I don't think this model is realistic. Because it puts too much weight on cross pollination in one direction, and too little in the other.
In my model, maths progress doesn't really slow to a crawl waiting for the geologists to make a breakthrough. Sure, cross pollination is nice, but you can keep a field going without it. So the fields with the massive speed boost keep going, pollinated only by themselves and each other.
Meanwhile, cross pollination flows outwards, the vast amount of work happening in the fast fields, ends up having some significant effects on the slow fields, perhaps speeding them up too.
You’re likely right that there are more self-contained fields like math where this dynamic will be less harmful. It would probably be relatively easy to adjust the model to have direction-specific cross-field dependence, with variability across fields in their respective in-dependence and out-dependence strengths – I’d be interested to see if/how that changes things, but I will note that the main findings still hold even if you drop overall cross-field dependence quite low.
I think the intuition for why the findings still hold is twofold:
1. You don’t need direct paths from geology to math for math to end up slowed down. It could be that slowed materials research progress leads to slowed computing progress leads to slowed math. Or slowed geology leads to slowed energy tech leads to slowed high-energy physics leads to slowed theoretical physics leads to slowed math (obviously just toy examples)
2. The model already allows for the cross-pollination to flow outwards from fast fields to slow fields, in that the really fast fields do quickly unlock all of the prerequisites they can for the slow fields, but that’s insufficient if prerequisites remain that only the slow fields themselves can unlock
In the short- and medium-run, this model also already predicts that fast fields will race ahead, in exactly the way math is likely to in the coming years. The macro bottleneck is farther out, and is somewhat by definition a function of the kinds of prerequisites that we can’t easily forecast (and might not even notice when they’ve occurred).
All that said, I do think your suggestion would make the model more realistic (and would love for some economists to take this question on in a more formalized way!)
> You don’t need direct paths from geology to math for math to end up slowed down. It could be that slowed materials research progress leads to slowed computing progress leads to slowed math.
I am not claiming that the slow down effect is 0. Suppose that, if all other fields would somehow keep up, maths progress would go at 100x it's current rate, but with other fields falling behind, maths progress goes like 90x it's current rate. (wild guess numbers) In this model, maths progress is slowed down by lack of geology. But the effect isn't nearly as big as the originally posited AI speed boost.
For maths to be rate limited to the speed of geology, there needs to be a lot of very smart AI mathematicians twiddling their digital thumbs, with absolutely nothing to do until a new geology breakthrough comes in.
I think in your model, the prerequisites are hard requirements. You absolutely have to have the prerequisite. It isn't just somewhat useful, it's so absolutely vital the field can't progress without it. And I think that real world prerequisites are useful but not vital.
> I think in your model, the prerequisites are hard requirements. You absolutely have to have the prerequisite. It isn't just somewhat useful, it's so absolutely vital the field can't progress without it. And I think that real world prerequisites are useful but not vital.
> For maths to be rate limited to the speed of geology, there needs to be a lot of very smart AI mathematicians twiddling their digital thumbs, with absolutely nothing to do until a new geology breakthrough comes in.
On 1, I agree - in a footnote I say "the model assumes these two prerequisites are binding, such that new discoveries cannot be made until all prerequisites have been met. Scientific dependencies don’t quite work like this; a more realistic model would probably have more, softer prerequisites with substitute pathways". But I think the best way to conceptualize the nodes in this simulation are larger, framework-level developments; more like "we do or do not crack quantum computing, which determines whether we can access a new paradigm for math research", rather than "an unknown fact about the structure of wissahickon schist is blocking improvement on the Riemann lower bound"
It's true that there wouldn't be complete rate limiting even if these big frameworks shifts were blocked, and incremental within-framework progress could still be made, but I think whether most fields can fully route around major prerequisites is not an obvious one - e.g. if we had taken 20 more years to develop computing or 20 more years to develop AI, math wouldn't have routed around the lack of those prerequisites and still gone 90% as fast as it ended up going, it would instead have been stuck at its previous much slower pace.
Your points are well taken though! I am certainly open to being wrong on this, and if a model with more, softer prerequisites and differential in-dependence and out-dependence strengths made the effect go away that would be useful information
What are your thoughts on how we train (and incentivize) young scientists to conduct research in this context?
One would think that for the fields that could be clear “future bottlenecks” (either because automation isn’t an accelerator or the field is adoption-skeptical), we would invest more resources to those areas so we could yield higher returns on the dramatically improved areas. Right now I see the opposite happening in my field of population health.
Yeah this is an important question and I wish I had a better answer to it (and sorry for not seeing it until now!). To some extent there might be some built-in correction mechanisms - if everybody ends up pivoting into the AI-accelerated subfields, they will get overly crowded and individual contributions will be hard to come by, thus incentivizing people to identify and carve out niches in less crowded spaces (to some extent this has been an interplay between buzzy and non-buzzy subfields since long before AI!). But the other main lever is funding, so I think it'll be important to maintain broad-based funding to ensure we continue to make progress across the ecosystem.
I do think, though, that "adoption-skeptical" and "non-accelerable" will (and should) lead to different approaches. If there are fields that can be uplifted with AI but haven't yet, there's value in encouraging and supporting that uplift rather than funding status-quo approaches for the sake of tradition/preference
I don't think this model is realistic. Because it puts too much weight on cross pollination in one direction, and too little in the other.
