Hume called it the problem of induction; a catchier name is the No Free Lunch theorem, although it’s about as far from being a “theorem” as it’s possible to get. And it is simply this: there is no general, systematic way to go from observation to understanding.
If you haven’t encountered it before, it’s likely you don’t see what the big deal is. Don’t we all do this all the time, without even thinking about it? We do, but we don’t know how we do it, which means we don’t know how to teach it, how to automate it, or even if we’re doing it right.
What’s needed is a simple, concrete example which illustrates the idea without any particular need for mathematical sophistication. I’m going to give just such an example, show how various algorithmic approaches fare, and try to explain the unavoidable trade-off at the heart of the problem.
If all goes well, you’ll not only learn something important about one of the most fundamental unsolved problems out there, you’ll have developed a practical intuition that will help you understand, for example, why François Chollet introduced the ARC-AGI benchmark, why AI researchers keep talking about world models, and what it means to say the transformer architecture hits a sweet spot for language models.
From the article: