whom the “20 catches with three balls” condition is very unrepresentative of their skill; or possible hunter-gatherers whose hand-eye coordination is honed to be very good by everything else. But my probability that a random person picked off the street meets that condition is, for example, below one in a million.
(Which is a very different claim from expecting one in a million people to be able to do it – my median estimate for the number of such people is 0. I mean that I have so little model uncertainty that I’d be willing to bet at a million-to-one odds that a random passerby can’t do it.)
Maybe readers find this a completely obvious and boring claim. The interesting thing here is that back when I was, say, in high school, I would have been quite baffled by such a claim. I’d have thought: “sounds plausible, but how can you be so sure, how can you know?”
Here’s an illustrative anecdote about high-schooler-Olli: I had received an invitation to a coding camp held at the University of Helsinki. This was among my first times in Helsinki, perhaps my first time alone there, so getting from the railway station to the university by public transport was an effort. I ended up taking a tram and, in my confusion, walking long distances.
Somehow I didn’t quite see taking a bus as an option, and indeed the camp organizer asked why I didn’t just take a bus. I answered “well, with a bus you can’t be sure whether it’ll decide to go the right route, or turn off onto a different route at some point, but a tram is certain because it runs on rails.” The camp leader smiled and said “Right.”
When I said that, I was aware of the comment’s comedic value, and that probably contributed to my expressing the thought, but clearly some thought along those lines had influenced my decision-making. I’d describe it like this: since I had hardly ever used a bus myself (in Helsinki or anywhere else), they were like unpredictable black boxes; my mental model of buses and bus drivers didn’t rule out the option “the bus just decides to drive off elsewhere.”
(Although in a way I could deduce that if even one percent of buses decided to behave like that, it would be quite a farce and people wouldn’t use buses.)
(…or would they?)
Today, while crossing a crosswalk, I thought: “That car could just floor it and that’d be that.”
(The car stayed put.)
Imagine that a child – say, seven years old – asks you: “How can you know that when you start crossing a crosswalk, the cars won’t start moving and run you over?”
Or: “How can you know that a bus driver will drive the agreed route?”
Or: “How can you know that no one can learn to juggle that fast?”
What do you answer?
Especially when younger, I was often in the kind of mental state where people are unpredictable black boxes. I was baffled roughly every time someone, in any context, talked about “the predictability of human behavior.” Nothing rules out (I thought) that some day a driver just decides to run you over.
Often, when I said things like that, I got responses like “Right.” or “Olli, people don’t behave like that.”
And yeah, they were funny thoughts.
but how can you know
Once a friend and I pondered what might be the longest distance any Finn has walked today. (The conversation happened to take place during a multi-hour walk.) At the same time we pondered whether the answer to that question could be found out, given that people carry GPS-equipped phones with them when they’re on the move.
I argued that people don’t necessarily really carry them; my friend, on the other hand, was very skeptical that anyone would go on a 50km+ walk without taking their phone along. Or that people don’t behave like that and it’s a pretty absurd idea.
But shortly before that I had (perhaps thinking of multi-hour walks) ended up reading the Wikipedia page on ultralight backpacking. And in light of that, the idea of a phoneless hiker started to look less absurd.
Language models are, in a big enough picture, fairly similar to humans. No one knows how they work. In strange and difficult situations they can do surprising things or behave foolishly. Still, they’re in a way fairly predictable.
If you ask modern frontier language models which is bigger, the Earth or the Moon, they answer correctly, over 99.9% of the time. If you ask them to list the days of the week, they get the list right in both Finnish and English, over 99.9% of the time. If you ask them to write a grammatically correct sentence containing the word “reliably”, they succeed, over 99.9% of the time.
I haven’t checked any of those claims myself or seen anyone else check them. Someone might ask how I can know, if I haven’t checked. But that’s just how language models work.
And it’s just as clear that if you ask current language models “Is 5 + 8 = 13?”, they answer affirmatively, over 99.9% of the time.
(Except.)
Imagine I’m writing a children’s book that contains true and false claims. One of these claims is “There exists a person who can learn to juggle five balls in an hour.” I write that this claim is false. But this answer of course needs an explanation.
How would I respond?
It’s a bit of a long story.
(So long, in fact, that it doesn’t fit in the imagined margin of the imagined book, and thus this claim’s existence in that book is itself only imagination.)
There are worse answers than: “Juggling five balls is hard: hobbyist jugglers typically take years to learn it (if they learn it at all). Learning to juggle five balls in even 30 hours of practice would be an exceptionally fast pace. Although there is variation in learning speeds between people, there’s plenty of documentation online of the achievements and developmental trajectories of the world’s best jugglers, from which you can deduce that the ranges in learning speeds are more like twofold or fourfold, certainly not thirtyfold.”
In reality there are also other, harder-to-articulate reasons why I believe that claim is false. So if the child who asked were still interested in hearing a more detailed answer, one could perhaps talk to them more broadly about how, by observing the world and thinking carefully, you can deduce all sorts of things.