In my model, maths progress doesn't really slow to a crawl waiting for the geologists to make a breakthrough. Sure, cross pollination is nice, but you can keep a field going without it. So the fields with the massive speed boost keep going, pollinated only by themselves and each other.
Meanwhile, cross pollination flows outwards, the vast amount of work happening in the fast fields, ends up having some significant effects on the slow fields, perhaps speeding them up too.
You’re likely right that there are more self-contained fields like math where this dynamic will be less harmful. It would probably be relatively easy to adjust the model to have direction-specific cross-field dependence, with variability across fields in their respective in-dependence and out-dependence strengths – I’d be interested to see if/how that changes things, but I will note that the main findings still hold even if you drop overall cross-field dependence quite low.
I think the intuition for why the findings still hold is twofold:
1. You don’t need direct paths from geology to math for math to end up slowed down. It could be that slowed materials research progress leads to slowed computing progress leads to slowed math. Or slowed geology leads to slowed energy tech leads to slowed high-energy physics leads to slowed theoretical physics leads to slowed math (obviously just toy examples)
2. The model already allows for the cross-pollination to flow outwards from fast fields to slow fields, in that the really fast fields do quickly unlock all of the prerequisites they can for the slow fields, but that’s insufficient if prerequisites remain that only the slow fields themselves can unlock
In the short- and medium-run, this model also already predicts that fast fields will race ahead, in exactly the way math is likely to in the coming years. The macro bottleneck is farther out, and is somewhat by definition a function of the kinds of prerequisites that we can’t easily forecast (and might not even notice when they’ve occurred).
All that said, I do think your suggestion would make the model more realistic (and would love for some economists to take this question on in a more formalized way!)
> You don’t need direct paths from geology to math for math to end up slowed down. It could be that slowed materials research progress leads to slowed computing progress leads to slowed math.
I am not claiming that the slow down effect is 0. Suppose that, if all other fields would somehow keep up, maths progress would go at 100x it's current rate, but with other fields falling behind, maths progress goes like 90x it's current rate. (wild guess numbers) In this model, maths progress is slowed down by lack of geology. But the effect isn't nearly as big as the originally posited AI speed boost.
For maths to be rate limited to the speed of geology, there needs to be a lot of very smart AI mathematicians twiddling their digital thumbs, with absolutely nothing to do until a new geology breakthrough comes in.
I think in your model, the prerequisites are hard requirements. You absolutely have to have the prerequisite. It isn't just somewhat useful, it's so absolutely vital the field can't progress without it. And I think that real world prerequisites are useful but not vital.
> I think in your model, the prerequisites are hard requirements. You absolutely have to have the prerequisite. It isn't just somewhat useful, it's so absolutely vital the field can't progress without it. And I think that real world prerequisites are useful but not vital.
> For maths to be rate limited to the speed of geology, there needs to be a lot of very smart AI mathematicians twiddling their digital thumbs, with absolutely nothing to do until a new geology breakthrough comes in.
On 1, I agree - in a footnote I say "the model assumes these two prerequisites are binding, such that new discoveries cannot be made until all prerequisites have been met. Scientific dependencies don’t quite work like this; a more realistic model would probably have more, softer prerequisites with substitute pathways". But I think the best way to conceptualize the nodes in this simulation are larger, framework-level developments; more like "we do or do not crack quantum computing, which determines whether we can access a new paradigm for math research", rather than "an unknown fact about the structure of wissahickon schist is blocking improvement on the Riemann lower bound"
It's true that there wouldn't be complete rate limiting even if these big frameworks shifts were blocked, and incremental within-framework progress could still be made, but I think whether most fields can fully route around major prerequisites is not an obvious one - e.g. if we had taken 20 more years to develop computing or 20 more years to develop AI, math wouldn't have routed around the lack of those prerequisites and still gone 90% as fast as it ended up going, it would instead have been stuck at its previous much slower pace.
Your points are well taken though! I am certainly open to being wrong on this, and if a model with more, softer prerequisites and differential in-dependence and out-dependence strengths made the effect go away that would be useful information
If I may reference my own research, we recently did a study exploring potential limits to AI research acceleration in biomedical research: https://www.nature.com/articles/s41598-025-32583-w
What are your thoughts on how we train (and incentivize) young scientists to conduct research in this context?
One would think that for the fields that could be clear “future bottlenecks” (either because automation isn’t an accelerator or the field is adoption-skeptical), we would invest more resources to those areas so we could yield higher returns on the dramatically improved areas. Right now I see the opposite happening in my field of population health.
Yeah this is an important question and I wish I had a better answer to it (and sorry for not seeing it until now!). To some extent there might be some built-in correction mechanisms - if everybody ends up pivoting into the AI-accelerated subfields, they will get overly crowded and individual contributions will be hard to come by, thus incentivizing people to identify and carve out niches in less crowded spaces (to some extent this has been an interplay between buzzy and non-buzzy subfields since long before AI!). But the other main lever is funding, so I think it'll be important to maintain broad-based funding to ensure we continue to make progress across the ecosystem.
I do think, though, that "adoption-skeptical" and "non-accelerable" will (and should) lead to different approaches. If there are fields that can be uplifted with AI but haven't yet, there's value in encouraging and supporting that uplift rather than funding status-quo approaches for the sake of tradition/preference
All reasonable points! Thanks for engaging!