Grant Sanderson: prediction

Transcript context

…I think this is an important thing to think about. We often think about how smart a single system is. And we don’t think about AIs having advantages that are more the result of other facts about them. So in this context, the key fact about them is that we can just parallelize and arbitrarily scale them. Whatever level of capability they have, it’s not just one idiosyncratic genius in the history of mathematics who makes a few connections and then dies in a duel. It’s universally applying that waterline across all problems that are accessible at that level of capability. This is among the many advantages that digital minds inherently have that we don’t think enough about. The other ones being that they can merge all their knowledge together—or at least that there will be techniques that allow this to happen—and that you can spawn off copies with identical levels of knowledge. This parallelization is quite an important property. I’d be curious about your predictions. Even if they’re not as smart as human mathematicians, the fact that for PR reasons the AI companies are just throwing billions and billions of dollars at this means that quantity has a quality all of its own. That seems in the right direction. If we take that conversation between Montgomery and Dyson at the IAS that suggests some connection between the Riemann hypothesis—or the Riemann zeta-function zeros—and random matrices, that feels like the kind of thing that you could try to automate. You have agents representing expertise in all these fields. We all know that an institute is smarter than an individual. The reason for having people all in the same geographic location is that you want those serendipitous conversations to happen. What does it look like to engineer those between agents? It’s interesting, because you point out that you can pool all your knowledge, but I really wonder if one of the advantages is that you can do the opposite of that. Sometimes when an AI is failing, it’s because it gets into a bad chain of thought and it’s really hard to get it out. So you say, “I’ll just start again.” Same deal with humans. Sometimes you start thinking about it in a certain way, and what’s required is to just back up. There are stories about people trying to prove something for a long time, and then at some point they say, “Hang on a second. What if I tried to prove that it’s impossible, or prove the opposite?” Unwinding your own context and going at it with a fresh mind… You could imagine systematizing that, or having multiple different agents deliberately given different pieces of context and trying to compare and contrast there. We don’t have the same level of manipulation on our own context. In this AI and math series, the first episode we’ll do will be about when they solved the IMO. I want to focus on one specific IMO problem that they failed on, which is one that a lot of very smart students failed on. Terry Tao also failed on it. People were very mad at the problem because they called it a troll problem. I almost don’t want to spoil it, because I want to construct the episode around leading someone in without their knowing that it turns out to have a simple solution. You can really empathize with what it’s like to be a student solving this. Basically, there’s a really elegant way of going down what you really feel like is going to be the solution based on the context of it being an International Math Olympiad problem. The character of the solution is really enticing, but it’s hard to prove that it’s the best. The reason is that it’s not. There’s this almost brain-dead solution that is the best. The relevance of that to the whole AI story is that for a human, what’s required to answer that question is to escape your context. Escape the context of being in the IMO. Escape the context of the way you’ve been trained to solve these contest math problems. If you just approached it like a brain teaser that I throw at someone off the street, they’d probably answer it well. You want the same sometimes for human research in other contexts, just being able to refresh your thinking and come at it completely differently. omeone off the street, they’d probably answer it well. You want the same sometimes for human research in other contexts, just being able to refresh your thinking and come at it completely differently. Of all the advantages that digital minds have, that might actually be one of them: a more systematic approach to refreshing your thinking. Spin off two agents, one who’s trying to prove it and one who’s trying to disprove it, one who tries it this way and one who tries it another. They deliberately have different contexts. I would be curious to see, if we’re having this conversation three years from now, how many of the significant results that make headlines have that character of basically erasing the context previously, trying a bunch of different things as opposed to merging the results of a bunch of different agents.…

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